mb-207 research methodology

COLLEGE OF MANAGEMENT AND ECONOMICS STUDIES (CMES)

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MBA OIL AND GAS MANAGEMENT

MB-207

RESEARCH

METHODOLOGY

Course Code: MB-207

Course Name: Research Methodology

© UNIVERSITY OF PETROLEUM & ENERGY STUDIES (For this print run)

Contents

Unit 1 Introduction .......................................................................................................... 1

Unit 2 Defining Problem ............................................................................................... 31

Unit 3 Relationship between Management and Research Problem ........................ 69

Unit 4 Research Design ................................................................................................. 75

Unit 5 Hypothesis Design ........................................................................................... 109

Unit 6 Sampling Procedures ....................................................................................... 141

Unit 7 Data Collection Methods ................................................................................ 169

Unit 8 Data Analysis–Methods .................................................................................. 203

Unit 9 Report Writing ................................................................................................. 275

Introduction

Research may be defined as a documented prose work.Documented prose work means organized analysis of thesubject based on borrowed materials with suitableacknowledgment and consultation in the main body of thepaper. Research in management is particularly importantto find out different phenomena. At the outset we shoulddistinguish between research in different areas. Managementresearch comes within the purview of social science researchand there are other different types of research which broadlyfall into the category of physical science research. Carryingout research in social science subjects, i.e., commerce,management, economics, sociology, etc., is basically differentfrom physical science because, here we need to study thesociety based on certain trends and for this the laboratory isthe society.

Research in management is particularly difficult because ofits convergence with different disciplines. As we know,

1

Objectives

After reading this unit you will be able to:

y Understand the meaning of research.

y Define the objectives of research.

y List the features of a good research study.

y List types of research studies.

y Explain the role of research in business.

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Unit 1

Introduction

2 Research Methodologyu

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management is not a particular discipline and in any studyon management we need to integrate the different approachesborrowing suitably from different disciplines. Similarly,before we understand the complexity of research in commerceand management, we need to define certain importantconcepts.

First is variable. What exactly is a variable? Variable is thequantity, in which we are interested, that varies in the courseof the research or that has different variables for differentsamples in our study. In one word, we can define variable asa factor whose change or difference we study. Now, thereare two types of variables. The first one is dependent variableand the second is independent variable. Dependent variableis that quantity or aspect of nature whose change at different,stages the researcher wants to understand or explain. Incause and effect investigation, the effect variable is thedependent variable.

Now, what exactly is an independent variable? Independentvariable is a variable, whose effect upon the dependentvariable we try to understand. There may be severalindependent variables. For instance, we may simultaneouslyinvestigate the effect of mother’s cigarette smoking, mother’sexercise, parents’ weights and other variables upon theweight of a baby. In this case, mother’s cigarette smoking,mother’s exercise, parents, weights and other variables areindependent variables, which we want to study, upon theweight of the baby which is, dependent variable.

Now, there are certain other areas. First is universe. We candefine it as the total population. It is the laboratory for theresearch. In our research we may have or we may take theentire population of India. In that case, as it is obvious, noresearcher can carry out research on the entire populationof India to find out the truth or to find out some areas of hisresearch interest. In some cases, universe or population maybe a particular group. To clarify this point further, let usassume we want to study some effects on some particulargroup of people, religions; Hindu, Muslim, Christian, Jainetc., or certain particular age-group, the age of 25 to 35. Inthat case our universe is getting limited to that particular

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3UNIT 1 Introductionu


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number or to that particular age-group of people. Even onthat particular group it of people having those religious.Similarly even then we find that carrying out research onthe universe, i.e., on the entire population of that particulargroup may not be always possible because of the time factorand the money involved. In that case, what we usually do isto take out samples selected from the entire population. Inselecting samples, we use the available sampling techniquesto draw from the total population. Apart from these, we needto clarify certain other concepts. For example, what doesthe term empirical mean?

Empirical means the observations and propositions whichare primarily based on some sense experiments or derivedfrom experience by methods of inductive logic includingmathematics and statistics. This technical definition isdifficult to understand. To be more clear we can defineempirical research as that type of research where we try todeduce some logic and principles based on our surveyreports. In other words, when we want to analyze the surveyreport using some mathematical and statistical tools anddeduce logic to authenticate our findings, we are said tofollow the empirical research method.

Other important things are attitude and opinion. Attitudeas we all know is the psychic change and it can neither bedemonstrated publicly nor can it directly be observed,because most of the psychological variables as we know aredormant or latent and to can never be measured unless weuse the most sophisticated tools, like scales etc., with suitableweight factors. To be more clear if we try to measure it, usethe technical scales fixing or affixing weights for each andevery individual response. There are different schools ofthought which define attitude in different ways. We are notinterested to go in to those details but the measurement ofattitude is primarily done on the scoring.

What is an opinion? Opinion and attitude differ principallyin, that opinion is a verbal statement of a person and givenmerely for the sake of responding or rather to answer aparticular question without any object or aim and based onsuperficial and or partial information of the object or

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situation about which the opinion is passed. But, attitude,as we have already defined, is a state of mind. So it can wellbe understood in the context of our discussion, that incarrying out research, based on survey responses, it is betterto rely more on attitude than on opinion, because, throughattitude in a survey we can really understand the inner mindor the inner psychology or inner perception of the individualor the respondent, while, through opinion survey we cansimply provide superficial answers from the respondentswhich obviously do not serve the purpose of any research.

Now, before we proceed into the depth of research we needfurther clarifications on social science research. As hasalready been mentioned, management research falls withinthe category of social science research. Social scienceresearch as we all know, is carried out on the society,considering society as the field of experiment or to be moreprecise as a laboratory. Research on management or researchon social sciences may be fundamental in nature when wewant to build a new theory and approach on any particulardiscipline. For example, in the case of management, beforethe Hawthrone experiment was carried out by Elton Mayo,it was not known that work environment and humanrelations have an effect on workers’ productivity. But EltonMayo and his colleagues by varying the work environmentcould substantiate with their findings for the first time thatwork environment has got some direct relationship withworkers’ productivity. This is certainly a fundamentalresearch which helped us to build a theory on managementscience. But there are certain other areas of research onmanagement too, where we cannot simply develop any theoryor where we cannot put our contribution in to thedevelopment of certain basic theories, etc. But we cancontradict, modify or alter any existing theory for betterunderstanding. For example, consider Maslow’s hierarchyof needs theory, which defines various needs of a humanbeing in order of priority. To be precise, in our approach theworkers are having certain needs in order of theirimportance or in order of their requirements. Maslowbelieved fulfillment of one need leads to satisfaction andmotivate the workers and after the lower level need is

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fulfilled, the workers strive for fulfillment of higher levelneeds. To contradict Maslow’s need hierarchy theory,Alderfer Clayton with his existence, relatedness and growthapproach to motivation, substantiated that there may becertain need factors important for workers, which may evenarise before the needs of the lower level had actually beenfulfilled. For example, we know that there are physiologicalneeds related to shelter, clothing and food, etc. Unless theseprimary needs are fulfilled one cannot have the needs ofhigher level like social needs, etc. But today if we just try tofind out from our society, we can get examples of differentworkers who get motivated simply by fulfilling certain socialneeds. So in that case, these social needs or the fulfillmentof social needs is primarily important for that group ofworkers, even though for them the physiological or otherneeds have not been met to the required level. To give apractical example, let us assume the case of journalistsemployed by different newspaper houses. If we follow theMaslow’s hierarchy of needs theory for their motivation, itwould obviously fail because journalists value their jobenvironment most. So obviously fulfillment of physiologicalneeds is not relatively more important for the journalists.We have tried to analyze the difference between thefundamental research, which help us to build a new theoryor a new approach to management and other types ofresearch which merely help us to contradict, alter, or modifythe existing research findings. We have focussed on theexample of Maslow deliberately, as his findings have beenaltered, contradicted, or modified, in the context of newfindings or new research. Subsequent approaches tomotivation have been developed after contradicting Maslow.Such approaches tried to define motivation from a morescientific perspective.

Research, unless it is understood in its right spirit, cannotbe undertaken with success. What is important forresearchers is to take research more as a passion than forcareer progress. From our experience, we see that most ofthe students are interested in research merely to fulfil theircareer prospects. In this way, certain researches are carriedout in a mechanical way. The researcher should have thenatural interest in the research.

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There are still certain things which we need to considerbefore we go into the research matter in more depth. Whatare the management areas and what is the scope availablefor research in this field? Now to define management,without going into the traditional approach we may put it inmore simplistic terms like: management is a deliberate effortto achieve some defined goals. With definition alone we canunderstand management from a broader perspective. Nowwhat is a ‘deliberate effort’? No management can succeedunless the efforts or actions are initiated as a deliberateprocess from the top. So the action should be initiated as adeliberate policy on the part of the company or the industryor the union whatever it may be. Now what is the ‘definedgoal’? We know that unless some one is having a definedgoal, the question of achieving it does not arise at all. So,there should be some definite goal on the part of themanagement or on the part of the country or organization,whatever may be the case, and this definite goal obviouslyshould fulfil the requirements of law, legislation etc. Theforegoing discussions help us to understand that there aredifferent functional areas of management. Such functionalareas may be listed as follows:

1. Marketing

2. Human resource management

3. Production

4. Finance and accounting

5. Information technology

6. Material planning and production control

7. Purchasing function

8. Advertising and sales promotion function

9. Social functions, which enables a company to fulfil thesocial responsibility, etc.

There may be certain other function too which, however,depends more on the requirements of the environmentor particular environment that prevails in a company.

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So even beyond these functional areas, we have scope to doresearch.

Let us try to understand what happens exactly in India. Ifwe try to understand the Indian economy as a whole, we geta clear picture that we are lagging behind many otherdeveloped countries for obvious functional deficiency inmanagement amongst other things.

The functional deficiency in different management areas isprimarily responsible for the backwardness of economicdevelopment of our country and may be grouped under thebelow mentioned broad categories.

One is the financial management research. Research onfinancial management includes different operations like:financial analysis, capital structure, ratio analysis, etc.Capital structure and ratio analysis enable a company toration the requirement of resources. Rationing of resourcesmeans optimum utilization of different funds available for acompany. Unless the resources available in a company areutilized we may need to find out various sources of fundsand costs of capital, liquidity constraint, for a more clearunderstanding. As we all know unless a company is able tomaintain the required liquidity level for ensuring therequirements of the working capital, the company is boundto suffer from operational problems which in the long runmay affect profitability. Apart from such an affect, the non-availability of working capital in time, and holding of excessliquidity again affects the company’s profitability. So whatis needed is to ensure the minimum or the optimum holdingof the liquid assets of the company. Other areas of financialmanagement research may be the management of differentfunds, management of assets and financial market analysisetc. Now we all know that in any company, profitabilitylargely depends on the efficient handling of financialresources. Financial Management Research enables us tocompare the operation of different companies with the helpof financial analysis. If a major portion of the working capitalis invested for purchase of raw-materials and inventoriesalone, companies will unnecessarily hold capital in excessof requirement and thereby strain their profitability. Apart



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from holding of raw-materials and inventories which needto be controlled, companies may have the problem of excessstorage costs for finished products. When we produce morewithout taking in to cognizance the market potentialities,we face the problem of storing finished products, whichoccupy maximum godown space and involve a lot of costs.

Although rationing of resources is primarily a concern forthe cost management function, with the help of financialmanagement research, using different cost indicators orusing different ratios, we may find out what exactly is theoptimum resource holding and in what way a company isable to hold that optimum level of the resources.Management of funds and assets and analyzing the financialmarket are also equally important for financial managementresearch. Management of funds requires an efficient planningof borrowing long-term, short-term and medium-term loansas per the requirements. When to borrow, how to borrowand what to borrow is important for the company tounderstand in the context of different data of the companyitself. The company may have some traditional way ofborrowing, like, borrowing from banks, borrowing from otherfinancial agencies like different development banks or, theymay borrow by issuing debentures in the market or they mayraise their capital by issuing shares, etc. All thesealternatives need to be compared and analyzed and the mostcost effective one needs to be chosen to ensure maximumprofitability.

Similarly, production research is vitally important for acompany specially those who are engaged in themanufacturing operation. Unless goods or products aremanufactured right in time, or made available in time in themarket, the company may loose the market stake or themarket share. Thus, what is primarily important for aproduction department is to ensure manufacturing of theright goods and products in the right quantity and to makeit available in the market for the ultimate users. Thus thereis need for development of, different cost minimizationalternatives, work simplification, inventory control, productdesign, process improvement, quality control, etc. With thehelp of suitable capital budgeting unless the required

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machines and equipments are made available right in timeor unless the available machines are replaced with themodern available technology right in time, the productionprocess itself will suffer. Product development and productdesign research is also equally important. The changingdemands of the consumers heavily influence the productdesign and product innovation. A good number of companiesgradually find themselves out of market simply because theyare not able to produce the right quantity or the right productfor the consumers as per their changing requirements. Freemarket or free competition to a great extent exerts pressureon the company. Thus unless a product is developed suitably,based on consumer requirements the production in the longrun is bound to suffer. Similarly, product development andproduct innovation with work simplification and performanceimproving approaches ensure cost minimization also. Withthe help of industrial engineering, development of theproduct with simultaneous reduction of the total costs ispossible. Cost efficiency, work simplification, workmeasurement with the help of industrial engineering,development of the product with value engineering approach,among other things, enable us to find out the exact workunit required for doing a job which in the long run helps usto decide wage rate more scientifically. Unless inventory iscontrolled rightly or the optimum utilization of inventoryresources is ensured, the production operation will definitelysuffer in the long run and will ultimately affect the company’sprofitability.

In marketing survey we have different areas of research likemarketing policy which involves, pricing, advertising service,channels of distribution product research etc. Productresearch helps us to find out the changing consumers’requirements by carrying out survey. Improvement and usevalue of the present product may be carried out, as also in'packaging, based on consumers’ preferences. Marketingresearch, as we all know, is primarily initiated to find outthe market potentiality of a particular company. With thehelp economic and sales forecasts with the help of the surveyof consumers or the potential consumers of the society atlarge, a company can take suitable decisions on expansion

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or design or outline their production process exactly copingwith the requirements. Unless a company is undertakingsuitable marketing research it will definitely suffer in thelong run. As we all know, no company can afford to remainin a static product or system indefinitely. To clarify this pointfurther, if a company remains in producing a static quantityof some products keeping in view the market stake that theyare having for this much quantity alone, in future thecompany may find themselves out of place because of theircompetitors who may gradually grab the increased marketpotentiality for that particular product or products.Moreover unless suitable expansion programmes areundertaken, from costing point of view, no company canachieve production efficiency. Cost efficiency is only possiblewhen a company enjoys the benefit of producing aneconomically run quantity and developing by-products. So,undertaking suitable marketing research is of utmostimportance for a company. Apart from all these things, thereare other areas of research on marketing like, research onchannels of distribution, etc. A company sends its productsto the ultimate consumers through different channels ofdistributions. Products may not reach the ultimateconsumers and users for reasons of inefficient channels ofdistribution. Thus, a company needs to ensure that itsproducts reach the ultimate users on time. Efficient channelsof distribution also ensure development of further marketingpotential. Apart from the channels of distribution,advertising as well as sales promotion research areimportant areas of marketing.

Thus, a prospective researcher on management getsimmense scope to investigate into these three core functionalareas of management, i.e., finance, production and marketing.

Research in human resources strategy, its integration withcorporate planning and the development of human resourcepolicies are certain new areas in management research. Theresearch requires in depth understanding of HumanResource Management in a business context, which addressesa number of fundamental questions as under:

1. Is strategic HRM a reality?



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2. Are all cross-sections of people involved in decisionmaking?

3. How can human resource strategies and practices bedeveloped to meet perceived threats and to reapopportunities in a changed business environment?

Strategic Human Resource Management (SHRM) requiresformation of HR objectives, strategies and policies. SHRMalso requires the provision of the skills and abilities matchingorganizational overall objectives. In other words, SHRMprovides the framework, which ensures that anorganization's people needs are met.

Change strategies are inevitable consequence of manyhuman resource strategies. There are various types of changeinitiatives that may interest a researcher. Turn aroundchange is financially driven to ensure corporate survival byreducing unprofitable products and services. It involvesredesign of organizational structures, out-sourcing of non-core activities and may even manpower redundancies.Behavioural transformations are changing behaviour patternthroughout the organization. Restructuring is the mostcommon form of major organizational change. Restructuringneed not be a defensive cost-cutting process but rather aproactive attempt to achieve innovative products andservices. The goal should be synergy. Hence enthusiasticresearchers provided they understand the business issuesholisiticaly can do research on change strategies.

Research on competency development is also anotherimportant aspect, which focuses on integration of businessplan of the company with selecting the right individual forthe job. Competency is defined as the smallest unit of on-the-job behaviour that is observable, measurable, andchanges over time.

Similar contemporary areas of research interest are;Innovation and creativity, Six-sigma practices, Supply chainmanagement, Knowledge management issues, Businessprocess outsourcing, Human resource outsourcing, CustomerRelationship Management (CRM), e-CRM, Web marketing,Financial re-engineering, etc.

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In selecting a research topic, out of several potential topics,the first task is to narrow down to the most potential oneout of the different alternatives. Selection of a research topicis the first task of the research process. The research processconsists of a series of actions or steps necessary to carry outresearch in a sequential and logical manner. Selection ofresearch topic although primarily depends on the guides’instructions, the researcher should also take independentdecisions to a great extent for influencing the guide in thismatter. Certain pertinent factors in this regard are:

1. The selected topic should have some current implication.

2. There should be scope and amenities to carry outthe intended research, as for example; availabilityof required data, feasibility of carrying out surveyetc.

3. The selected research topic should contribute toknowledge in the desired field.

4. The selected topic should receive the necessaryconcurrence from the research guide.

In our country most of the researchers, specially those whocarry out research under the universities’ or institutions’affiliation, depend on the guides’ choice. Without dependingon the guides’ selection, the researcher should on hisown select the topic which has some interesting elementsin it. In cases where independent researches are carriedout, however, the question of guides’ consent does notarise.

After selection of the research topic, the first and foremosttask for a researcher is to define the research problem. Indefining the research problem, what is important is to reviewthe existing literatures available in this field. The researchershould study the existing or available literature with aninterdisciplinary perspective to base his research topic onsome acceptable background. The research problem shouldalso focus on the relevance of the present research with thepast works.

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The next task, after selection of the research topic anddefining the problem, is to mention the objective of thepresent research. By the term, ‘objective’, we mean to whatextent the present research differs from earlier ones by dulypointing out the deficiencies in the past research workrelated to this field. In simplistic terms the objective means,what the researcher aims to achieve.

The third step involves survey of existing literature. In ourearlier discussion we have mentioned, that research is adocumented prose work resulting from an organized analysisof a subject. In all social science researches we need toproceed through some pre-assumption which helps todevelop our premises for research. To understand thepremises for research, what is important is to review theexisting literatures from an interdisciplinary perspective.Whatever literature is available, related to the topic of ourresearch we should focus on the basic principles, dulysumming them up. Literature review has two basic elementsin it: (a) to survey the existing books available in the field,(b) to review all other published form of works like articles,seminars, other research findings published in the form ofpapers, etc. What is important in this case is to draw out asuitable abstract of published works related to our researchtopic. In drawing an abstract, we can take the help ofavailable published social science bibliographies for booksand various indices on social sciences for articles. In Indiawe have the problem of non-availability of an abstractparticularly for carrying out research on management. Theresearcher here should prepare his own index duly goingthrough the related journals, etc., for a period inchronological order in addition to his consultation of variousindices.

The next step after extensive literature survey is to developa hypothesis. Hypothesis is an assumption on which we baseour research premises and which we all test in the light ofour findings. In any social science research, the developmentof a hypothesis is important as this helps us to authenticateour research findings with due quantification and test. Informulating the hypothesis what is important to remember

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is to first ensure conceptual clarity. Apart from this,hypothesis should be empirically testable, closest to theobservable, specific in nature, related to the body of theory,simple and brief. Testing of hypothesis involves applicationof both parametric and non-parametric (which helps us toquantify the qualitative data) statistical tools after analysisand interpretation of collected data. The various forms andmethods of hypothesis testing are left for subsequentdiscussion.

Next task for a researcher is to draw out the methodologyfor the research subject. Methodology here means in whatway the research is going to be carried out. Researcher hereshould mention the logical sequence as follows:

1. Selection of samples with reasoning.

2. Sampling methods.

3. Survey outline.

4. Relating the survey results after necessary analysis andinterpretation with the main body of research.

5. Building of model, if any.

6. Interview methods and techniques, etc.

Next task for the researcher is to conclude his research byrestating his objective with due mention whether hypothesisis accepted or rejected. Conclusion and suggestion shouldbe with respect to the objectives of the study. Conclusionshould also focus/suggest the scope of further research inthe area, possible implication of the study for building atheory, model and should also focus on the extent to whichthis research enriches knowledge of a particular disciplineor disciplines.

There are other different ways to formulate research steps.But the above form is the most acceptable one. In someresearch cases, analysis and interpretation of data is coveredunder a separate head.

After designing the research steps in the above order, theresearcher should chalk out his chapter planning keeping

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in view the research area. The most pragmatic approach tochapter planning first involves analyzing the research matterfrom a historical perspective. It should not be forgottenthat no present is possible without a past and unless weanalyze the past by maintaining due sequences, we cannotunderstand the process of development of the subject in itspresent.

The next task in chapter outline is discussing the definitionalaspects. After this, the research should mention the presenttrends from an international perspective. To relate thepresent theories with the subject for research in chapterplanning, the researcher should duly focus on the extent towhich the present theory suffers from its own limitation andin what way the researcher can contradict and rebuild thetheory/theories.

The next task for the researcher is to review his researchtopic from an inter-disciplinary perspective. After outliningthe chapters in the above form or order, the researchershould come to his own area of research with a more specificapproach. Here he should mention about his studyspecialities and survey pattern. While elaborating the surveydata in chapters, he should duly point out surveymethodologies, particularly sampling procedures, interviewtechniques, etc., and his survey area. He should analyze andinterpret the survey results and relate the survey findingswith the hypothesis.

The next task in chapter planning involves stating the modeldeveloped after survey findings. Conclusions and suggestionsshould follow later. Since research is documented work, itshould not be forgotten that the researcher should dulyauthenticate his findings whenever he is taking referencesfrom any existing publications for theoretical reasoning. Heshould also authenticate his survey findings dulyacknowledging the sources or mentioning the survey pattern/structure as and when it is necessary. To introduceuncommon terms, he should take the help of foot noteswhich should either be in the body of his research paper orat the end of the research paper in the form of explanatorynotes.

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Research steps and chapter outline, unless discussed with apractical example, cannot be understood in their true spirit.For that purpose we have given a sample research topic anddiscussed the same in the light of our above discussion. Theintention is to prescribe an acceptable framework forresearch. Its application varies, and also to a great extentdepends, on the research guides’ prescriptions.

In our subsequent chapters we will discuss writingprocedure of synopses, research paper, practical selectionof research topic, survey procedure, testing of hypothesisetc., in more elaborate form. Our main focus is to developresearch so that the reader can become an independentresearcher by following a structured map.

Meaning of Research

Research has been defined by various authors in differentways. It always begins with a question or a problem. It'spurpose is to find answers to questions through theapplication of systematic and scientific methods. Thus,research is the systematic approach towards purposefulinvestigation. This needs formulating a hypothesis,collection of data on relevant variables, analyzing andinterpreting the results and reaching conclusions either inthe form of a solution or certain generalizations.

Research is an academic activity and a systematized effortto gain new knowledge.

Objectives of Research

The objective of research is to find out answers to questionsthrough the application of systematic and scientific way.

Though there is a specific purpose behind each researchstudy, however, the objectives can be broadly classified asunder:

u To obtain familiarity of a phenomenon.

u To determine the association or independence of anactivity.

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u To determine the characteristics of an individual or agroup of activities and the frequency of its (or their)occurrence.

Features of A Good Research Study

i. Objectivity: A good research is objective in the sensethat it must answer the research questions. Thisnecessitates the formulation of a proper hypothesis,otherwise there may be lack of congruence between theresearch questions and the hypothesis.

ii. Control: A good research must be able to control allthe variables. This requires randomization at all stages,e.g., while selecting the subjects, the sample size andthe experimental treatments. This shall ensure anadequate control over the independent variables.

iii. Generalizability: We should be able to have almost thesame result by using an identical methodology so thatwe can apply the result to similar situations.

iv. Free from personal biases: A good research shouldbe free from the researcher’s personal biases and mustbe based on objectivity and not subjectivity.

v. Systematic: A good research study must have variouswell planned steps, i.e., all steps must be interrelatedand one step should lead to another step.

vi. Reproducible: A researcher should be able to getapproximately the same results by using an identicalmethodology by conducting investigation on apopulation having characteristics identical to the onein the earlier study.

Hence, the following points must be ensured:

u Purpose clearly detailed.

u Research design thoroughly planned.

u High ethical standards applied.

u Limitations frankly revealed.

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u A complete and proper analysis.

u Findings presented unambiguously.

u Decision based conclusions.

Types of Research Studies

In carrying out research, we follow scientific norms. Scienceis an organized knowledge. The essential feature of scienceis the application of scientific method. In any science,concepts, theories and other accumulated knowledge developfrom hypotheses, experimentation and analysis. In ourearlier discussion we have distinguished between physicaland social science and also introduced the concept offundamental research which helps us to build an originaltheory and applied research aimed to contradict, modifyand is after an existing theory on social science. In otherwords, research may be grouped under two majorcategories:

1. Fundamental research

2. Applied research

Fundamental research here means research of a scientificnature which has practically no connection or if at all thereis any connection, it is absolutely remote in nature as far associal science research is concerned.

Applied research, on the other hand, means application ofbasic scientific principles in different areas of social scienceresearch.

The science of psychology has certain assumptions regardinghuman behaviour which, in general, may be termed asfundamental in nature. But, when we apply theseprinciples in different fields of management, say, personalmanagement (where we are more concerned with humanrelations, etc.), marketing management (where we need tostudy the marketing behaviours of consumers,advertising response, etc.) our research becomes applied innature.

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Without going into the rigours of technical jargon, in socialscience research, we are more concerned with applicationof basic scientific principles in different functional areas ofmanagement on the one way and testing of all existingtheories of management on the other. Social science researchmay be categorized under the following major heads:

1. Fundamental or basic research: Fundamental orbasic research is primarily intended to find out certainbasic principles, viz; John Robinson's imperfectcompetition theory in economics, Maslow's hierarchy ofneeds theory in motivation, Elton Mayo's hawthroneexperiment relating productivity with workenvironment, etc.

2. Applied research: Applied research, as already stated,is the application of available scientific methods in socialscience research which helps to contradict, alter ormodify any existing theory or theories and helps toformulate policy. Applied research, thus, is moreconcerned with actual life. It also suggests remedialmeasures to alleviate social problems. Example ofapplied research may be:

a. John Huberman's: Discipline without punishmenttheory.

b. Alderfer Clayton's: Existence relatedness andgrowth theory which contradicted Maslow'shierarchy of Needs theory and suggested a betteralternative.

3. Descriptive research: Descriptive research is usuallya fact finding approach generalizing a cross-sectionalstudy of the present situation. For example, a study onproblems of industrial relations in India with an inter-disciplinary approach. It is classified under conclusiveresearch.

4. Historical research: Historical research is theresearch on past social forces which have shaped thepresent. For example, to study the present state ofIndian labour we may research on past historical forces.

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5. Formulative or exploratory research: Formulativeor exploratory research helps us to investigate anyproblem with suitable hypothesis. This research onsocial science is particularly important for clarificationof any concept and throwing new light for furtherresearch on principles of developing hypothesis and itstesting with statistical tools.

6. Experimental research: Although experimentalresearch is primarily possible in areas of physicalsciences, with the help of hypothesis, may also be carriedout in social sciences if such research enables us toquantify the findings, to apply the statistical andmathematical tools and to measure the results thusquantified. It is also classified under conclusiveresearch.

7. Ex-post-facto research: Ex-post-facto research is anempirical enquiry for situations that have alreadyoccurred. For example, market failure for anycompanies' product if studied or researched later maybe categorized as ex-post-facto research. Apart fromthis, declaration or slow rate of growth in nationalincome when studied to reformulate the future policieson this account, is classified as ex-post-facto research.

8. Case study approach: Case study approach to socialscience research is particularly initiated at the microlevel. For example study of a particular industrial unitor units, study of some banking units, etc., may becategorized as a case-study. This type of study isintensive in nature and data compilation requiresexhaustive study of the units with utmost sincerity. Wehave discussed case study method separately.

Apart from the above research methods, there are certainother general methods in social sciences. As for example,survey research. Survey research, in one way, may becategorized as a separate research method but in other waymay be defined as a tool which we follow in carrying outsocial science research of any other methods alreadymentioned above. Survey research invalues study of

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population or sample based on some questionnaire to findout intended characteristics. When it is not possible to studythe population because of obvious time constraint and costfactor, sampling method is applied, which ensures theprobability of inclusion of each and every part of thepopulation. Apart from research on management and inbusiness, survey research is widely used in different otherareas of social sciences like economics, sociology, psychology,etc.

Some other types of research like evaluation research, etc.are directed to study or evaluate the performance of anyprogrammes/projects that have already been implemented.

Assessment research describes a situation that prevailswithout any suitable explanation and suggestion for anyremedial actions. Comparative research is intended forcomparative study by collecting data from units undercomparison.

It may be mentioned that it is very difficult to categorizeany particular research under any above major heads. Thus,our effort to nomenclate any research on social sciencesunder above categories, in reality, is meaningless. However,for the sake of our clear understanding such categories areimportant. Commonly, we find that research on socialsciences are carried out with suitable development of ahypothesis. After compilation and interpretation of datacollected for the purpose of such research, hypothesis istested and necessary conclusions are drawn. Whatever maybe the nature or methods of research, we should not forgetthat inter-disciplinary treatment of research problem isessential. By inter-disciplinary treatment, we meanborrowing ideas from related disciplines connected with theresearch topic for more authenticity. Research onmanagement and commerce discipline particularly requiresan integral approach to various disciplines for obviousreasons as management is not a separate discipline in itsown right.

As has been said at the outset, research is a documentedprose writing. Documentation here means acknowledgement

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of different sources particularly from where we have takenreferences.

Organized analysis of a subject selected for research is theprerequisite of success. While writing a research paper, thesubject of first and foremost importance is to select theresearch topic. In doing so, we should also find out thefeasibility of locating information about the subject. Whatevermay be the method employed in carrying out research, weshould not forget that this should invariably be symptomaticin nature.

Scientific Method

The application of valid and reliable research methods iscalled scientific method. It has three distinct characteristics:

i. Objectivity: The scientific method should enable us toclassify facts accurately and carefully, without any bias.

ii. Accuracy of measurement: A mere collection andclassification of the facts may not be sufficient, one mustbe able to make observations of their correlation andsequence, which can be denied as a result of dissipationimagination and painstaking efforts of the scientists.

iii. Self criticism: Scientist should critically examine theirown research as they are a group of people who arenever sure that they have can found the ultimate truth,thus their studies are continuing an exhaustive. Ifresearchers are completely objective, theirmeasurements are accurate and their studies areexhaustive, then their results will be valid and reliable.

Comparison of the Scientific Method andNon-scientific Method

i. Objectivity: The scientific method is more objective ascompared to the non-scientific method, the reason beingthat its development is normally a result of long yearsof experience and good deal of thought by the scientist.The hypothesis, a back bone of scientific method, can beverified with the help of statistical techniques and

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principles. This ensures better and more objectivity ascompared to subjectiveness in decision making by non-scientific methods.

ii. Degree of accuracy: The scientific method is moreprecise than non-scientific methods. Thoughmeasurement is not always attempted in every scientificinvestigation, but wherever attempted even thequantitative concept can be defined precisely, measureeffectively and helps in achieving results with higherdegree of accuracy.

iii. Continuing and exhaustive: The scientific methodtakes cognizance of the existing knowledge. The resultsachieved by various researchers lend to the sameconclusions. This helps in accumulation of systematicknowledge which is continuous and unending. However,the same is not true in case of non-scientific method.

Research Methods and Research Methodology

u Research methods are the methods or techniquesemployed by researchers in conducting researchoperations.

u Research methodology is a scientific and systematic wayto solve research problems. A researcher has to designhis methodology, i.e., in addition to the knowledge ofmethods/techniques, he has to apply the methodologyas well. The methodology may differ from problem toproblem. Thus, the scope of research methodology iswider than research methods. In a way, researchmethodology deals with the research methods and takesinto consideration the logic behind the methods, we use.

Organizing the Research Function

The research function as in research & development for amanufacturing unit can be organized within an organizationof medium or large size but a marketing researchorganization shall be very much different in nature asthe requirements and emphasis on research will bedifferent.

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Many a time, companies do not set up their own departmentsbut prefer to engage outside agencies for their marketingresearch requirements. The following points should be keptin mind while hiring the services of outside agency:

u Technical expertise.

u Objective(s) of research studies.

u Economic considerations.

u Standing/reputation of the agency.

Some advantages of using an outside agency are:

i. It may propose a research proposal without anyconstraint and may be worth considering.

ii. Timely advice can be sought which may have farreaching effects on the business policy.

iii. The relevant problem to us today may have already beenstudied by consultants and hence it shall help in savingcompany’s time, money and energy.

Importance of Research in Management Decisions

The role of research has greatly increased in the field ofbusiness and economy as a whole. The study of researchmethods provides you with the knowledge and skills youneed to solve the problems and meet the challenges of today’smodern pace of development. Three factors stimulate theinterest in a scientific research to decision making:

i. The manager’s increased need for more and betterinformation.

ii. The availability of improved techniques and tools tomeet this need.

iii. The resulting information overload.

The usefulness and contribution of research in assistingmarketing decisions is so crucial that it has given rise to theopening of a new field altogether called ‘marketing research’.Market research is basically the systematic gathering,

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recording and analyzing of the facts about business problemswith a view to investigate the structure and development ofa market for the purpose of formulating efficient policies forpurchasing, production and sales. Research with regard todemand and market factors has great utility in business.Market analysis has become an integral tool of businesspolicy. Once sales forecasting is done, the Master ProductionSchedule (MPS) and Material Requirement Planning (MRP)can be efficiently done within the limits of the projectedcapacity based on the MPS. Budgetary control can be mademore efficient, thus, replacing subjective business decisionswith more logical and scientific decisions.

Modern industry with its large scale operations tends tocreate a gulf between the customer and the manufacturer.Particularly when business is too big and operations are toofar-flung, one cannot depend upon casual contacts andpersonal impressions. Research methodology has beendeveloped as the tool by which business executives keep intouch with their customers. If an entrepreneur has to makesound decisions, he must know who his customers are andwhat they want. To a certain extent he relies on his salesmenand his dealers to supply him with market information butin recent years, more and more firms/executives haveturned to research methodology as a medium ofcommunication between the customer and the company.

Marketing research is the link between the manufacturerand the consumer and the means of providing consumer-orientation in all aspects of the marketing function. It is theinstrument of obtaining the knowledge about the market andthe consumer through objective methods which guard againstthe manufacturer’s subjective bias.

Many researchers define marketing research as gathering,recording and analyzing of all facts about problems relatingto the transfer and sale of goods and services from producerto consumer.

Research methodology is an essential prerequisite forconsumer-oriented marketing. It is necessary for developingthe marketing strategy where in factors under the control

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of the organization viz., product, distribution system,advertising, promotion and price can be utilized so as toobtain maximum results in the context of the factors outsidethe control of the organization viz., economic environment,competitor and laws of land.

Role of Research Methods/Research Methodologyin Business/Industry

Before undertaking any research it is essential to delimitthe primary objectives of the project and then to define themethodology in as much detail as possible. This shall helpthe researcher to utilize the research for decision making.Any research done on an arbitrary basis, i.e., withouthaving explicit objectives or applying one’s personalconvenience in data collection and interpretation etc. shallbe of no use.

Common Uses of Research in Decision Making

The following are the areas in which research methodologycan help in better decision making:

1. Marketing research:

i. Product research: Assessment of suitability ofgoods with respect to design and price.

ii. Market characteristics research (qualitative): Whouses the product? Relationship between buyer anduser, buying motive, how a product is used,analysis of consumption rates, units in whichproduct is purchased, customs and habits affectingthe use of a product, consumer attitudes, shoppinghabits of consumers, brand loyalty, research ofspecial consumer groups, surveys of local markets,basic economic analysis of the consumer market,etc.

iii. Size of market (quantitative): Market potential,total sales quota, territorial sales quota, quota forindividuals, concentration of sales and advertisingefforts; appraisal of efficiency, etc.

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iv. Competitive position and trends research

v. Sales research: Analysis of sales records.

vi. Distribution research: Channels of distribution,distribution costs.

vii. Advertising and promotion research: Testing andevaluating, advertising and promotion.

viii. New product launching and product positioning.

2. Government policies and economic system: Researchhelps a decision maker in a number of ways, e.g., it canhelp in examining the consequences of each alternativeand help in bringing out the effect on economicconditions. Various examples can be quoted, such as;problems of big and small industries due to variousfactors – upgradation of technology and its impact onlabour and supervisory deployment, effect ofgovernment’s liberal policy, WTO and its new guidances,ISO 9000/ 14000 standards and their impact on ourexports allocation of national resources on nationalpriority basis, etc.

3. Solving various operational and planningproblems of business and industry: Various types ofresearches, e.g., market research, operations researchand motivational research, when combined together,help in solving various complex problems of businessand industry in a number of ways. These techniques helpin replacing intuitive business decisions by more logicaland scientific decisions.

Market research helps in deciding forecasting whichhelps in efficient production and investmentprogrammes such as purchasing and financial planswhich ultimately result in projected profit and lossaccount.

4. Social relationships: Research in social sciences isconcerned with both – knowledge for self and knowledgefor helping in solving immediate problems of humanrelations. It is a sort of formal training which helps an

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individual in a better way, e.g.

i. It helps professionals to earn their livelihood.

ii. It helps students to know how to write and reportvarious findings.

iii. It helps philosophers and thinkers in their newthinkings and ideas.

iv. It helps in developing new styles for creativework.

v. It may help researchers, in general, to generalizenew theories.

Other areas have been already highlighted in ourintroductory discussion. Also in subsequent chapters wehave discussed various contemporary areas encompassingall functional areas of management.

Current Status of Research in India

Research in India can still be said to be in the growing phase.Although there is an enormous interest evinced in researchby our business, they are not as yet completely sold on itsvalue of or as an aid to marketing. This is due partly to thefact that in India, many product groups are still enjoying asellers’ market and consequently management is preoccupiedwith problems relating to production and raw materials.

Secondly, there is a general misconception among Indianbusinessmen that research is a very costly affair and hencea luxury that they can ill afford. This is particularly true ofsmaller firms and industries but paradoxically, it is they whorequire research even more than the larger firms in orderto make marketing effort more efficient and to reduce oreliminate wastage.

However, it is important for businessmen to realize that noproduct can have a sellers' market in perpetuity, particularlyin a developing economy. When the reversal occurs, themanufacturer who has kept in touch with the consumer allthrough and practised consumer-oriented approach will reapthe rewards. Further, it should be realized that research

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increases the efficiency of marketing efforts, reduces wastageand thereby pays.

Limitations of Research

In India, research based decision making has just made abeginning. There are still a number of gaps in understandingbetween the researchers and its users.

It may be made clear that research is there to help in decisionmaking and is not a substitute of decision making. Some ofthe limitations are given below:

i. Research can provide a number of facts, but it doesn’tprovide actionable results.

ii. Some problems just cannot be researched, e.g., a preciseestimate of sales directly attributable to advertising.

iii. It cannot provide the answer to any problem but canonly provide a set of guidelines. Thus, management willhave to consider research findings in the light of otherfactors such as production, finance and personnel, inarriving at the decision.

iv. Managers normally do not include research in theoverall problem or total decision making. Partialdecisions on specific issues and without proper timingand budget may not help in satisfactory solutions.

v. Managers rely more on intuition and judgement ratherthan on research.

Review Questions

1. What is “research”? What are the two broad categoriesin which it can be divided?

2. Distinguish between:

i. Basic research and applied research.

ii. Exploratory and conclusive research.

iii. Research methods and research methodology.

iv. Scientific and non-scientific method.

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3. Do you agree with the statement “research is muchconcerned with proper fact finding, analysis andevaluation?” Give reasons in support of your answer.

4. A multinational company is thinking of introducing ageneral type of credit card. Before its launch, it wantsto know more about the current methods in use forgoods or services costing more than Rs 1000 . Thecompany wants to have the following information:

i. Method preferred by consumers : cash, cheque,credit card or electronic fund transfer.

ii. Which method is mostly used in a 30-day period?

iii. Do people of different age, education, sex, andincome matter?

iv. Do people use different methods of payments forpersonal expenses versus business expenses?

5. Explain the role of research in management decisionmaking.

6. Explain how research helps in making better decisionin following areas:

i. Marketing research

ii. Motivational research

iii. Government policy and economic decisions

iv. Solving business and industry related operationalproblems.

v. Social sciences.

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Unit 2

Defining Problem

Objectives


y Have an insight about various components which affect a decision.

y Describe various types of models classified under (i) certainty (ii)risk (iii) uncertainty and steps to be followed while calculatingexpected monetary value.

y Understand decision tree diagram.

Formulation of the Problem

Formulation of the problem means defining the problemprecisely. In other words, A problem well defined is halfsolved. In operations research, we say that formulation ofproblem is often more essential than its solution becausewhen the problem is formulated, an appropriate techniquecan be applied to generate alternative solutions. Choosingthe best alternative is the best decision under the givencircumstances.

Steps involved in defining a problem are:

i. Statement of the problem in a general way.

ii. Understanding the nature of the problem.

iii. Surveying the available literature.

iv. Developing the idea through discussions.



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v. Rephrasing the research problem into a workingproposition.

Once the problem has been selected, the same has to beunderstood thoroughly and then the same has to be reframedinto meaningful terms from an analytical point of view. Thebest way is to discuss the problem with friends or colleaguesor with those who have the knowledge of it. Both parties,the researcher and/or the concerned manager or customer,must agree on the specific nature of the research problem.Ideally, both the parties must ascertain the priorities of theissues involved, scope or potential benefits, cost as well asthe time required to conduct the study. Researcher mustspecify the exact issues being examined and the underlyinglogic in setting the priorities. Moreover, the research mustdefine the boundaries of the population covered in theproposal.

In essence, a proper formulation of the research problemstarting with objectives would enable a researcher to goahead in the proper direction. Finally, it may be noted thatproblem formulation would have focus on what sort ofdecision issues are tackled. In other words, it gives a clearidea of the research itself.

Formulation of Hypothesis

Concept of Hypothesis

A hypothesis is a proposition – a tentative assumption whicha researcher wants to test for its logical or empiricalconsequences. Hypotheses are more useful when stated inprecise and clearly defined terms. It may be mentioned thatthough a hypothesis is useful it is not always necessary,specially in case of exploratory researches. However, in aproblem-oriented research, it is necessary to formulate ahypothesis or hypotheses. In such researches, hypothesesare generally concerned with the causes of a certainphenomenon or a relationship between two or more variablesunder investigation.

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Hypothesis Testing

A number of steps are involved in testing a hypothesis:

i. Formulate a hypothesis.

ii. Set up a suitable significance level.

iii. Choose a test criterion.

iv. Compute the statistic.

v. Make decision.

u Formulate a hypothesis: Let us discuss aboutintroduction of a new drug. The drug is tested on a fewpatients and based on the response from patients, adecision has to be made whether the drug should beintroduced or not. We make certain assumptions aboutthe parameter to be tested – these assumptions areknown as hypotheses.

We start with a ‘null hypothesis’: H0 : m = 100. This is aclaim or hypothesis about the values or populationparameters.

This is tested against alternate hypothesis , m1 : m ¹ 100.

The null hypothesis is tested with available evidenceand a decision is made whether to accept this hypothesisor reject it. If the null hypothesis is rejected, we acceptthe alternate hypothesis.

u Setting up a suitable significance level: There aretwo types of errors that can be committed in makingdecisions regarding accepting or rejecting the nullhypothesis:

– Type I error: An error made in rejecting the nullhypothesis, when in fact it is true.

– Type II error : An error made in accepting the nullhypothesis, when in fact it is untrue.

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The level of significance signifies the probabilityof committing Type I error and is generally takenas equal to 5% (a = .05). This means that even aftertesting the hypothesis, when a decision is made, we maystill be committing an error in rejecting the nullhypothesis. Sometimes, the value of ‘a’ is taken as.01 but it is the discretion of the investigator, dependingupon the sensitivity of the study.

u Choose a test criterion: This means selection ofa suitable probability distribution that can be usedfor the available information under consideration.The different distributions that are normally usedare :

– Normal distribution: Z characteristic, this ismost often used, when the samples are morethan 30.

– T-distribution: ‘T’ test is used for small samplesonly.

– F – test and chi-square test.

u Compute the test characteristic: This involves theactual collection and computation of the sample data.For the case under consideration , we have to find thesample mean () and then compute the calculated ‘Z’. Thiscalculated value (absolute) is compared with tabulatedvalue obtained from normal distribution table againstthe decided criterion ( value of ‘a’ and one tail or twotail).

u Make a decision: If the calculated value of the testcharacteristic is greater than the tabulated value, thenull hypothesis is rejected and the alternate hypothesisis accepted. Talking in terms of critical region, the valueof calculated characteristic falls outside the acceptanceregion.

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Figure 2.1

Developing the Research Plan

The next step of the research process calls for determiningthe information needed, developing a plan for gathering itefficiently and presenting the management of theorganization. The plan outlines sources of secondarydata and spells out the specific research approaches,contact methods, sampling plan and instruments that theresearcher will use to gather primary data. First of allresearch objectives must be translated into specificinformation needs. To meet the management informationneeds, the researcher can gather secondary data and primarydata or both.

Implementing the Research Plan

The researcher next puts the research plan into action.This involves collecting, processing and analyzing theinformation.

Interpreting and Reporting the Findings

After collecting, processing and analyzing the informationcollected, the researcher must now interpret thefindings, draw conclusions and then report to themanagement.

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How To Prepare A Synopsis

Synopsis is an abstract form of research which underlines the researchprocedure followed and is presented before the guide for evaluating itspotentiality. In one sentence it may be described as a condensation ofthe final report. The structure of synopsis varies and also depends on theguides’ choice. However, for our understanding a common structure maybe framed as under:

1. Defining the problem: In defining the problem of the researchobjective, definition of key terms, general background information,limitations of the study and order of presentation should bementioned in brief.

2. Review of existing literature: In this head, researcher shouldstudy the summary of different points of view on the subject matteras found in books, periodicals and approach to be followed at thetime of writing.

3. Conceptual framework and methodology: Under this head theresearcher should first make a statement of the hypothesis.Discussion on the research methodology used, duly pointing outthe relationship between the hypothesis and objective of the studyand finally discussions about the sources and means of obtainingdata should also be made. In this head the researcher should alsopoint out the limitations of methodology, if any, and the naturalcrises from which the research is bound to suffer for such obviouslimitations.

4. Analysis of data: Analysis of the data involves testing of hypothesisfrom data collected and key conclusions thus arrived.

5. General conclusions: In general conclusions, the researchershould make a restatement of objectives. Conclusion with respectto the acceptance or rejection of hypothesis, conclusion with respectto the stated objectives, suggested areas of further research andfinal discussion of possible implications of the study for a model,group, theory and discipline.

Finally the researcher should mention about the bibliographies andappendices. The above format is drawn after a standard frameworkfollowed internationally in preparation of a synopsis. However, in ourcountry, keeping in view the object of research, style and structure ofsynopsis varies and quite often it is found that the research guideexercises his own discretion in synopsis preparation than following someacceptable international norms. A standard format for preparation ofsynopsis commonly used in management and commerce research inIndia may be drawn as follows:

1. Introduction: This includes definition of the problem and its reviewfrom a historical perspective.

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2. Objective of the study: It defines the research purpose and its

speciality from the existing available research in the related field.

3. Literature review: It includes among other things, different sourcesfrom which the required abstract is drawn.

4. Methodology: It is intended to draw out the sequences followed inresearch and ways and manners of carrying out the survey andcompilation of data.

5. Hypothesis: It is a formal statement relating to the research problemand it need to be tested based on the researchers’ findings.

6. Model: It underlies the nature and structure of the model that the

researcher is going to build in the light of survey findings.

And finally the chapter outlines.

Any chapter outline follows a logical sequence right from reviewing the

research problem from a historical perspective to the conclusions andsuggestions part. In the chapter outline, we also need to review researchproblem duly drawing it in several supporting chapters with inter-

disciplinary connotation.

Most universities require the researcher to submit a synopsis duly drawingout the research problem, following suitable norms, in approximately athousand words at the time of registration. The research guide, after

thorough checking of the synopsis, suggests necessary changes, if any,and after evaluating the potentiality, clears the registration. Theresearcher, after sometime, which varies from university to university, is

directed to submit the said synopsis with some elaboration containingapproximately 4000 words. In some universities, a seminar is arrangedfor the said research topic with some experts and the researcher

is required to answer the different questions raised by those experts.After successful seminar, the researcher is given final clearance forgoing ahead with the research problem in consultation with the

research guide from time to time. While preparing the synopsis of 4000words before the seminar, the researcher needs to include at least someportion of the survey results which he has carried out for the purpose of

research.

In some other universities, of course, the seminar is not required andresearcher is given final clearance for going ahead with the research

problem merely after submitting the synopsis of thousand words. In suchcases where an abstract of 4000 words is required, the researcher needsto incorporate very carefully the survey results of some units or some

samples with due condensation, following the structured framework. Theresearcher also needs to submit the details of books and journals he hasconsulted for satisfaction of the experts.

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Marketing research provides information about consumers,channel members, competitors, changes, and trends in themarketplace, and other aspects of the firm’s environment.The purpose of marketing research is to assess informationneeds and provide the relevant information so as to improvemarketing decision-making.

Marketing research may be conducted internally or may bepurchased from external supplies. The statistical decisiontheory in the present context refers to value of informationunder conditions of uncertainty. In this case the probabilitytheory has a vital role.

Introduction

Decision in any aspect refers to the selection of the best orfavourable alternative out of several alternatives. In earlierdays decisions were made mainly on personal judgement.

Now-a-days in marketing one has to consider various aspectssuch as planning, organization, direction, command andcontrol. While performing so many activities, marketing hasto face many situations from which the best choice is to betaken. This choice making is known as decision-making.Simply, decision is a selection from two or more courses ofaction. Decision-making may be defined as–‘a process of bestselection from a set of alternative courses of action, which issupposed to meet objectives upto the satisfaction of thedecision maker’.

The knowledge of statistical techniques help to select thebest action. Measures of central tendency show the averagevalue, dispersion measures the average deviations ofvariables. Techniques of correlation and regression help inestablishing functional relation of variables, whereforecasting helps in scientific prediction. Again, time seriesanalysis gives us an estimation of variables subject tocondition. The test of hypothesis procedures were designedto test a statistical statement about a population (the nullhypothesis) for a given level of significance.

The statistical decision theory (also known as Bayesiandecision theory) in the present context refers to value of

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information under conditions of uncertainty. In this case theprobability theory has a vital role. As such, this probabilitytheory will be used more frequently in the decision-makingtheory under uncertainty and risk.

The statistical decision theory tries to analyze the logicalstructure of the problem in alternative actions, states ofnature, possible outcomes and likely payoffs from each suchoutcome.

Components in Decision-making

The management of an industry or an organization is involvedin taking decisions about the development or expansion ofthe concern. No doubt the concern has to face many problemsfrom time to time. The management has to overcome or solvethese problems. These problems may be regarding theavailability of resources, quality of production, costing,publicity or promotion, etc. To illustrate for the publicity ofgoods produced, the manufacturer or seller may take thehelp of TV, radio, newspapers or door-to-door promotion.Many such endless problems are there. In each of thesedecision-making problems, there are some commoncomponents. These are discussed as follows.

Course of Action

Decision-making problems deal with the selection of a singleact from a set of alternative acts. If two or more alternativecourses of action occur in a problem, then making a decisionis necessary to select only one course of action. In the aboveexample of advertising goods produced, there are so manyalternative courses of actions. The final choice of any onewill depend on the payoff (or money value) of each strategyunder the circumstances.

Let the acts or actions be symbolised by a1, a2, a3, a4, ...........;then the totality of all these actions is known as action spacedenoted by A. For four actions a1, a2, a3, a4; A = actionspace = {a1, a2, a3} or A = {A1, A2, A3}. In a tree diagram theacts or actions are given after the initial fork as shown inFigure 2.2. Acts may be also be represented in the followingmatrix form, i.e., either in row or column way.

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Figure 2.2

States of Nature (Events)

If the outcome of some action (or act) is not known inadvance, then that outcome is uncertain, but is vital for thechoice of any act. When there are many possible outcomes(or states of nature) of an event, one cannot predict whatwill happen–it is only in terms of probability that one mayforecast. The various states of nature are outside a firm and,as such, not under their control, e.g., consumer demand,change of taste, improvement of technology, etc. These affectthe payoff and, hence, the choice of an act. A set of states ofnature may be represented in any one of the following ways:

S = {S1, S2, S3, ......., Sn}or E = {E1, E2, E3 ......., En}or W = {q1, q2, q3 .......}

For example, if a cosmetic product is marketed, it may behighly liked by customers (outcome q1) or it may not appealat all (outcome q2), or it may satisfy only a small fraction, say20% (outcome q3).

\ W = {q1, q2, q3}

In a tree diagram the places are text to acts. We may alsoget another act on the happening of an event in Figure 2.3.

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........

Acts

A4

An

A2

A3

A1

OR

Acts Æ AnA

2A

3A

1A

4......

Acts

A1

A2

A3

Start

A1

A2

A3

E1

E2

a1

a2

a1

a2

A1

A2

A3

E1

E2

E1

E2

E1

E2

EventsActsEventsActs Second Act

Figure 2.3



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In matrix form they may be represented in either of thefollowing two ways:

States Acts

of ®nature S

1 S

2 ............ OR States A

1 A

2 ..........

Acts ¯ ofnature ̄

A1

S1

A2

S2

Outcomes

There is an outcome (or consequence) of the combination ofeach act with each possible state of nature. This outcome isalso known as conditional value. In a tree diagram, outcomesare placed after events.

Acts Events Outcomes

E1

O11

E2

A1

O12

E1

A2

O21

E2

A3

O22

E1

O31

E2

O32

Figure 2.4

In general, if there are m possible actions and n admissiblestates of nature, the consequences will be m × n innumber.

It may be noted here that these consequences may beevaluated in several ways such as (i) in terms of profit (ii) interms of cost (iii) in terms of opportunity loss (iv) utility.

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Consequences of m × n in number are shown in centre cell inrow and column of a matrix:

Table 2.1

States ofnature S

1S

2... S

j... S

n

®

Acts ̄A

1O

11O

12... O

1j... O

1n

A2

O21

O22

... O2j

... O2n

... ... ... ... ... ...

... ... ... ... ... ...A

iO

i1O

i2... O

ij... O

in

... ... ... ... ... ...

... ... ... ... ... ...

Am

Om1

Om2

... Omj

... Omn

Here outcome O21 means 2nd row and 1st column andOij means ith row and jth column and so on.

Example 2.1

In case of supply of goods and demand in a market, theoutcome may be unsold goods (+), shortage of goods (-) or nostock (0). In the following matrix form, outcomes of supplyand demand are shown in Table 2.2.

Table 2.2

States of

nature Demand®

Acts 100 101 102 103¯

100 0 -1 -2 -3101 +1 0 -1 -2102 +2 +1 0 -1

103 +3 +2 +1 0

These outcomes will clearly indicate if there is monetarygain or loss, i.e., payoff for each outcome.

Payoff: The result of combinations of an act with each of thestates of nature is the outcome and monetary gain or loss ofeach such outcome is the payoff. This means that theexpression payoff should be in quantitative form.

Payoff may be also in terms of cost saving or time saving.

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Utility: Utility of each outcome is also a quantitativeexpression, but takes the preference of the individualdecision-maker.

Regret (or opportunity loss): The difference between thehighest possible profit for a state of nature and the actualprofit obtained for the particular action taken is known asopportunity loss.

Thus, this is the loss incurred due to failure of not adoptingthe best possible course of action. Opportunity losses arecalculated separately for each state of nature.

Refer the Table 2.3. Let the payoff of the outcomes in the 1strow be P11, P12, ......, P1n and similarly for the other rows.

Table 2.3: Payoff Table

States ofnature

®Acts S

1S

2... S

n

¯

A1

P11

P12

... P1n

A2

P21

P22

... P2n

... ... ... ...

... ... ... ...

Am

Pm1

Sm2

... Pmn

If now m1 is the maximum profit (or payoff) correspondingto S1, then the regret or opportunity loss will be maximumpayoff under state of nature–payoff, i.e.,

Table 2.4: Regret (or Opportunity Loss) Table

States ofnature

®Acts S

1S

2... S

n

¯

A1

M1�P

11M

2�P

12... M

n�P

1n

A2

M1�P

21M

2�P

22... M

n�P

2n

Am

M1�P

m1M

2�P

m2... M

n�P

mn

Example 2.2

A restaurant prepares a food item at a total average cost ofRs 3 per plate and sells it at a price of Rs 5. The food is



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prepared in the morning and is sold during the same day.Unsold foods at the end of the day are spoiled and must bethrown away. According to past sales number of plates isnot less than 20 or greater than 23. You are to formulate the(i) action space, (ii) state of nature space, (iii) payoff table,(iv) loss table.

Solution

The shopkeeper will not prepare less than 20 plates or morethan 23 plates. Thus, the acts or courses of action open tohim are:

a1 = prepare 20 plates Thus, action space or

a2 = " 21 " A={a1 a2 a3 a4}

a3 = " 22 "

a4 = " 23 "

The state of nature is the daily demand for food plates. Thereare four possible states of nature, i.e.

S1 = demand is 20 plates Hence, the state of nature

S2 = " " 21 " space or W = {S1 S2 S3 S4}

S3 = " " 22 "

S4 = " " 23 "

The uncertainty element in the given problem is the dailydemand. The profit of the shopkeeper is subject to the dailydemand.

Let n = quantity demand

and m = quantity produced

For n ≥ m, Marginal Profit (MP) = 5 – 3=Rs 2

For m > n, Marginal Loss (ML) = Rs 3 due to unsold stock

So, the conditional values for each consequence (or cell) inthe payoff table are:

(MP) × units sold — (MP) × units unsold.

For example, in case a2 = 21, S3 = 22, here m = 21, n = 22

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i.e., n > m, net payoff = 2 × 21 - 0 = 42

Again, for a4 = 23, S2 = 21 i.e. m = 23, n = 21, m > n

net payoff = 2 × 21 - 4 × 2 = 42 – 8 = 34 and so on.

Table 2.5: Payoff Table

Demand(n)® (S

1) (S

2) (S

3) (S

4)

Supply 20 21 22 23(m) ̄

(a1) 40 40 40 40

20 40

(a2) 36 42 42 42

21

(a3) 32 38 44 44

22

(a4) 28 34 40 46

23

To calculate the opportunity loss we first determine themaximum payoff in each state of nature:

In first state, maximum payoff = 40

Second, " " = 42

Third, " " = 44

Fourth, " " = 46

Table 2.6: Loss Table Corresponding to theabove Payoff Table

Demandn

®Supply 20 21 22 23

m ̄

20 40 � 40 = 0 42 � 40 = 2 44 � 40 = 4 46 � 40 = 6

21 40 � 36 = 4 42 � 42 = 0 44 � 42 = 2 46 � 42 = 4

22 40 � 32 = 8 42 � 38 = 4 44 � 44 = 0 46 � 44 = 2

23 40 � 28 = 12 42 � 34 = 8 44 � 40 = 4 46 � 46 = 0

Types of Decision Models

The aim of the decision theory is to guide the decision-makerin choosing the best course of action. Depending upon the

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available information about the occurrence of various statesof nature and environment, the decision models may beclassified into the following types: (i) certainty (ii) risk(iii) uncertainty.

Decision-making Under Certainty

In this case the decision-maker can easily select the courseof action, as he presumes that only one state of nature isrelevant for his purposes. For example, suppose a persondesires to deposit Rs 10,000 for a certain period. Bankdeposit gives 12%, Unit Trust of India offers 14% andGovernment bond’s rate is 11% p.a. All the investments arefully secured. Then surely investment in Unit Trust of Indiais the best choice.

Decision-making Under Risk

Here the decision-maker faces many states of nature. Assuch, he is supposed to believe authentic information,knowledge, past experience or happenings to enable him toallot probability values to the likelihood of occurrence ofeach state of nature. Sometimes with reference to pastrecords, experience or information, probabilities to futureevents could be allotted. On the basis of probabilitydistribution of the states of nature, one may select the bestcourse of action having the highest expected payoff value.

The expected value (or expected monetary value, i.e., EMVis widely used to evaluate the alternative course of action(or act). The expected value is calculated by the followingformula for one row only:

S Pj Oij = P1 Oi1 + P2 O12 + ............ + Pn Oin’

Where P1 to Pn indicate the probabilities of states of nature(or events) and Oij the payoffs of the outcomes due tocombination of each event and act.

Steps for Calculating Expected Monetary Value(EMV)

1. Construct the payoff table listing the different coursesof action and states of nature.



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2. List the payoffs thus obtained with the correspondingprobability of each state of nature.

3. Multiply the payoffs with the associated probabilitiesand add up these values for each course of action whichgives the expected value.

4. On the basis of these expected values, determine thebest course of action or strategy.

Example 2.3

The payoff table for three courses of action (A) with threestates of nature (E) (or events) with their respectiveprobabilities (P) are given. Find the best course of action.

Events E1 E2 E3

(P) .3 .4 .3Acts

A1

2.5 2 -1

A2

4 2.6 0

A3

3 1.8 1

Solution

Let us calculate the expected value of each act:

A1 : 2.5 (.3) + 2 (.4) + (-1) (.3) = .75 + .8 - .3 = 1.25

A2 : 4 (.3) + 2.6 (.4) + 0 (.3) = 1.2 + 1.04 + 0 = 2.24

A3 : 3 (.3) + 1.8 (.4) + 1 (.3) = .9 + .72 + .3 = 1.92

From the above calculations we find that A2 is the best. Sothe decision-maker will select the alternative A2 amongstthe three courses of action.

Example 2.4

You are given the following payoffs of three acts A1, A2, A3

and the events E1, E2, E3.

Acts

States of nature A1

A2

A3

E1

25 -10 -125

E2

400 440 400

E3

650 740 750

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The probabilities of the states of nature are, respectively,0.1, 0.7 and 0.2. Calculate and tabulate EMV and concludewhich of the acts can be chosen as the best.

Solution

Calculation and Tabulation of EMV

Events Prob. ActsA

1A

2A

3

E1

.1 25 × .1 = 2.5 -10 × .1 = -1 - 125 × .1 = -12.5

E2

.7 400 × .7 = 280 440 × .7 = 308 400 × .7 = 280

E3

.2 650 × .2 = 130 740 × .2 = 148 750 × .2 = 150

EMV 412.5 455 417.5

A2 is best.

Example 2.5

The management is facing the problem of selecting one ofthe following two products for manufacturing. After marketresearch and survey, the probability matrix is as follows:

States ofnature Good Fair Poor

Acts

Table fan .3 .5 .2

Ceiling fan .4 .45 .15

The profits that the management can make for differentlevels of market acceptability of the two types of fans are asfollows:

States ofnature Profit in Rs if the market is

Acts Good Fair Poor

Table fan 10,000 15,000 3,000

Ceiling fan 14,000 16,000 Loss 4,000

Calculate the expected value of the choice of alternativesand accordingly advise the management.

Solution

Let us put the above information in a payoff table withassociated probabilities and the states of nature, i.e., marketconditions.

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Marketconditions Good Fair Poor

Strategy¯

Table fan Probability .3 .5 .2profits (Rs) 10,000 15,000 3000

Ceiling fan Probability .4 .45 .15

profits (Rs) 14,000 16,000 -4000

Expected value for:

Table fan = .3 × 10000 + .5 × 15000 + .2 × 3000 = Rs 11, 000

Ceiling fan = .4 × 14000 + .45 × 16000 + .15 × (-4000) = Rs 12,200

As the expected payoff for ceiling fans is higher, so thisproduct should be preferred by the management.

Example 2.6

Management is faced with the problem of choosing one ofthe three products for manufacturing. The potential demandfor each product may turn out to be good, moderate or poor.The probabilities for each of the states of nature wereestimated as follows:

Nature of Demand

Product Good Moderate Poor

X 0.70 0.20 0.10

Y 0.50 0.30 0.20

Z 0.40 0.50 0.10

The estimated profit or loss under the three states may betaken as:

Rs Rs Rs

X 30,000 20,000 10,000

Y 60,000 30,000 20,000

Z 40,000 10,000 -15,000 (loss)

Prepare the expected value table and advise the managementabout the choice of product.

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Solution

Demand Expected

Æ Good Moderate Poor value

ProductØ (in ’000 Rs)

X Probability 0.70 0.20 0.10 26

Profit (in ’000 Rs) 30 20 10

Y Probability 0.30 0.30 0.20 43

Profit (in ’000 Rs) 60 30 20

Z Probability 0.40 0.50 0.10 19.5

Profit (in ’000 Rs) 40 10 -15

Calculation of expected value (in ’000 Rs) for:

X : .70 × 30 + .20 + 20 + .10 × 10 = 21 + 4 + 1 = 26

Y : .50 × 60 + .30 × 30 + .20 × 20 = 30 + 9 + 4 = 43

Z : .40 × 40 + .50 × 10 + 10 × (-15) = 16 + 5 – 1.5 = 19.5

As the expected value of Y is higher, the management shouldchoose this product.

Example 2.7

If you make a unit product and it is sold, you gain Rs 5; if youmake a unit and it is not sold you lose Rs 3. Suppose theprobability distribution of the number of units demanded isas follows:

No. of units

Demanded 0 1 2 3 4 5 or above

Probability .20 .20 .25 .30 05

How many units should you make?

Solution

Let m = no. of units produced or stocked.

n = no. of units demanded.

Now for n ≥ m, profit = 5 m

and for m ≥ n, profit = 5n - 3 (m – n) = 8n – 3m

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Payoff Table

Demand (n)0 1 2 3 4 5

Supply (m)

0 0 0 0 0 0 01 -3 5 5 5 5 52 -6 2 -10 10 10 103 -9 -1 7 15 15 154 -12 -4 4 12 20 20

5 -15 -7 1 9 17 25

Unit-wise expected gain are is follows:

Supply Expected gain

(m)

0 0(.2) + 0(.2) + 0(.25) + 0(.3) + 0(.05) + 0(0) = Rs 0

1 -3(.2) + 5(.2) + 5(.25) + 5(.3) + 5(.05) + 5(0) = Rs 2.5

2 -6(.2) + 2(.2) _ 10(.25) + 10(.3) + 10(.05) + 10(0) = Rs 5.3

3 -9(.2) + (-1)(.2) + 7(.25) + 15(.3) + 15(.05) + 15(0) = Rs 5.0

4 -12(.2) + (-4)(.2) + 4(.25) + 12(.3) + 20(.05) + 20(0) = Rs 2.4

5 -15(.2) + (-7)(.2) + 1(.25) + 1(.25) + 9(.3) + 17(.05) + 25(0) = Rs 2.1

Thus, the highest expected gain is Rs 5.20 when 2 units areproduced.

So, 2 units should be produced.

Example 2.8

A retailer has to decide as to the optimum number of unitsto be stocked of a certain item under the following conditions:

(a) Cost price in season is Rs 12.

(b) Selling price in season is Rs 18.

(c) Bargain price after the season is Rs 9.

(d) Cost of holding an item beyond the season is Re 1.

The probability distribution of demand based on past data isas follows:

Units demand: 7 8 9 10 11

Probability : .20 .20 .25 .15 .20

Determine the optimum stock level on the expected monetaryvalue criterion.

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Solution

Let m = no. of stock.

n = no. of demand.

For n ≥ m, total profit= 6m, as profit per unit = 18 – 12 = Rs 6

For m ≥ n, total profit= 18n – 12m + (m–n) (9 – 1) = 10n – 4m

As the bargain price is Rs 9 and cost of holding is Re 1, sonet receipt = 9 - 1. Now, according to number of stock anddemand, the payoff Table is as follows:

Payoff Table

Demand

(n)

Stock 7 8 9 10 11

(m)

7 42 42 42 42 42

8 38 48 48 48 48

9 34 44 54 54 54

10 30 40 50 60 60

11 26 36 46 56 66

Expected Gain Table

Demand 7 8 9 10 11

Probability.20 .20 .25 .15 .20

Stock

7 42(.20) + 42(.20) + 42(.25) + 42(.15) + 42(.20) = Rs 42

8 38(.20) + 48(.20) + 48(.25) + 48(.15) + 48(.20) = Rs 46

9 34(.20) + 44(.20) + 54(.25) + 54(.15) + 54(.20) = Rs 48

10 30(.20) + 40(.20) + 50(.25) + 60(.15) + 60(.20) = Rs 47.5

11 26(.20) + 36(.20) +46(.25) + 56(.15) + 66(.20) = Rs 45.5

From the above calculation it is clear that the expected gainis maximum (Rs 48) when the number of stock is 9.

So, the optimum stock level is 9.

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Decision-making under Uncertainty

In this case the probabilities associated with the differentstates of nature are unknown. Moreover, there is no previousdata or information available which could allot theprobability of the occurrence of states of nature. As such,the decision-maker cannot calculate the expected payoff forthe course of action. The decision-maker faces problems whenhe desires to introduce new plant or production. A numberof decision criteria have been provided for decision-makingunder such a state of nature. The decision-maker may chooseany one of the following:

(i) Maximin, (ii) Maximax, (iii) Minimax regret, (iv) Hurwitzcriterion, (v) Criterion on rationality.

(i) Maximin: The course of action that maximizes theminimum possible payoff is selected. The decision-maker lists down the minimum outcome within eachcourse of action (or act) and then selects the strategywith the maximum number.

This is also known as a pessimistic decision criterion asit locates the strategy having the least loss.

Refer Example 2.2, the row minimums of the differentcourses of action are:

a1 : 40 By this criterion the choicewill be a1 which has the

a2 : 36 maximum payoff amongstall the minimums of four

a3 : 32 acts

a4 : 28

(ii) Maximax: In this case the course of action thatmaximizes the maximum payoff is taken. The decision-maker lists down the maximum payoff associated witheach course of action, then selects that alternativehaving maximum number.

This may be called an optimistic decision criterion asthe decision-maker selects the alternative of highestpossible gain.

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In the same example as mentioned above, the maximumpayoff of each course of action is:

a1 : 40 Since the course of action a4

has the maximum payoff,a2 : 42 so the decision-maker will

select this alternative.

a3 : 44

a4 : 46

(iii) Minimax regret: The regrets (i.e., opportunity loss) foreach course of action are to be calculated with referenceto the payoff list of various alternative acts. Now obtainthe maximum regret and hence select the course ofaction with minimum of the maximum regret values.

Refer the Loss Table 2.6 given in Example 2.2.

State of (20) (21) (22) (23) Maximum

nature S1

S2

S3

S4

Regrets

Acts

(20)a1

40 – 40 = 2 42 – 40 = 2 44 – 40 = 4 46 – 40 = 6 6

(21)a2

40 – 36 = 4 42 – 42 = 0 44 – 42 = 2 46 – 42 = 4 4

(22)a3

40 – 32 = 8 42 – 38 = 4 44 – 44 = 0 46 – 44 = 2 8

(23)a4

40 – 28 = 12 44 – 34 = 8 44 – 40 = 4 46 – 46 = 0 12

Thus the maximum regrets is in a2.

(iv) Hurwitz criterion (or criterion of realism): Thiscriterion makes a compromise between maximax andmaximin, i.e., and optimistic and pessimistic decisioncriterion. At first, a coefficient of optimism a (0 £ a £ 1)is selected, which is assumed to be degree of optimism.Now, according to Hurwitz, select that alternative whichmaximizes.

a (maximum payoff) + (1 – a) (minimum payoff)

Example 2.9

Choose the list product applying the Hurwitz method withthe coefficient of optimism a=.60 to the following data.

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States of Profit (in Rs) if the market is

nature

Acts Good Fair Poor

Product A 10,000 8,000 2,000

Product B 12,500 9,000 -1,000

Solution

Maximum and minimum payoff are tabulated for each act.

Strategy Max. value Max. in

Product A 10,000 2,000

Product B 12,500 -1,000

As a = 0.6, so (1 – a) = 1 – 0.6 = 0.4.

We have for Product A : 10000 × 0.6 + 2000 × 0.4 = 6800 Product B : 12500 + 0.6 + (-1000) × 0.4 = 7100.

As the expected value of Product B is higher, so Product Bshould be accepted.

(v) Criterion of rationality: This criterion is based on theprinciple of equal n likelihood. The decision-maker firstcalculates the average outcome for each course of actionand then selects the maximum number.

Average outcome is 1

n(0i1 + 0i2 + ..... + 0in)

Example 2.10

Events S1

S2

S3

Acts

A1

400 600 200

A2

650 800 -100

A3

400 500 60

Solution

Average for A1 :

1

3

× 1(400 + 600 + 200) = 400

A2 :

1

3

× 1(650 + 800 – 100) = 450

A3 :

1

3

× 1(400 + 500 + 60 ) = 320

Here the choice is for A2.

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Example 2.11

Apply (i) Maximin (ii) Maximax (iii) Minimax regret to thefollowing payoff matrix:

States ofnature S

1S

2

Acts

A1

-6 2A

24 1

A3

7 -4

Solution

(i) Maximin: Minimum course of action

A1 -6 Now maximum ofminimum is 1, so A2

A2 1 is acceptable.

A3 -4

(ii) Maximax: Maximum of strategies

A1 2 Maximum of themaximum is 7 for

A2 4 Act A3.

A3 7

(iii) Minimax Regret:

S1

S2

Maximum

regrets

A1

7�(�6) = 13 2�2 = 0 13

A2

7�4 = 3 2�1 = 0 3

A3

7�7 = 0 2�(�4) = 6 6

Minimum of the maximum regrets is 3 in A2.

Example 2.12

A pig breeder can either produce 20 or 30 pigs. The totalproduction of his competitors can be either 5,000 or 10,000pigs. If they produce 5,000 pigs, his profit per pig is Rs 60; ifthey produce 10,000 pigs, his profit per pig is only Rs 45.Construct a payoff Table and also state what the pig breedershould decide.

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Solution

With the given data let us construct the payoff Table:Payoff Table

State of 5,000 10,000

natureActs

A1 (20) 20 × 60 = 120 20 × 45 = 900

A2 (30) 30 × 60 = 1,800 30 × 45 = 1,350

Assuming the pig breeder to be conservative, we use maximinapproach. As such, the minimums of act A1 is 900 and that ofA2 is 1350, which is, of course, maximum. So the pig breedershould accept the course of action A1.

Further, by maximax approach also 1800 is maximum whichalso corresponds to A2.

Example 2.13

Given is the following payoff matrix:

Course of action

Do not Expand ExpandStates of nature Probability expand 200 units 400 units

Rs Rs Rs Rs

High demand 0.4 2,500 3,500 5,000 Medium demand 0.4 2,500 3,500 2,500

Low demand 0.2 2,500 1,500 1000

What should the decision be if we use: (i) expected monetaryvalue criterion (ii) the maximax criterion (iii) maximax regretcriterion?

Solution

Let us form the payoff Table as follows:

Payoff Table

States of nature High Medium Low

probability demand demand demand

Course of 0.4 0.4 0.2action

(A1) Do not expand 2,500 2,500 2,500

(A2) Expand 200 units 3,500 3,500 1,500

(A3) Expand 400 units 5,000 2,500 1,000

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(i) Expected monetary value:

forA1 = .4 × 2,500 + .4 × 2,500 – .2 × 2,500 = Rs 2,500

A2 = .4 × 3,500 + .4 × 3,500 + .2 × 1,500 = Rs 3,100

A3 = .4 × 5,000 + .4 × 2,500 + .2 × 1,000 = Rs 3,200

(ii) Row minimums of the different courses of action are:

A1 : 2,500 Maximum of these minimums is 2,500,so the choice is A1, i.e., the decision-maker.

A2 : 1,500 Under this criterion the decision-makerwould decide not to expand.

A3 : 1,000

(iii) Row maximums of the different courses of action are:

A1 : 2,500 The maximum of these maximums is5,000, i.e., choice is A3. In otherwords the decision-maker under thiscriterion would decide to expand 400

A2 : 3,500 units.

A3 : 5,000

(iv) Let us find the regret matrix from the payoff matrix bysubtracting each of the values in a column from thelargest payoff value in the same column.

Regret Table of the Payoff Table

State ofnature High Medium Low Maximum

demand demand demand regretsCourseof action

Do not expand (A1) 5,000 � 2,500 = 2,500 3,500 � 2,500 = 1,000 2,500 � 2,500 = 0 2,500

Expand 200 units (A2) 5,000 � 3,500 = 1,500 3,500 � 3,500 = 0 2,500 � 1,500 = 1,000 1,500

Expand 400 units (A3) 5,000 � 5,000 = 0 3,500 � 2,500 = 1,000 2,500 � 1,000 = 1,500 1,500

Minimum of maximum regrets is 1,500 that occurs in A2 andA3. So the decision-maker must choose to expand 200 unitsor expand 400 units.

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Expected Opportunity Loss (EOL)

If P(S1), P(S2), ......., P(Sn) be the prior probabilitiescorresponding to the respective states of nature S1, S2, ......,Sn, then expected opportunity loss (EOL) of acts:

A1 = (M1 – P11)P(S1) +(M2 – P12)P(S2)+.............+(Mn – P1n)P(Sn)

A2 = (M1 – P21)P(S1) +(M2 – P22)P(S2)+.............+(Mn – P2n)P(Sn)

Example 2.14

Refer the Example 2.13. If 0.3, 0.4, 0.3 be the respectiveprobabilities of three states of nature (i.e., high demand,medium demand and low demand) then EOL of acts:

A1 = 2500 × .3 + 1000 × .4 + 0 × .3 = 1150A2 = 1500 × .3 + 0 × .4 + 1000 × .3 = 750A3 = 0 × .3 + 1000 × .4 + 1500 × .3 = 850

In case of Act A2, EOL is minimum.

Expected Value of Perfect Information (EVPI)

The expected value with perfect information is the expectedreturn in the long run, provided there is perfect informationbefore a decision is taken.

Calculation

Expected payoff with perfect information (EPPI) = (max. payoffin 1st state of nature) × (prob. of 1st state of nature) + (max.payoff in 2nd state) × (prob. of that state) × ..... up to last state.

Now EVPI = EPPI – maximum EMV.

Example 2.15

Payoffs of three acts A, B and C and states of nature X, Yand Z are given below:

Payoff (in Rs)

ActsA B C

States of nature

X -20 -50 200Y 200 -100 -50

Z 400 600 300

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The probabilities of the states of nature are 0.3, 0.4 and 0.3

Calculate the EMV for the above data and select the bestact. Also find the EVPI.

Solution

Let us find the expected monetary value (EMV) of each act.

Act A = –20 × .3 + 200 × .4 + 400 × .3 = Rs 194

Act B = –50 × .3 – 100 × .4 + 600 × .3 = Rs 125

Act C = 200 × .3 – 50 × .4 + 300 × .3 = Rs 130

EMV of Act A is highest as seen in the table, so it should beselected.

Payoff (Rs)

Max. for

States of Prob. A B C state of Max. payoffnature nature × prob.

X .3 �20 �50 200 200 200 × .3 = 60

Y .4 200 �100 �50 200 200 × .4 = 80

Z .3 400 600 300 600 600 × .3=180

Total 320

EVPI = Expected payoff with perfect information (EPPI) –EMV = 320 – 194 = Rs 126.

Example 2.16

Mohan Products Ltd. produces a drums which must be soldwithin a month of it being produced, if the normal price ofRs 100 per drum is to be obtained. Anything unsold in thatmonth is sold in a different market for Rs 20 per drum. Thevariable cost is Rs 55 per drum.

During the last five years, monthly demand was recordedand showed the following frequencies:

Monthly demand (No. of drums) 2000 3000 6000

Frequency 24 12 24

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(i) Prepare an appropriate Payoff Table.

(ii) Advise the production management on the number ofdrums that should be produced next month.

Solution

Gain (on sale) = 100 – 55 = 45, Loss (for unsold) = 55 – 20 = 35(in Rs)

Payoff Table

Demand 2000 3000 6000 Expected value

Prob. 24 12 24Stock 60 60 60

2,000 2,00 × 45 90,000 90,000 90,000 × .4 += 90,000 90,000 × .2 +

90,00 × .4 = 90,000

3,000 90,000 � 35,000 3,000 × 35 1,35,000 � 3,000 × 35 55,000 × .4 += 55,000 = 13,500 = 30,000 1,35,00 × .2 +

30,000 × .4 = 61,000

6,000 90,000 � 4,000 × 35 1,35,000 � 3,000 × 35 6,000 × 45 �50,000 × .4 += -50,000 = 30,000 = 2,70,000 30,000 × .2 +

2,70,000 × .4 = 94,000

Since the expected value is highest (Rs 94,000), in the nextmonth there should be 6,000 drums in stock.

Decision Tree Diagram

A decision problem may also be represented with the helpof a diagram in the form of a tree, for a clear and systematicidea. In this case alternative courses of action, states ofnature, likely outcomes, etc., are diagrammatically orgraphically depicted as if they are the branches, sub-branchesof a horizontal tree. Hence, it is known as a tree diagram.

The tree consists of a network of nodes, probability estimates,payoffs.

Standard Symbol

Nodes: There are two types of nodes (i) decision node(symbolized as square) and (ii) chance node (marked as circle).

Alternative courses of action originate from the decisionnode in main branches. Now, at the terminal point of decision

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node, chance nodes exist from where chance nodes emanateas sub-branches. Probability and outcomes are shown alongthese sub-branches. Each sub-branch can form a branch againso that we can build a tree-like structure representing allpossible outcomes.

Types of decision trees: (i) deterministic (ii) probabilistic.These again can be divided into single stage and multi-stagetrees.

In a single stage decision tree we can find only one decision(i.e., no chance event).

In a multi-stage decision tree, a chain of decisions is to bemade.

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Acts Events Outcomes

E1

O1

decisionA

1E

2node

O2

E1

O1

A2

chanceE

2node

O2

Figure 2.5: Decision Tree Diagram

Example 2.17

There is 40% chance that a patient admitted to the hospitalis suffering from cancer. A doctor has to decide whether aserious operation should be performed or not. If the patientis suffering from cancer and the serious operation isperformed, the chance that he will recover is 70%, otherwiseit is 35%. On the other hand, if the patient is not sufferingfrom cancer and the serious operation is performed,the chance that he will recover is 20%, otherwise it is100%. Assume that recovery and death are the only possibleresults.



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Solution

Construct an appropriate decision tree. What decision shouldthe doctor take?

The decision tree has been constructed as follows:Probability of recovery on operation = 0.28+0.12 = 0.40Probability of recovery for no operation = 0.14+0.60 = 0.74.As 0.74 > 0.40, so operation should not be done for recovery.

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Example 2.18

A manufacturing company has to select one of the twoproducts, A or B, for manufacturing. Product A requiresan investment of Rs 20,000 and product B Rs 40,000.Market research survey shows high, medium andlow demands with corresponding probabilities and returnsfrom sales, in Rs 1000 for the two products, in the followingTable:

Market Probability Return from sales

demand A B A B

High 0.4 0.3 50 80Medium 0.3 0.5 30 60

Low 0.3 0.2 10 50

recovery 0.7(0.28)

operatedeath 0.3

(0.12)cancer 0.4

recovery 0.35(0.14)

not operatedeath

(0.26)recovery 0.2

(0.12)operate

death 0.8(0.48)

no cancer 0.6recovery 1.0

(0.60)not operate

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Construct an appropriate decision tree. What decision thecompany should take?

Solution

Market A B

demandx p px x p px

(�000) (�000)

High 50 0.4 20 80 0.3 24

Medium 30 0.3 9 60 0.5 30

Low 10 0.3 3 50 0.2 10

Total 32 64

Product Returns (Rs) Investment (Rs) Profit (Rs)

A 32,000 20,000 12,000

B 64,000 40,000 24,000

The company should take decision in favour of B since theprofit is high.

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(20)

(9)

(3)

(24)

(30)

(10)

high demand (50)0.4

product A medium demand (30)0.3

low demand (80)0.3

high demand (80)0.3

product B medium demand (60)0.5

low demand (50)0.2

Example 2.19

Y.K. Sachdeva has two independent investments A and Bavailable to him; but he can undertake only one at a timedue to certain constraints. He can choose A first and thenstop, or if A is successful then take B or vice versa. Theprobability of success of A is 0.6 while for B it is 0.4. Both



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investments require an initial capital outlay of Rs 10,000 andboth return nothing if the venture is unsuccessful. Successfulcompletion of A will return Rs 20,000 (over cost) andsuccessful completion of B will return Rs 24,000 (over cost).Draw decision tree and determine the best strategy.

Solution

The appropriate decision tree is as follows:

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(�10,000)

(�10,000)

(24,000)

(0)

(0)

(�10,000)

(20,000)

(�10,000)

D2

Fail (.6)

Do Nothing

Accept B

Fail (

.4)

Acc

ept A

ACC BSuccess

(.6)

Success

(.4)

ACC A

D1

D3

(Outcome Rs)

Fail (.6)

Success (.4)

Stop

Stop

Fail (.4)

Success (.6)

We find three decision points D1, D2, D3 in the previousdecision tree diagram. For an analysis of tree we startworking backward.

Decision Outcome Probability Conditional Expected

point values values

D3

(i) Accept A success .6 20,000 12,000

failure .4 �10,000 �4,0008,000

(ii) Stop 0D

2(i) Accept B success .4 24,000 9,600

failure .6 �10,000 �6,0003,600

0D

1(i) Accept A success .6 20,000 + 3,600 14,160

failure .4 �10,000 4,00010,160

(ii) Accept B success .4 24,000 + 8,000 12,800failure .6 �10,000 �6,000

(iii) Do nothing 6,800

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From the column of expected values see Table 2.7, we findthe best strategy is to accept A and, if it is successful, thenaccept B.

Summary

This unit presented the fundamentals of the Bayesianapproach to decision-making under uncertainty andcertainty.

The unit first emphasized the need for information indecision-making. The unit also discussed the conceptof probability and indicated the basic sources ofassigning probabilities. In the present days, theprobability theory has a vital role, as such, thisprobability theory will be used more frequently in thedecision-making theory under uncertainty and risk. Themanagement of an industry or any concern is to takedecisions about the development or expansion of theconcern. No doubt the concern has to face many problemsfrom time to time. The management has to overcome orsolve the problems. This unit concluded with briefdescriptions of industry applications of Bayesiandecision analysis and related methods.

Review Questions

1. What is the ‘expected value’ approach to decision-making?

2. What are the advantages of Bayesian analysis over othermethods?

3. Why is it necessary to estimate the value and cost ofinformation before conducting research?

4. Carry out a full decision analysis for M/s Excel Ltd, usingthe following information:

Events Actions Expert Delay Delay

Now (Rs) 1 Year (Rs) 2 Years (Rs)

Economic conditions remain good (A) 7,00,000 5,60,000 4,10,000

Moderate downturn in economy (B) 5,20,000 4,00,000 3,00,000

Economic recession (C) �2,96,000 26,000 29,000

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Prior probabilities for the various events for the nexttwelve months are:

(A) = 0.3

(B) = 0.4

(C) = 0.3

Carry out a pre-posterior analysis and find the expectedvalue of perfect information.

5. Describe the process of specifying the informationneeded.

6. What do you understand by the term EVPI?

7. Suppose you are given the following Payoff Table:

S1 S2

A1 10 4

A2 2 5

(i) Assuming that the states of nature S1 and S2

exhaust the possible environmental conditions,what probability would have to be associated withthe occurrence of S1 if the expected payoffs ofalternative A1 and A2 are to be equal?

(ii) Suppose in the above Payoff Table, the payoffcorresponding to the A2S2 combination were 4instead of 5, would the knowledge of theprobabilities assigned to S1 and S2 be required?

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Management and Research Problem

An old saying is "A problem well defined is half solved". Thisis held true in the area of research. Hence, the researchactivities start with defining the problem. Problem isprimarily a situation of dilemma of decision situation andthe simplest of decision situations can be characterized bythe following conditions:

1. There is an individual operating within someenvironment to whom the problem can be attributed.

2. The individual has at least two courses of action thatcan be pursued, and is able to make a choice from theavailable courses of action.

3. There are at least two possible outcomes of that choice,and one of these outcomes is preferred to the other.

4. There is a chance, but not an equal chance, that eachcourse of action will lead to the desired outcome.

69

Objectives


y Understand the meaning of problem.

y Present the classification of problem.

y Explain the respective role of management and researcher.

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Unit 3

Relationship betweenManagement and ResearchProblem



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Thus, a problem is the dilemma of choosing one alternativeamong various alternatives for making a choice on coursesof action. Which course of action needs to be selected, givesrise to the need of research.

One of the best ways to approach the research process is tostate the basic dilemma that arises the need for researchand than to develop other questions by progressively breakingdown the original question in more specific ones. This originalquestion is called the management problem which when isbroken in specific ones is called the research problem.

Management problem is the actual problem that themanagement is facing, viz;

u Rising cost

u Sales decline

u Increasing LTO

u Market contraction and expansion decisions; etc.

Breaking down the management problem into specific onerequires an step wise analysis. First, the managementdilemma needs to be defined which is not a difficult task asall modern organizations keep track of their performancefactors (Like: Sales, Profits, Employees Turnover; etc). Forarriving at final management dilemma the first stage isexploration where a researcher needs to review publishedresources and interview information gatekeepers. Bycollecting and recording the exploratory information, theresearcher needs to word the dilemma or the correction ofthe symptom in the question form, usually starting with, "Howcan the organization…?"

Once the management dilemma is worded in the questionform then further exploratory research is taken to find outthe possible management actions that might be taken to solvethe management dilemma. This requires qualitative researchtechniques to be used viz; Brain storming with the experts,Interviews with information gatekeepers, secondary sourcesstudy, etc. Finally, several research questions is to be framedwhich could be used for further investigation by using bothqualitative as well as quantitative study. Each question is analternative action that management might take to solve the

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management dilemma. Among them the most plausibleaction, or the one that offers the greatest gain using the fewestresources should be researched first.

Figure 3.1

Respective Roles

The Management's Role

The manager must move from the management dilemma tomanagement question to proceed with the research process.Management problems are too numerous to list, but they canbe categorized in:

u Choice of purpose or objective: "What do we want toachieve?"

u Generation and evaluation of solution: "How can weachieve them?"

u Troubleshooting or control situation: "Why are we facingthe present situation?"

Researcher�s Role

Once the researcher has a clear statement of the managementquestion, they with the help of the manager must translatethem into research question. The research question shouldbe a fact - oriented, information - gathering question. Onlyrelevant alternatives should be considered. To have an ideaof relevant alternatives the insight of manager must betaken. This will also help the researcher having idea ofmanager's decision making environment.

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DiscoveringManagement Exploration

DefiningManagement

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The researchers task is to assist the manager in formulatinga research question that fits to resolve the managementdilemma. A Research question is the hypothesis of choicethat best states the objective of the research study. It is morespecific management question that needs to be answered andthis can be more than one. After exploration is complete theresearch questions must be fine tuned.

After the research problem is formulated it should furtherbe broken down in Investigative question and Measurementquestion. Investigative questions are questions theresearcher must answer to arrive at a Conclusion about theresearch question. These questions reveal the specific pieceof information the manager feels to know to answer theresearch question. Measurement questions are the questionsthat the researcher asks to the respondents. They appearon the questionnaire and are in line with the informationneeded for the research question.

All these steps can be shown as:

Figure 3.2

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Management Dilemma

Management Question

Research Question(s)

Investigative Question

Measurement Question

Management Decision

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Summary

This unit presented the classification of problems anddetailed the need of converting management's probleminto researchers problem.

The unit first stated and cleared what is a problem andthan has gradually proceeded in explaining the role ofmanagement and researcher to convert managementsproblem into precise detail on which further study canbe made feasible.

Review Questions

1. Define the role of management in the formulation ofresearch problem.

2. Elucidate the difference between management problemand research problem.

Research design or model indicates a plan of action to becarried out in connection with a proposed research work. Itprovides only a guideline for the researcher to enable himto keep track of his actions and to know that he is moving inthe right direction in order to achieve his goal. The designmay be a specific presentation of the various steps in theprocess of research. These steps include the selection of aresearch problem, the presentation of a problem, theformulation of the hypothesis, conceptual clarity,methodology, survey of literature and documentation, datacollection, testing of the hypothesis, interpretation,presentation and report writing. When Apple India Ltd.launched its Apple juice with extraordinary caution nocomprehensive study had ever been done by Apple India Ltd.

In this chapter various types of research designs areexplained with suitable examples.

Introduction

The purpose of marketing research is to provide informationwhich will aid in management decision-making. A marketing

75

Objectives


y Define research design, classify various research design, andexplain the differences between exploratory and conclusive.

y Compare the basic research design: exploratory and descriptive.

y Explain research design and different types of research design.

y Describe the various factors to be considered in the selection ofan experimental design.

y Describe the procedure for reduction of error through design.

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Unit 4

Research Design



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manager, for example, in a large consumer goods companymay want to collect information to assess whether or not tolaunch a new product or to determine why the sales of aparticular product are declining. In collecting thisinformation, three major steps may be identified. First andthe foremost is establishing of research objectives. Then aresearch plan needs to be formulated and implemented; andfinally data analyzed followed by a presentation of researchfindings. A clear and precise definition should be made bythe management of the decision problem, this should beexpressed not only in terms of problem symptoms such as adecline in market share but also with possible contributingfactors such as changes in competitors’ strategies or inconsumers’ tastes, as well as the actions the managementmight take based on research findings. Otherwise, irrelevantinformation may be collected.

Development of a research plan requires what data are to becollected; what research techniques and instruments are tobe used; how a sample is to be selected; and how informationis to be collected from this sample. Sometimes the requiredinformation may already be available in secondary sourcessuch as the government or trade reports, company records,or sales force reports. This will not, however, have beencollected with the particular problem in mind. Consequently,primary data collection may be required, in other words,collect information specifically for the particular problem.

Where primary data are collected, observational or otherqualitative techniques, experimentation or survey researchmay be conducted. Observations and other qualitativetechniques, such as projective techniques (word association,sentence completion tasks and focus group interviewing) aremost appropriate in the initial stages of research, when littleis known about the problem. The onus of interpretation is,however, placed on the researcher and consequently, suchtechniques are open to criticisms of subjectivity.

Experimental techniques are also potentially applicable, butthey are rarely used except in-store experiments study, forexample, the impact of in-store promotions on sales. Testmarketing can also be viewed as a field experiment. Survey

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77UNIT 4 Research Designu


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research is the technique most commonly used in marketingresearch. A standard questionnaire can be administered tolarge samples and systematically analyzed usingcomputerised techniques.

In observational or qualitative research instruments suchas coding scheme, recording sheets and other tests may needto be designed. The most common instrument used is aquestionnaire. For unstructured interviews and focusgroups, only an interview guide indicating the topics to becovered may be required. A crucial aspect of survey researchis, however, the design of a carefully worded questionnaireto elicit desired information from respondents. Attention toquestion form and sequencing is also essential in order toavoid biased responses.

Three principle methods of data collection may beconsidered–telephone, mail or personal interviewing.Telephone interviewing is quick and can be conducted froma central location where interviewers are controlled by asupervisor. However, only with this method the personshaving telephones can be interviewed and a limited numberof questions can be asked. Mail questionnaires are thecheapest method of survey administration, but suffer fromlow response rates and also assumes that the respondentclearly understands and can respond to questions. Personalinterviewing is the most flexible method since theinterviewer can select the sample by judgement orconvenience sampling and is able to explain questions to therespondent. It is, however, an expensive method of datacollection and susceptible to interviewer bias. Inimplementation of the research plan, this is where majorsources of data inaccuracy and unreliability often arise. Inthe case of surveys, for example, respondents may biasfindings by refusing to cooperate, by providing inaccurateanswers, for example on income or by giving sociallyundesirable responses. Interviewers may also bias resultsby encouraging a specific response, by inaccurate recordingof responses or in extreme cases, by falsifying responses.

Current developments in telecommunications and computertechnology are rapidly changing data collection procedures

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and improving their efficiency. The results can also beanalyzed and updated with each successive response, thus,considerably reducing research time and costs. Data analysisincludes tabulating, classifying and interpreting theinformation collected. The complexity of the analysisdepends to a large extent on management needs. In manycases tabulation or cross-tabulation of results with averagesand other summary statistics may suffice. In other cases,more sophisticated multivariate techniques such as factoror cluster analysis or multidimensional scaling may berequired, if more complex interactions in the data are to beexamined. Finally the presentation of research findings maybe verbal and/or written. In either case, the main focus shouldbe on clear presentation of key research findings and theirimplications on the decisions to be made by the management.As it is obvious, the most vital element in this process isresearch plan or the research framework/design. For theresearch to be valid and reliable it is imperative that properthought should go into the design of research, otherwise itmay lead to GIGO (Garbage In, Garbage Out) or mere datacollection exercise with no information to the managementfor its problem-solving exercise.

A marketing research design may be described as a series ofadvance decisions that, when taken together, comprises amaster plan or model for the conduct of the investigations.It is the blueprint that is followed in completing a study. Anappropriate design requires careful consideration of theproblem and objectives to be met in relation to the time andresources available for the study. The design or plan of aresearch investigation is best put in writing and it ordinarilycovers the following aspects:

(a) Objectives of the research including a statement ofgeneral objectives and other operational objectives inas specific form as possible.

(b) The relation of these objectives with the problem athand.

(c) The form in which the results will be obtained and howthey may be used.

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(d) The methods to be used in attaining each of theobjectives of the research.

(e) A time schedule for the entire research, includingspeculations, deadlines for specific phases of theresearch.

(f) Personnel and administrative set-up, with dutiesspecified for each person working on the researchproject.

Types of Research Design

On the basis of objectives of the marketing research, theresearch can be classified into: (i) Exploratory research (ii)Conclusive research. On the basis of character of data MR isoften classified into: (A) Quantitative research (B)Qualitative research. The research design for exploratoryresearch is best characterized by its lack of structure andflexibility. It is generally used for the development ofhypothesis regarding potential problems and opportunities.Exploratory research is further subdivided into (a) Searchof secondary data (b) Case study (c) Survey of experts.Conclusive research which is used to provide informationfor the evaluation of alternative courses of action can be sub-classified into (a) Descriptive research (b) Causal orexperimental research.

Descriptive market research is used to describe marketingphenomena while trying to determine the association amongvariables. It also seeks to predict future marketingphenomena.

In cross sectional design, which is typically used indescriptive research projects, a sample of populationelements is taken at one point of time. In descriptiveresearch, we can make use of both case study and statisticalstudy. Causal or experimental research seeks to unearthcause and affect relationships. A good causal research designseeks to minimize the interference of external variableswhile studying the relationship between variables. There is,however, a third type of research, also termed as performancemonitoring research, that is an important part of marketing

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research activity of a firm. It typically requires a longitudinalresearch design (panel design), in which a fixed sample ofpopulation elements is measured repeatedly. In thetraditional panel, the same variables are measured everytime, as opposed to an omnibus panel where differentvariables are measured each time. In both types of panels,the sample of respondents remains fixed.

Figure 4.1: Research Design in Marketing Research

Exploratory Research Design

Flexibility and creativity characterize exploratory researchstudy since the aim of its investigation is to find newhypotheses. Hence, formal design is rare in this type ofresearch and much is left to the creative imagination of themarket researcher. He could conduct a study of secondarysources of information or get views from the experts orresort to case study analysis. Market researchers exercisetheir individual initiative in spotting and following leads inan organized way.

(A) Exploratory research using secondary sources of information

Many companies who regularly conduct market researchstudies have maintained a record of research findings overthe years, the access to which is both quick and economicalfor a market researcher. Looking for hypotheses, a marketresearcher could consult basic research findings reportedin professional journals. Other fruitful sources of secondarydata are public libraries, newspapers, government reports,

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Problem

Exploratory Research

Hypothesis New Relationships

Descriptive Research/Causal or Experimental Research

Performance Monitoring Research



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trade journals, general books, etc. Computerization ofdatabase and quick search systems have made this type ofresearch more organized, exhaustive and quick. At the sametime there comes the problem of information overload andmarket research is the only way of shifting the relevantinformation by use of creative solutions to get insights onwhich management can act.

(B) Exploratory research using expert opinions/individuals with ideas

Experts can give valuable insights into a marketing problembecause of their experience with the problem at hand, abilityto act as an observer and an ability to express ideas unlikeany other individual. Despite the desire to find individualswith ideas, it is important not to concentrate theinvestigation only among the better educated or morearticulate persons. A practical solution is to carry outexploratory research using a mix of cooperative, imaginativepersons as well as randomly selected persons. Respondentsshould be given full freedom to respond to get new ideas.Various techniques called qualitative research techniqueshave been developed to unearth consumers’ beliefs, values,attitudes, feelings that influence consumer behaviour. Thesequalitative techniques can be further divided into:

(a) Depth interviews: These are one to one interviewsbecause most people do not have clear ideas why theymake particular purchase decisions. Individualsnormally do not report decisions. They normally do notreport socially unacceptable motives. So marketresearcher in-depth interviews attempt to influencerespondents to talk freely about their subject of interest.Market researcher leads and probes the topic to getadditional information. As such respondents are notapproached with a fixed list of questions but theresearcher has an outline in mind. No two interviewswill proceed the same way as, for example, in astructured questionnaire interview. The marketresearcher has the flexibility to probe beyond superficialreasons, this is its strong as well as negative point inthe sense that it makes it difficult to compare results.There is total reliance on the skill of the market



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researcher which makes it expensive to hire suchknowledgeable persons. Depth interviews werediscredited after being in limelight in Ditcher’s timebut have been lately beginning to make a comeback inunderstanding the consumer better for better consumerservice.

Direct questions to consumers about their attitudes ormotives seldom elicit useful information. Directquestions do not measure the relative importance of thevarious types of reasons, and many individuals will notrespond to what might be considered sociallyunacceptable.

Instead of approaching respondents with a fixed list ofquestions, the interviewer, in depth interviews,attempts to influence respondents to talk freely aboutthe subject of interest. This is intended to putrespondents at ease so they express any ideas they haveon the subject. If some idea of interest is passed overtoo quickly, the interviewer may seek additionalinformation by “probing”.

The advantages of depth interviews:

u They bring out information that would not beobtained in a normal interview.

u The interviewer has a great deal of flexibility andcan use his ingenuity to stimulate respondents toreveal more of their attitudes and motives.

The disadvantages of depth interviews:

u No two interviewers will proceed in exactly thesame way, thus it is difficult to compare results.

u This creates difficulty in securing respondentscooperation and increases costs.

u The depth interview is the difficulty and cost ofinterpretation.

(b) Focus group interviews: When the management wantsto get a first person feel of consumer reactions on its

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marketing mix variables, a market researcher canconvert a focus group with him/her acting as amoderator. The discussion is guided from the genericproduct category to the product specific category to thespecific brand under consideration. The interviews areusually recorded so that the market researcher may notlose information while keeping the discussion on thetrack. Reports based on focus groups typically maycontain direct quotations from the interview session.These can be highly useful and stimulating to marketingpeople. The guiding concept in selecting samples forfocus groups is never to use only one focus group but tokeep running groups until the researcher is getting nomore ideas. Individuals for a focus group are selectedon quota basis. Again the disadvantage is that a skilledmodulator is crucial to the success of focus groups. Alsocritics of focus groups argue that the results obtainedare little more than creative ideas of the researcher.

Focus groups too, like in-depth interviews, have theiradvantages like:

u Bringing out the inner motivations of theconsumers.

u Letting the researcher have a first handexperience of the consumer reactions.

u Generating new ideas.

Focus groups have their disadvantages too:

u Excessive reliance on the skills of the moderator.

u Wrong combination of consumers in focus groups,resulting in no tangible output.

u Using qualitative discussions quantitativelywithout checking them out.

Focus groups are, however, being used increasingly byresearchers. Usually more than one focus group is usedto get a clear and unbiased understanding of the targetmarket behaviours and attitudes.

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(c) Projective techniques: In projective techniquesinterviewing, the respondents are asked to projectthemselves into a particular situation. The consumersthen express different images they may have ofcompetitive brands of a given product. A consumer maybe asked to match a brand and a person’s image or askedfor role reversal. It is another approach to gettingrespondents to reveal more than their surface feelings.For example, consumers might be asked such questionsas:

If brand A were a motorbike, what would it be?

If brand B were a TV, which one might it be?

The responses depend on the personality of a consumer.Every person has certain individual characteristicscalled basic personality. This basic personality is verystable and very difficult to change. These personalitytraits are present due to an individual’s biological make-up. A marketer should remember that it is not possibleto predict an individual’s purchase behaviour based onhis personality only. Nevertheless, by understanding theproduct or segment the market aims at the target groupwith certain major personality traits.

(d) Exploratory research using case analysis: Althoughthis method has long since attracted skeptics ire becauseof its non-scientific nature, it is making a comeback. Itinvolves the comprehensive study of one of a few specificsituations and particularly the study of complexsituations in which interrelations of several individualsare important. A situation is called a ‘case’.

The design of a research project is the plan that ties thedata to the conclusions that will be drawn. This methodis based on finding the differences and the similaritiesso as to find the answers. Case research is not aquantitative exercise but is used to enhanceunderstanding. It requires a rare combination ofjudgement to select cases and insight in interpretingthem. Its strong points are holistic orientation, real lifesituation, i.e., in case study method inferences are made



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on the entire picture and not some of its parts; all thepeople actually concerned with the problem arecontacted and data is obtained informally as well.

The disadvantages are mainly owing to its timeconsuming procedure; heavy reliance on investigatorsand the absence of formal information gatheringtechniques resulting in very generalized and randominformation which might not be useful at all.

Conclusive Research

When a marketing manager has to select one course of actionamong a number of alternatives, conclusive researchprovides him information that helps him to evaluate variousalternatives and select among them a course of action. Thistype of research provides a rational basis for his decisions.The alternatives may be well or vaguely defined. Conclusiveresearch design is characterized by formal researchprocedures. The research objectives are accurately definedand so are information needs. Conclusive research studiescan be classified either as descriptive or experimental.

(A) Descriptive research

The research objectives in this type of research are generallydescribing the characteristics of consumer segment, viz.,demographic, socio-economic, geographic, psychographic andbenefits sought. Descriptive studies can also portray buyerperceptions of brands; audience profiles for media types, viz.,TV, radio, newspaper, journals and magazines, etc. They canalso portray buying power of consumers, availability ofdistributors, product consumption patterns, price sensitivityof consumers, market share, etc. These are just a fewrepresentative studies out of numerous studies that comeunder descriptive research in marketing. Despite theemphasis on description, it should not be concluded that thestudies should be simply fact-gathering expeditions. Theycan also be used to make predictions about the occurrenceof a marketing phenomenon. The data regarding the presenceof an association among variables can only be used forproductive purposes but statements regarding cause and

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effect relationships are not possible with descriptiveresearch (As may be possible in experimental or causalresearch).

The purpose and nature of descriptive research is quitedifferent from that of exploratory research. Many descriptivestudies are made with only hazy objectives and withinadequate planning. Much of the data collected in suchstudies turns out to be useless. Descriptive studies of thistype are actually more of exploratory type. Effectivedescriptive research is marked by a clear statement of thedecision problem, specific research objectives and detailedinformation needs. The research design should be fairlystructured. Since the purpose is to provide informationregarding specific questions or hypothesis, the research mustbe designed to ensure accuracy of the findings. Sincedescriptive studies may cost huge amount of money to carryout, there is then this necessity of its formal design.Descriptive research often makes use of survey researchdesign which consists of a cross-sectional research design,that is, collecting data on few factors from a number of casesat one point of time. This is the most popular type of researchdesign and is useful in describing the characteristics ofconsumers and determining the frequency of marketingphenomenon. As already mentioned it is often expensive andrequires skillful and competent market researchers toconduct it effectively. It is also termed as statistical methodin contrast to case method which focuses on many factors offew cases. This method ceases to focus on individual casesand focuses instead on classes, averages, percentages,measures of dispersion and more sophisticated statisticalprocedures. For example, cluster analysis can be used togroup customers into different classes on the basis of fewcustomer attributes or characteristics. Factor analysis canbe used to group attributes into few factors which areimportant from consumers’ point of view vis-à-vis a product,etc. In fact descriptive research presupposes that a soundcausal model of marketing system exists in the mind of thedecision-maker in contrast to exploratory research whichseeks to generate hypotheses. A market researcher has tohave a tentative hypothesis for carrying out descriptive

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research for the sole reason that he knows what data tocollect from his respondents in the survey. Descriptiveresearch designs can also use one or more of the followingsources of data:

(a) Interrogation of respondents

(b) Secondary data

(c) Simulation.

The analysis techniques used in descriptive research arethose specifically for mass data. Each individual item tendsto lose its identity. This is both an advantage and adisadvantage. The advantage lies in the objectivity withwhich the analysis can be made. Averages or variance can becomputed and compared; two independent researchers willarrive at similar results which is not the case with the casemethod. But the disadvantage lies in its mobility to provecause and effect relationships which is the domain ofexperimental (causal) research. Even the direction of causaleffect may not be visible through statistical study, e.g. whenadvertising and sales co-vary, it is often not clear whetheradvertising causes sales or sales cause the expenditure ofmore advertising effort because of greater apparent potentialsales results. Simulation of marketing phenomenon consistsin an incomplete representation of the marketing system orsome aspect of this system. It is relatively a new source ofdata which is largely computer-oriented. Simulation can beused to gain insight into the dynamics of the marketingsystem by manipulating the independent variables(marketing mix and situational variables) and observing theirinfluence on the dependent variables. A marketingsimulation requires data inputs regarding the characteristicsof the phenomenon to be represented and the relationshipspresent. Simulations should neither over-simplify nor over-complicate. The limitations are its validity and time/cost ofupdating the model as conditions change. Simulation modelscan be classified on the basis of the purpose they serve, viz.,predictive and descriptive.

Very often descriptive research may take the route ofanalyzing already existing data on respondents, e.g., census

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data. Secondary source of data is much cheaper to accessthan carrying out a full-fledged survey and hence a greattemptation for a market research. But the validity andappropriateness of such a secondary data descriptiveresearch should always be borne in mind before embarkingon one.

Example 4.1

The exploratory research on the drinking habit of milkyielded a set of three hypotheses to be tested. Theinformation requirements were met by collecting data fromover 100 respondents belonging to the upper-income group.A statistical frequency analysis and cross-classificationanalysis revealed the following:

1. 64 per cent of the respondents preferred milk forthemselves or their children as a breakfast drink. A mere32 per cent respondents responded positively towardstea/coffee as breakfast drink. Rest of them opted for juicein the morning.

2. 76 per cent of the respondents were positive about thetaste of the flavoured milk with the teenagers liking itmuch more.

3. 40 per cent elders preferred tea/coffee in the evening,whereas 35 per cent of the teenagers preferred milk asa breakfast drink.

4. 80 per cent of the respondents wanted to give theirchildren milk during the day when they return fromschool.

5. 62 per cent of the respondents considered it a statussymbol to offer tea/coffee to their guests or at socialgatherings.

(B) Experimental or causal research

Although, it is the nature of marketing decision-making thatall the conditions allowing the most accurate causalstatements are not usually present but in thesecircumstances, causal inference will still be made by

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marketing managers. Because in doing so they would wantto be able to make causal statements about the effects of theiractions. “The new advertising campaign we developed hasresulted in p% increase in sales” or the “sales discountstrategy we followed has resulted in p% increase in sales”,etc. In both of these examples, marketing managers aremaking a causal statement.

However, the scientific concept of causality is complex anddiffers substantially from the one held by the common personon the street. The common sense view holds that a singleevent (the ‘cause’) always results in another event (the‘effect’) occurring. In science, we recognize that an event hasa number of determining conditions or causes which acttogether to make the effect probable. Note that in thecommon sense notion of causality, the effect always followsthe cause. This is deterministic causation in contrast toscientific notion which specifies the effect only as beingprobable. This is termed as probabilistic causation. Thescientific notion holds that we can only infer causality andnever really prove it. That is, the chance of an incorrectinference is always thought to exist. The world of marketingfits the scientific view of causality. Marketing effects areprobabilistically caused by multiple factors and we can onlyinfer a causal relationship. The conditions under which wecan make causal inferences are:

(a) Time and order of occurrence of variables.

(b) Concomitant variation.

(c) Elimination of other possible causal factors.

The fundamental research tool used to identify causalrelationships is the experiment. The objective of anexperiment is to measure the effect of explanatory variablesor independent variables on a dependent variable, whilecontrolling for other variables that might confuse one’s abilityto make causal inferences. Such research leads to questionslike:

“Is a given print advertisement more effective in colour thanblack and white?”

“Which of the several promotional techniques is mosteffective in selling a particular product?”

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“Can we increase the sales of a product by obtainingadditional shelf space?”

As Cox and Enis quote:

“The usefulness of experimental design in marketing extendsacross the functional areas of promotion, distribution, pricingand product policies. Whenever marketing management isinterested in measuring the effects of alternative courses ofaction, experimentation may be a practical means of reducingthe risk involved in deciding among the alternatives.”

An experiment is executed when one or more independentvariables are consciously manipulated or controlled by theperson running the experiment and their effect on thedependent variable or variables is measured. In surveysthere is no manipulation of independent variables by theresearchers. This is a fundamental difference between theexperimental and non-experimental research.

Treatments are independent variables that are manipulatedor whose effects are measured. Dependent variables are themeasures taken on test units. Test units are the entities towhom the treatments are presented and whose response tothe treatments is measured. It is common in marketing forboth people and physical entities, such as stores orgeographic areas, to be used by as test units. For example,people may be asked to try a product and then have theirattitudes towards it measured. Here people are test units,product type is the independent variable and attitude is thedependent variable.

Two concepts of validity are important in experimentation,internal and external. Internal validity is concerned by withthe question of whether the observed effects on the test unitscould have been caused variables other than the treatment.Without internal validity the experiment is confounded.External validity is concerned with the ‘generalability’ ofexperimental results. A researcher, obviously, would likean experimental design to be strong in both kinds of validity.Unfortunately, it is often necessary to trade off one type ofvalidity for another. There are three true experimentaldesigns in which a researcher is able to eliminate all

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extraneous variables as competitive hypotheses to thetreatment:

(1) The Pre-test—Post-test control group design:

Experimental group R 01 X1 02

Control group R 03 03

(2) The solomon four group design:

Experimental group 1 R 01 X 02

Control group 1 R 03 04

Experimental group 2 R X 05

Control group 2 R 06

(3) Post-test only control group design:

Experimental group R X 01

Control group R 02

Symbols used:

X Represents exposure of a test group to an experimentaltreatment, the effects of which are to be determined.

0 Refers to processes of observation or measurement ofthe dependent variables on the test units.

R Indicates that individuals have been assigned at randomto separate treatment groups or that groups themselveshave been allocated at random to separate treatments.

Movement from left to right indicates movement throughtime. All symbols in any one row refer to a specific treatmentgroup. Symbols that are vertical to one another refer toactivities or events that occur simultaneously.

e.g. 01 X1 02 indicates that one group received ormeasurement of the dependent variable both prior to (01)and after (02) the presentation of treatment (X1). Further thesymbols:

R X1 01

R X2 01

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indicate that two groups of subjects were randomly assignedto two different treatment groups at the same time. Further,the groups received different experimental treatments andthe dependent variables were measured in the two groupsat the same time. These purely experimental researchdesigns control extraneous variables like history,maturation, interactive testing effect, instrumentation,statistical regression, selection bias and test unit mortality.

Table 4.1: Types of Experimental Designs

Type of Experimental DescriptionDesign

1. "After only" design Difference between the experimental group'sresponse before and after the experiment

2. "Before after" design The experimental group's reaction is firstmeasured before and after the experimentalvariable is introduced to them to check out thedifference in behaviour. The disadvantage isthat some uncontrollable variable might beresponsible for the change in opinion orbehaviour.

3. Before after with control The design consists of having a control groupgroup which is not subjected to the variable, versus

the experimental group which is subjected tothe variable. The difference of their differenceswould give an idea of the extent of uncontrollablevariablespresent.

4. Four group six study To remove the bias which exists on account ofdesign the 'before' measurement four groups are made,

two as in the before after with control group whenthe before measurement is not made – onecontrol group and the other experimental.Theoretically, it will be the solution of fourunknown quantities to find their differences.

5. After only with control In this case, no 'before' measurementgroup is made but only the after measurement is made

on the experimental group. The differencebetween the two would indicate the effect of theexperimental variable.

6. The latin square design If the effect of a single variable is to be studiedover different time periods and differentgeographic regions a design which takes intoaccount possible combinations is made andthe differences arising on account of either thegeographic region or the time period are studied.

Situation in which it is used

Measurement of advertising recall, day afterrecall, etc. or measurement of increase in salesafter a sales promotion scheme.

A consumer entering a departmental store,having various brands of shirts, may be askedhis brand preference. The salesman at the storewould be instructed to influence the choicetowards a particular brand. The brand purchasedby the consumer finally would indicate whetherthe sales people have been successful ininfluencing the brand choices of the consumer.A consumer's intention to purchase earlier iscompared with any changes at the time of finalpurchase on account of external stimuli like anadvertisement or influence of the dealer, etc.

In the experiment described earlier, there couldbe consumers to whom the salesman does notdeliberately push a particular brand. This wouldconstitute the control group. The differencesbetween the purchase behaviour of the controlgroup and that of the experimental group wouldindicate whether uncontrollable variables hadcaused the change in behaviour.

The experiments of four groups six study designare difficult to set up and difficult to interpret andhave little practical application although theyare ideal.

The experimental group may be sent certainprivileged discount coupons for a sale, whereasthe control group is not, the results of the salewould indicate whether the discount couponsare indeed useful in increasing the sales of theproduct.

Suppose the owner of franchised outlets, sayBata, would like to know whether there is adifference in sales occurring on account ofdifferences in three types of display used bythree similar Bata stores, situated at differentlocations in Mumbai, for a period of three months.The design would be:

Month ® 1 2 3

Bata store location

Crawford market A C B

Linking road C B A

Andheri B A C

where A, B, C are different sales displays.

Latin square designs are extensively used toestablish cause-effect relationships inmarketing situations.

Steps in planning an experimental design:

1. Selection of the problem: Every problem cannot bestudied through experimental method. One example of

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major conditions being capacity to manipulate theindependent variable the effect of which is decided tobe studied.

2. Proper description of the selected problem: Afterselecting the problem, it must be put in proper language,i.e., the hypothesis must be stated in clear and conceptualterms. The variables that affect the phenomenon mustbe known and conceptualized.

3. Selecting the setting: The background in which theexperiment relating to phenomenon is to be carried outis termed as setting. In case of laboratory experiment itis created artificially and the experimenter decides howit can be done. In case of a field experiment, naturalsetting has to be located where the experiment can bemade.

4. Pilot study: In planning an experiment, a pilot studymay be necessary so that the researcher is brought faceto face with realities and many problems that he hadnot thought of. This also will enable him to know moreprecisely the various causative factors involved, thenature and working of the institution, the extent ofcooperation or resistance that he is expected to meet.

5. Research design: The most vital past of the researchis research design as it lays down the manner in whichthe researcher will manipulate the situation in orderto study the desired effect. This in itself leads to problemor control over the phenomenon.

Extensions of True Experimental Designs

There are four designs that permit the researcher to studymore than one level of an independent variable.

Completely Randomized Design

This is the simplest of the designs in which the treatmentsare applied to the experimental units by a chance process.The researcher is making an assumption that there are nodifferences in the test units and as a result, all the test unitsare treated alike and are randomly assigned to test groups.

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For instance, to find out the most appropriate price for anew product, three different price levels–high, medium andlow can be tested. The different price levels can be tested inthree different stores. The analysis would reveal the averageamount of the product sold at each price level and disclosewhether there is any significant difference in sales betweenthe three price levels.

The main disadvantage of this design is that it does not takeinto consideration the influence of possible extraneousfactors. However, this design has the advantages ofsimplicity and inexpensiveness.

Randomized Block Design

This is an extension of the completely randomized design.In this design, a single extraneous factor is isolated byblocking out its effects. In the price illustration cited before,the type of store was not given consideration, but it could bean important influence on the sales of the product. Thus,the randomized block design enables the researcher toconsider the effect of one extraneous factor and provides aclear idea of the treatment’s effect on sales. In ourillustration, we might take six stores of each type likedepartment stores, speciality stores or grocery stores andassign them to three price levels. The results will be thesame as that provided by the completely randomized designbut it gives us the effect of one extraneous factor.

Latin Square Design

The Latin square design considers the effect of twoextraneous factors. As the name indicates, the layout of thedesign is a square. In this design, the treatments on eachsubject are tested one at a time in a sequence and thetreatment is rotated so that one extraneous factor will offsetthe other. For instance, if a marketer wants to test the effectof four window displays in four stores, he may do so byrotating the displays between the stores for two weeks ineach store with a week’s gap between each test. As the testwould form a square, there would be as many tests astreatments. With four stores and four displays, we have a

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4 × 4 design. This is a complex and expensive design, but itis more efficient than the previous designs.

Factorial Design

In the Latin square design, only one variable is tested,whereas in the Factorial design two or more variables canbe determined. For instance, a marketer wants to test theeffect of TV advertising and price reduction on the sales of aproduct. Suppose, he considers three price reduction andfour levels of TV advertising, then it would be 3 × 4 design.Hence, 12 markets have to be chosen to test the combinationskeeping the time period of the test constant. Factorialdesigns can be constructed for more than two variables also.

Selecting an Experimental Design

The researcher has to consider three important factors inthe selection of an experimental design. They are:

1. Time: The researcher may be required to provideresults at a speed, as marketing decisions are requiredto be fast due to competitive conditions. Hence, theresearchers have to plan for designs which take shortperiods to complete.

2. Cost: The cost of executing the research has tobe weighed against the possible outcome and itsvalue.

3. Secrecy: The major limitation of experimentation is thatit might reveal things to the competitors. Hence, ifsecrecy is needed, simulated laboratory experiments areadvisable.

Limitations of Experimentation

The manager should recognize the following limitations ofexperimentation:

1. It is not always possible to control the effectsof extraneous variables. Differential effectsamong treatment groups can easily occur in fieldexperiments.

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2. In field experiments, lack of cooperation from thewholesalers and retailers can limit the experimentalactivity.

3. Lack of knowledge about experimental procedures onthe part of marketing personnel may limit the usage ofexperimentation and in addition, it may lead toexperimental conclusions being discarded as notmeaningful.

4. Experiments can be costly and time consuming.

5. In using people as test units, care must be taken thatthe experimenter does not say and do things that biastest unit responses.

Difficulties in Experimental Designs

1. Problems in experimental setting: Generally it is noteasy to determine the conditions under whichexperiment should be setup. In case of scientificexperiments laboratory conditions may be establishedbut this may not be possible in case of sociological/psychological experiments. In case of conduct ofexperiment in a natural setting, problem arises invarying various treatments and other conditions.

2. Problems in getting cooperation: In case of businessand social research, to obtain cooperation from peoplewho form the subject of experimentation is not easy.Human subjects at times work according to their freewill.

3. Difficulties in establishing control: Control at timesin an experimental situation more so in case of complexbusiness and socio-economic research is lost since it isvery difficult to get complete knowledge of variousfactors influencing the experiments.

4. Problem of consciousness: In case of businessexperimental design, experimental subject is ratherfluid and possesses a consciousness which limits thedegree of experimentation.

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Designing Consumer Research

The purpose of the consumer study is determined by researchdesign. When descriptive information is required, aquantitative study is useful. If new ideas, e.g., positioning ofa new brand is needed, a qualitative study is likely to beconducted. The consumer research design can be classifiedinto two categories:

A–Qualitative research design

B–Quantitative research design

u Qualitative research design: The purpose of the studyand the type of data needed are considered whileselecting the appropriate research design for aqualitative study. The data collection techniquesinclude:

(i) Depth interviews: Lengthy non-structuredinterview between a respondent and a highlyexperienced interviewer, who minimizes his or herown participation in the interview.

(ii) Focus groups: Which consist of six to eightrespondents who meet with a moderator oranalyst for a group discussion focussed on aparticular product as product category.

(iii) Projective techniques: Consisting of a variety ofdisguised tests that contain ambiguous stimuli,such as incomplete sentences, untitled picturesor cartoons, word association tests, etc., which aredesigned to tap the underlying motivesof individuals despite their unconsciousrationalizations or efforts at a consciousconcealment.

u Quantitative research design: The design of aquantitative research study includes the method forcollecting the data, the sample design and constructionof the data collection instrument.

(i) Data collection methods: There are three basicways to collect primary data in quantitativeresearch.

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(a) Observational research–by observingconsumer behaviour.

(b) Experimentation–by designing experimentsto identify cause and effect of the relativesales appeal of many types of variables.

(c) Surveys–by questioning people in person, bymail or by telephone about their purchasepreferences and likings.

(ii) Data collection instruments: The primaryinstrument is the questionnaire. Other types ofinstruments are inventories and attitude scaleswhich include Likert scales, semantic differentialscales and rank order scales.

(iii) Sampling–it involves:

(a) The sampling unit–whom to survey:

(b) Sample size–how many to survey; and

(c) Sampling procedure–how to select them.

u Data collection: Highly trained social scientists arerequired to collect data in qualitative studies. But, inquantitative studies a field staff is generally used.

u Analysis: In qualitative researches, the moderator ortest administrator usually analyses the responsesreceived. In quantitative research, the analysis issupervised by the researcher.

u Report preparation: It includes a brief executivesummary of the findings. Depending on the assignment,it may or may not include recommendation for actions.The report will contain a full description of themethodology used.

Error Reduction Through Design

The basic purpose of research design is to guide theresearcher in answering the research problem. It isaccomplished through the careful construction of theresearch design so that the results obtained are as error free

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as possible. These errors and the researcher strategies fordealing with them are discussed in the following section:

1. Planning errors: Planning errors are those which dealwith the setup of the design to collect information.Researcher can think of planning errors as being allthose sources of misinformation because of which thestudy is inappropriately structured when the researchis undertaken.

2. Collection errors: They are associated with thecollection of information to answer the research problem.These errors are sources of misinformation due to theactual collection of data, given the study is actually wellstructured.

3. Analytical errors: They are those which are due to theinappropriate analysis of the data collected. Researchercan think of them as the actual manipulation of the data.To reduce analytical errors, it requires a justification ofthe analytical procedures used in manipulating andsummarising the data.

4. Reporting errors: They are those due to the incorrectinterpretation of the results of the study. They puterroneous meaning into the relationship and numbersidentified from data analyses.

Summary

A research design serves as a bridge between what hasbeen established (the research objective) and what is tobe done, in the conduct of the study, to realize thoseobjectives. It anticipates what the client will need interms of results and the analytical work on the gathereddata that will convert it to useful findings.

A formal design’s benefits are particularly appreciatedwhen the researcher is deciding specifically what dataare needed. If data are gathered that prove to beirrelevant, it is both inefficient and confusing. It is evenmore serious to have overlooked some data that arevitally needed, which may be discovered until too late,

Contd...

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at the analytical stage. A design also is appreciated whenanalyzing the data and interpreting and thinking on thepath to solutions and recommendations.

Although, research designs may be classified by manycriteria, the most useful one concerns the major purposeof the investigation. On this basis, we may identify thebroad classes of designs as exploratory, descriptive andcausal.

Review Questions

1. Discuss the application of exploratory research designin marketing.

2. Discuss the various types of experimental researchdesigns.

3. What do you understand by the term research design?What is its importance? What are the different types ofresearch design? What relationship exists betweenthem?

4. What is (A) Exploratory (B) Descriptive (C) Causalresearch? Using examples show how they differ fromeach other.

5. “The problem definition phase may never come to anend with one exploratory research leading to another.”Comment.

6. “In-depth interviews are similar to individual casestudies.” Comment.

7. A coffee marketer uses observational research to studyconsumer buying habits. The research design consistsof observing shoppers in supermarkets and recordingthe sex and approximate age of consumers who buycoffee.

(a) Is observation the best research technique tostudy this type of consumer behaviour? If notwhich method(s) is more appropriate and why?

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(b) In your view is the researcher using a samplingmethod? Is this technique appropriate in thissituation? Given the choice, what method wouldyou use and why?

8. You are the product manager for brand ‘Youth’ shavingcream, a nationally distributed brand. Brand ‘Youth’ hasbeen declining in absolute level of sales for the last fourconsecutive months. You ask the marketing researchdepartment to do a study to determine why sales havedeclined.

(a) Indicate whether this is an exploratory,descriptive or causal study.

(b) What data would be useful for determining thereasons for decline in sales?

(c) How would you design the study to obtain thesedata?

(d) What external secondary data are, in fact, availablethat would be useful for this purpose? From whatsources can they be obtained?

9. Describe the various methods for controlling sources ofextraneous variation in experimental designs.

10. Briefly explain the nature and scope of exploratoryresearch.

11. Describe the sampling design process.

12. A pro-life group wanted to test the effectiveness of ananti-abortion commercial. Two random samples, eachof 250 respondents, were taken from the city ofChandigarh. One group was shown the anti-abortioncommercial. Then, attitudes toward abortion weremeasured for respondents in both the groups.

(i) Identify the independent and dependent variablesin this experiment.

(ii) What type of design was used?

(iii) What are the potential threats to internal andexternal validity in this experiment?

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13. What is the relationship between exploratory,descriptive and causal research?

14. What are the requirements for inferring a causalrelationship between two variables?

15. Differentiate between internal and external validity.

16. List any five extraneous variables and give an exampleto show how each can reduce internal validity.

17. State the type of experiment being conducted in thefollowing situations. In each case, identify the potentialthreat to internal and external validity.

(a) A major distributor of office equipment isconsidering a new sales presentation programmefor its salespersons. The largest sales territory isselected, the new programme is implemented andthe effect on sales is measured.

(b) Procter & Gamble wants to determine if the newpackage design for “Aerial” is more effective thanthe current design. Twelve departmental storesare randomly selected in Delhi. Further, sixoutlets are randomly selected to sell Aerial in anew packaging. In the other six, the detergent issold in the old package. Sales for both groups ofdepartmental stores are monitored for threemonths.

18. You are the product manager for brand S margarine, anationally distributed brand. Brand S has beendeclining in absolute level of sales for the past fourconsecutive months. You ask the marketing researchdepartment to do a study to determine why sales havedeclined.

(a) Is this an exploratory, descriptive or causal study?

(b) What data would be useful for determining whysales have declined?

(c) How would you design the study to obtain thesedata?

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19. Explain what research design would you use if you wantto conduct a study regarding the demographic profileof the users of a particular brand of a product.

20. List out the uses of consumer research in the field of:

(a) F.M.C.G.

(b) Durable goods

(c) Consumer services

(d) Lubricants.

21. Every consumer is unique and the study thatconcentrates on the ‘average’ consumer is meaningless.Comment.

22. Compare qualitative and quantitative research.

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APPENDIX-1

STRATEGY FOR DESIGNING MARKETING RESEARCHPROGRAMME

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APPENDIX-2

A method of education should rest on some satisfactory theoretical basis.It should also provide the learner with the knowledge and backgroundhe needs in order to make positive contributions to thought and to society.

In this context there are three major levels of knowledge concerningmarketing that a student must attain. The first is the acquisition of certaininformation, that, in the aggregate, constitutes a description of marketinginstitutions and an explanation of marketing processes. This knowledgemay be interesting, but it is arid and purposeless.

The second level is the development of the principles and theoreticalconcepts that are key to understanding the dynamics of the marketingsystem.

The third level is the use of the information, principles and theories in theanalysis of marketing problems.

The young person beginning a business career is not expected toestablish the marketing policy for the company. He starts out by performingmore or less routine assignments under the direction of a supervisor. Butas he rises in rank and responsibility, he will have the opportunity tocope more and more with handling problems–with recommending anddetermining what should be changed and with communicating thesejudgements to others. If he has the educational experience that accustomcan his mind to problem solution, he will probably be ready foradvancement earlier and will show greater competence in handling theproblems assigned to him.

Although the case method is not a substitute for business experience it iscertainly one of the better types of preparation for making that experiencefruitful. It also provides the participant with the learning method by whichhe can enhance not only his knowledge but also develop a sounddiagnostic approach. In the final analysis, it is through the effective use ofone’s own knowledge and insight that he is able to exercise soundjudgement in making decisions.

Importance of Data

The student should attempt to secure general marketing information foreach case. As an example, if there is a question whether or not a companyshould use “primary” or “selective” appeals, the student should use somebasic marketing texts as a reference to determine under what conditionssuch strategies should be used.

A person having numerous years of marketing experience will certainlyhave a great quantity of information. He will know the types of merchandisethat are given counter display space in drug stores. He will know whatitems other than food are increasingly being offered in supermarkets. Hewill know something of the relative importance of direct selling and sellingthrough middlemen in department store merchandising. These and manyadditional facts will be familiar to him because he has learned them inthe course of his work. As a result, when a marketing problem is presentedto him, he may have many of the facts he needs and can proceedimmediately to analyzing the problem. Often, he may remember similarproblems, and know what solutions have been tried and which oneshave been successful in the past. The student, on the other hand, must

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generally search out the information from secondary sources, e.g. tradeassociation publications, trade publications, texts, industry studies,published corporation reports, government data, and primary efforts suchas interviews with business people and “spot surveys”.

The marketing student can also rapidly build up a large fund of technicaland trade information by observation and by asking questions in hisnormal contracts with merchants. For instance, many supermarkets andmany larger drug stores carry hardware store items. In what way doeshardware merchandise in food and drug stores differ from the samegeneral type of merchandise carried in hardware stores? This kind ofknowledge is important in some marketing problems and may be learnedbetter by observation than any other method.

Source: Management Accountant, April, 1998.

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CASE STUDY 4.1

Shri Ram Consultants

Shri Ram consultants have been appointed by a leading to prepare afeasibility report for opening a five-star hotel in Pune. The group hadbeen the most successful one in the hotel industry and had always keptits eyes open for new opportunities.

In view of the very fast industrial growth in the city of Pune, the city hadattracted the attention of the group. Pune, apart from being a modern city,has the added advantage of pleasant weather and several places oftourist attraction in the neighbourhood. Moreover, the closeness toMumbai, a city of international stature, made it very easily accessible tointernational tourists.

For Shri Ram consultants this was the first time that an assignmentconcerning the hotel industry had been received. They, however, soonrealized that the assignment was not as simple as it appeared to be inthe first place. The feasibility of such a hotel would depend essentially ontwo factors. Businessmen visiting the city for work would constitute onesegment of the market, while tourists would constitute the other. Further,the tourists could be Indians or foreigners. The success of such a hotelwould also depend upon the relative attraction of other tourist centres inthe vicinity.

Further, it was necessary to estimate fluctuations in demand for hotelaccommodation so that attractive discounts could be offered during theoff-season for business conferences, executive developmentprogrammes, etc.

The consultants realized that they would have to undertake a marketresearch on a national scale to assess the tourist potential of the city.They would also have to survey the foreign tourists to estimate one of themost important segments of the market.

The consultants wondered whether such a survey will have to extendover a period of one full year to completely take into account the seasonalvariations in tourists traffic. They were also undecided about the mannerin which the survey should be conducted. The company also feared thatin the absence of an accurate definition of the problem, they may land upsurveying the compete tourist market in India rather than studying thefeasibility of a hotel in Pune. They had heard that ITBC had appointedlady interviewers at several major airports for conducting such surveysand wondered if such a methodology could be of use to them.

The problem appeared well defined and they were concerned as thepreliminary report explaining methodology of the research and thequestionnaires to be used had to be submitted to the client along withthe estimate of expenses within one month.

Questions

(a) How would you define the problem of assessing the feasibility ofthe hotel so as to help design the survey?

(b) How would you plan a survey for actually collecting information onexpected demand for hotel space? How would you estimate thecost of such a survey?

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CASE STUDY 4.2

Excel Publishing House

Excel publishing house has been in existence for the past 15 years or so.The company was set up by an entrepreneur Shri Anurag Jain, whosemain emphasis is to publish management books and sell them atmoderate prices so that they may be within the reach of managementstudents.

After a few years of experience in the publishing house, Shri Jain felt thatthe company should concentrate on selected management books,according to prescribed course contents of the institutes. But he feelsthat the problem of selecting a particular textbook for publication is verycrucial in view of increasing competition in the textbook market. Mr Jainwants to develop a proforma to elicit relevant information from institutes/authors interested in having their works published.

Questions

1. What sample design is being used by Mr Jain?

2. What type of study is this?

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Marketing researchers can use secondary or primary data,or both, to satisfy their information-gathering needs.Marketing managers always use secondary data, becausepreviously collected information can benefit marketingmanagers and researchers in a number of ways: (1) Timesaving, (2) Relevance, (3) Availability, (4) Low cost, (5)Accessibility.

Definition

The distribution of all possible values which can be assumedby same statistics computed from samples of the same sizerandomly drawn from the same population is called thesampling distribution of the statistic.

Example 5.1

Let the population size = NLet the sample size = n

109

Objectives

After reading this unit you will be able to understand:

y Various steps involved while testing the hypothesis.

y The difference between the terms, "standard deviation" and"standard error".

y The applicability of standard error in testing the hypothesis.

y Conditions required while using the test of significance.

y The concept of X2 test and its features.

y Apply and interpret the results of the ANOVA and n-way ANOVAstatistical methods.

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Unit 5

Hypothesis Design



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Then we can draw a total number of NCn samples. Now wecan calculate any statistic (say mean) of these NCn samples.The distribution then obtained is called the samplingdistribution of the statistics (mean).

Figure 5.1

These NCn samples gives value of mean as m1, m2…m12. Thevalues form a distribution which is known as samplingdistribution. The sampling distribution has the followingimportant properties:

1. The arithmetic mean of the sampling distribution is thesame as the mean of the universe from which sampleswere taken.

2. The sampling distribution of mean has a standarddeviation (S.E.) equal to the population standarddeviation divided by the square root of the samples size.i.e.

S.E = n

6

3. The sampling distribution of the means is normallydistributed.

Steps in Testing the Hypothesis

Steps involved in the process of hypothesis testing are givenby the Figure 5.2.

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S1 Size n

Sn Size n

Population Size N

Mean m1

Mean m2

Mean mn

S2 Size n

111UNIT 5 Hypothesis Designu


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Figure 5.2

Hypothesis Testing and Associated Statistical Tests

Table 5.1

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__________________Determine thesignificance level

Determine the degreeof freedom

Problem definition

Clearly state thenull and alternate

hypothesis

Choose the relevanttest and the

appropriate probabilitydistribution

Select the criticalvalue

Decide if one or twotailed test

Compare test statisticand critical value

Compute relevant teststatistic

Does the test statisticfall in the critical region

Do not reject the nullhypothesis

Reject the nullhypothesis

No

Yes

Hypothesis

Testing

No. of Groups/

Samples

Purpose Statistical Test Assumptions/

Comments

Frequency One Goodness of Fit x2

Distributions Two Test of

Independence

x2

Proportions One Comparing sample

and populations

proportions

Z If r is known, and for

large samples

Two do t If r is unknown and for

small samples

Two Comparing two

samples proportions

Z If r is known

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Two conditions are required to use the test of significance:

Ist Condition: Researcher will have observed somedifference between two or more groups, i.e. town x versustown y, educated versus uneducated.

IInd Condition: Researcher will have asked same questionof each group and/or measured the same thing within eachgroup (e.g., usage of a certain product or brand.)

Standard Error

The standard deviation of a sampling distribution is calledstandard error of that statistic. For example,

1. The standard deviation of the means of all possiblesamples of the same size drawn from a population isknown as the standard error of the mean.

2. The standard deviation of the proportions of all possiblesamples of the same size drawn from a population isknown as standard error of proportion.

Note: The difference between the terms "standarddeviation" and "standard error" lies in the fact the S.D.

Notes

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do t If r is unknown

Means One Comparing sample

and population

mean

Z If r is known


Two Comparing two

samples mean

Z If r is known


From independent

samples

t If r is unknown

Two or more Comparing multiple

sample means

F Using analysis of

variance

Variance One Comparing sample

and population

variance

X2

Two Comparing sample

variance

F



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deals with original values and S.E. deals with statisticscomputed from the samples of original values.

Importance of the Concept of Standard Error

1. It can be used in testing hypothesis. For example, letthe level of significance for testing a particularhypothesis be 5%. We know that corresponding to thislevel the value of standard error is 1.96 S.E. Now if thedifference between the observed and expected meanscomes out to be more than 1.96 S.E. then the result ofthe experiment does not support the hypothesis whichit supports otherwise.

2. Standard error can be used to determine the limits forparameter values.

3. Standard error provides an idea about the unreliabilityof the sample. Because if the standard error has a largevalue then there is great difference between the actualand expected frequency. Hence greater is theunreliability of the sample. In general, we have,

Reliability (R) a E.S

1

Difference between Large and Small Samples

It is very difficult to draw a clear cut line of demarcationbetween large and small samples, it is normally agreedamongst statisticians that a sample is to be recorded as largeonly if its size exceeds 30. The tests of significance used fordealing with problems relating to large samples are differentfrom the ones used for small samples for the reason that theassumptions that we make in case of large samples do nothold good for small samples The assumptions made whiledealing with problems relating to large samples are:

1. The random sampling distribution of statistic isapproximately normal, and

2. Values given by the samples are sufficiently close to thepopulation value and can be used in its place forcalculating the standard error of the estimate.

Notes

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Example 5.2

Calculate standard error of mean from the following datashowing the amount paid by 100 firms in Delhi on theoccasion of Durga Pooja.

Mid Value (Rs.) 39 49 59 69 79 89 99

No. of firms 2 3 11 20 32 25 7

Solution

S.E. X = n

σ

Table

Notes

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m � 69/10 Mid-value

m f d fd fd

2

39 2 -3 -6 18

49 3 -2 -6 12

59 11 -1 -11 11

69 20 0 0 0

79 32 + 1 + 32 32

89 25 + 2 + 50 100

99 7 + 3 + 21 63

N = 100 ∑ fd = 80 ∑ fd 2= 236

s = iN

fd

N

fd22

×

∑−∑

= 10100

80

100

2362

×

−

= 13.11

S.E. = X =100

11.13= 1.311

Case I: Standard Deviation s Unknown and n ³ 30

In this case, the sample standard deviation is calculatedas:

( )n

xx2

1 −Σ=δ



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Notes

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This value of d is used as an estimate of s (provided that n ³30). In this case, the values are given by:

ns

x οµ−=

Here,

Critical values:

X oL −µ= n

δα when H1 : οµ<µ

+µ= υUX n

δα when H1: οµ>µ

Example 5.3

A sample of 64 farm labourers engaged in paddy harvestingoperations shows an average monthly wage rate of Rs 200with a standard deviation of Rs 9. Using 0.05 levelof significance, verify if the sample result indicates thattheir current average monthly wage rate is higher thanRs 198.

Solution

1. H0 : µ = Rs 198.

H1 : µ > Rs 198.

2. a = 0.05.

3. Critical region: αΖ≥Ζ , where αΖ = 1.645.

4. Computations:

For x = 200, σ = s = 9, and n = 64,

78.189

198200

ns

xz 0 =−=µ−=

5. Conclusion: since z = 1.78 is greater than za = 1.645, Ho

is rejected and we conclude that the current wage rateis higher than Rs 198.



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Case II: Population Standard Deviation Unknown

Many a times situations do arise when neither s is known,nor is it possible to draw a sample of size to allow the use ofS2 as an unbiased estimator of . That is, when n<30 and sunknown, testing H0 concerning the population mean m isbased on the sample statistic:

nS

XT 0

∧µ−=

Which is a random variable having t distribution withv = n – 1 df.

As usual, we draw a sample of size n<30 and compute thesample mean and the sample standard deviation

( )

1

2

−−Σ=

∧

n

xxS i

For a sample of size n<30,

( )

n

xxS

2i −Σ=

Example 5.4

15 workers are selected at random from a large no. of workersin a factory. The number of items produced by them on acertain day are found to be:

53 52 54 53 51 53 59 58 56 56 57 54 50 59 60

Would it be appropriate to suggest that the mean of thenumber of items produced in the population is 59.

Solution

Let us first calculate sample mean and standard deviation

X X-55 (X-55)2

53 -2 4

52 -3 9

54 -1 1

53 -2 4

Notes

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Contd...



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51 -4 16

53 -2 4

59 4 16

58 3 9

56 1 1

56 1 1

57 2 4

54 -1 1

50 -5 25

59 24 16

60 5 25

------ ------- -------

825 136

5515

825

n

xX ==Σ=

( )71.9

14

136

1n

xx ==−−Σ=δ

Test Involving Two Different Populations

There may be cases when we have to deal with populationsinstead of population and sample.

Example 5.5

1. A doctor may be interested in knowing whether a newmedicine A is better than new medicine B in curing aparticular disease.

2. A farmer may be interested in knowing whether a newvariety of wheat seed will result in more yield perhectare than that of some other variety.

Let the mean of first population = m1

Let the mean of second population= m2

In their case, we have,

Null hypothesis Ho = m1- m2 = do = (say)

Alternative hypothesis H = m1- m2 ¹ do (two in tail test)

Notes

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Notes

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= m1- m2 > do (in one tail test)

= m1- m2 < do (in one tail test)

Note: If mean of two populations are equal

i.e. 0do 2121 =µ−µ=⇒µ=µ

Then

210 :H µ=µ

212121 ,,H µ<µµ>µµ≠µ=α

Case

1. Population variances 2

1σ and 2

2σ are not known

2. 2

1σ = 2

2σ

3. 30n,n 21 <

This test is based on t-distribution null hypothesis andalternative hypothesis have already stated. In this case,t-test becomes

( )

+

−−=

21p

21

n

1

n

1S

doxxt

Here,

21 x,x are sample means.

do = ,21 µ−µ where 21, µµ are population means

21 nn + are size of the two random samples

Sp2 Common variance

221

222

211

−++=nn

snsnSP

Here degree of freedom,

2nnd 21f −+=



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Example 5.6

Consider two groups A and B of 10 and 15 students eachrespectively, Group A is being taught with traditionalmethod and group B with some new method. After thecompletion of the course a test was conducted with the samequestion paper for the two groups. It was found that on anaverage group A obtained 65 marks with a standard deviationof 7 marks and group B obtained 68 marks with a standarddeviation of 4 marks. Assuming the populations to be normaland having the same variance, test the hypothesis at 0.01level of significance that the two methods are equallyeffective.

Solution

Here we have to examine for the two methods to be equallyeffective. Let m1 and m2 be the average marks obtained bythe two groups respectively, then

1. Null hypothesis H0= 021 =µ−µ

= 21 µ=µ

2. Alternative hypothesis H1 = 21 µ≠µ

3. 01.0=α

4. d.f = 23215102nn 21 =−+=−+

Now,

t ( ) 807.223f.d −==

01.0=α

Apply t-test

( )

21P

2

n

1

n

1S

xxt 1

+

−=

Here, 65x1

= , 68x2

=

10n1 = , 15n 2 =

Notes

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2nn

snsnS

21

222

211

P −++=

21510

415710 22

−+×+×=

7.31=

So,

1511017.31

681165t

+−=

( )06.01.063.5

516

+×−=

16.063.5

516

×−=

4.063.5

516

×−=

252.2

516−=

129.229−=

Since calculated value is more. So,

Ho is accepted.

Case III: Population Variances 21σ and 2

2σ Unknown,

22

21 σ≠σ , and 30nn 21 <≠

Some decision problems involving tests concerning thedifference of means may be characterized by the following:

1. The two populations are approximately normal with22

21 σ≠σ , and

2. The sample sizes n1 and n2 are less than 30 21 nn ≠ .

In such problem situations, testing the null hypothesis

o210 d:H =µ−µ against the alternative hypothesis.

Notes

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0210210211 dor,d,d:H <µ−µ>µ−µ≠µ−µ

is based on the test statistic T whose distribution isapproximately like a t distribution with degrees of freedom

( ) ( )

−

+

−

+

=∧∧

∧∧

1nns1nns

n

s

n

s

v

2

2

2

2

21

2

1

2

1

2

2

2

2

1

2

1

where a particular t value is defined as:

( )

+

−−=∧∧

2

2

2

1

2

1

021

n

s

n

s

dxxt

Example 5.7

A random sample of 10 acres wheat crop selected fromRegion I showed an average yield of 20 qtls per acre with astandard deviation 5S1 =

∧ qtls. Another random sample of 15

acres of wheat crop selected from Region II offered an averageyield of 18 qtls per acre with a standard deviations 3S2 =

∧

qtls. Assuming that the per acre wheat yield in the two statesis normally distributed with different variances, test thehypothesis at 0.05 level of significance that the average peracre wheat yield is the same in the two regions against thealternative that it is higher in Region I than II.

Solution

Let m1 be the average per acre wheat yield in Region I andm2 in Region II.

1. H0 : m1 = m2

H1: m1 > m2

2. a = 0.05.

Notes

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3. Critical region:

For v =

( ) ( )

−

+

−

+

∧∧

∧∧

1nns1nns

n

s

n

s

2

2

2

2

21

2

1

2

1

2

2

2

1

2

1

= ( ) ( )

+

+

14

159

9

1025

15

9

10

25

22

2

= 13,

the tabulated T value for a = 0.05 with v = 13df is ta =

1.771, and the critical region is t ³ ta.

4. Computations: For 20x1 = , 5S1 =∧

, n1= 10,

18x2 = , 3S2 =∧ , n1= 15,

( )136.1

15

9

10

25

1820

n

S

n

S

xxt

2

2

2

1

2

1

21 =

+

−=

+

−=∧∧

5. Conclusion: Since t = 1.136 is less than ta = 1.771, Ho isaccepted. It means that there is no difference betweenthe average per acre wheat yield in the two regions.

X2 Test (Chi Square Test)

The X2 test is one of the simplest and most widely used non-parametric tests in statistical work. The symbol X2 is theGreek letter Chi. This test gives the magnitude ofdiscrepancy between theory and observation. It is definedas:

X2 = ( )

E

EO2−Σ

Notes

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Where O is observed frequency, E is expected frequency.

In general expected frequency is given by:

N

CTRTE

×=

Here, RT= Row Total containing the cell.

CT= Column Total containing the cell.

N = Total No. of observations.

Degree of Freedom (V)

The Chi square test is based on degrees of freedom. This isobtained as:

(i) In case of one dimension (row or column) there are K-1degrees of freedom, where K is number of categories ofobserved frequencies.

(ii) In case of contingency table

v = (r-1) (c -1)

Here, r = is total no. of rows

c = is total no. of columns

Characteristics of Chi Square Test

1. This test is based on frequencies or events as againstthe and the t tests based on parameters like the meanand standard deviation.

2. This is applied for drawing inference only.

3. This possesses additive properties so that when 21X and

22X are independent and have a Chi square distribution

with n1 and n2 degrees of freedom, will also bedistributed as a Chi square distribution with n1+ n2

degree of freedom.

4. It is a general purpose test and is very useful in researchwork.

Notes

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Chi square analysis can be used when the data satisfy fourconditions:

1. There must be two observed sets of data or one observedset of data and one expected set of data.

2. The two sets of data must be based on the same samplesize.

3. Each cell in the data contains an observed or expectedcount of five or larger.

4. The different cells in a row or column must representcategorical variables.

There are three main encountered applications of Chi squareanalysis. Perhaps the most common occurs when researchersobserve that, for a certain product, men show a differentdistribution of consumption rates than women. Researchersoften must test whether the difference in such distributionsare statistically significant.

Example 5.8

On the basis of the information given below about thetreatment of 200 patients suffering from a disease, statewhether the new treatment is better or not? (Check at 5%level of significance).

No. of Patients

Favourable Not Favourable Total

New 60 30 90

Conventional 40 70 110

100 100 200

Solution

1. Null hypothesis (Ho): There is no difference betweennew and conventional method.

2. Degrees of freedom V = (r–1) (c–1)

= (2–1) (2–1)

= 1

Notes

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3. Expected frequency for each cell = N

CTRT× i.e.,

expected frequencies are:

200

90100 ×200

90100 ×

200

110100×200

110100×

i.e.

We calculate value of X2 as following:

18.1820018.218NE

OX

22 =−=−

Σ=

or we can calculate( )

E

EO2−Σ

Here, table value of X2 for V= 1 and p = 0.5 is 3.84

Calculated value is 18.18 So,

2table

2col XX >

So, null hypothesis is rejected and so the new method isbetter.

Example 5.9

Following is the information about the number of clerkcommitting errors and not committing errors among trainedand untrained clerks.

Notes

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__________________45 45 90

55 55 110

100 100 200

O E O2

O2/E

60

40

30

70

45

55

45

55

3600

1600

900

4900

80.09

29.00

20.00

89.09

218.18



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No. of Clerks No. of Clerks notCommitting Errors Committing Errors

Trained 70 530

Untrained 155 745

Test the effectiveness of training in preventing the errors.

Solution

Ho: Training is not effective in preventing errors. Wecompute expected frequencies as:

Expected Frequencies

No. of Clerks No. of Clerks notCommitting Errors Committing Errors

Trained 901500

225600=

×510

1500

1275600=

×

Untrained 1351500

225900=

×765

1500

1275900=

×

We calculate the value of X2 as:

∴ 7147.8X2col =

Here V = (2–1) (2–l) = 1

205.0X (for v=1) = 3.84

2ColX > 2

05.0X

So, null hypothesis is rejected and training is effective inpreventing the errors.

Example 5.10

200 digits were selected at random from a set of tables. The frequenciesof the digits were:

Digit 0 1 2 3 4 5 6 7 8 9 Freq. 18 19 23 21 16 25 22 20 21 15

Notes

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Observed frequency

ο

Expected frequency

∈ ο � ∈

( ) ∈∈−ο 2

4.444

0.7843

0.29630

0.5230

70

530

155

745

90

510

135

765

-20

20

20

-20

X2

= 8.7147



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Use X2 test to test if the digits were distributed in equal nos.

Solution

Ho: The digits are distributed in equal nos.

Here expected frequency of each digit

= 2010

200

10

15........1918 ==++

X2 = 4.30

Analysis of Variance

It is an useful technique concerning researches in the fieldsof economics, education, business and in other disciplines.This technique is used when multiple samples cases areinvolved. The significance of the difference between themeans of two samples can be found out through Z test or ttest, but the problem arises when we happen to examine thesignificance of difference amongst more than two samplemeans at the same time.

Basic Principle of Analysis of Variance (ANOVA)

The basic principle is to test for difference among the meansof the populations by examining the amount of variationwithin each of these samples, relative to the amount ofvariation between the samples. In terms of variation withinthe given population, it is assumed that the value of (Xij)differs from the mean of this population only because of

Notes

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Digit Frequency o - ∈ ( )∈∈− 2o

o ∈

0 18 20 - 2 0.2

1 19 20 - 1 0.05

2 23 20 3 0.45

3 21 20 1 0.05

4 16 20 - 4 0.8

5 25 20 5 1.25

6 22 20 2 0.2

7 20 20 0 0

8 21 20 1 0.05

9 15 20 - 5 1.25



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random effects, i.e., there are influences (Xij) which areunexplainable, whereas in examining differences betweenpopulations we assume that the difference between the meanof the jth population and the grand mean is attributable towhat is called a ‘specific factor’ or what is technicallydescribed as treatment effect. Thus, while using ANOVA weassume that each of the samples is drawn from a normalpopulation and that each of these populations has the samevariance. We also assume that all factors other than the oneor more being tested are effectively controlled.

The F Test (Variance Ratio Test)

The F-test is named in honour of the great statistician R AFisher. It is used to find out whether the two independentestimates of population variance differ significantly. Forcarrying out the test of significance, we calculate the ratioF. F is defined as:

22

21

S

SF =

Where, 21S =

( )1n

XX

2

2

11

−−

and 22S =

( )1n

XX

2

2

22

−− Σ

Note that 21S is always greater than 2

2S

i.e. 21S > 2

2S

Therefore,

varianceofestimateSmaller

varianceofestimateerargLF =

V1 = n

1 � 1

V2 = n � 2

V1 = degrees of freedom for sample having larger variance.

V2 = degrees of freedom for sample having smaller variance.

Notes

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The calculated value of F is compared with the table value(given at 5% or 1% level of significance). If the calculatedvalue of F is larger than the table value of F, the nullhypothesis is rejected otherwise it is accepted.

Example 5.11

Two samples are drawn from two normal populations. Fromthe following data test whether the two samples have thesame variance at 5% level.

Sample 1: 60 65 71 74 76 82 85 87

Sample 2: 61 66 67 85 78 63 85 86 88 91

Solution

Null hypothesis Ho : 22

21 σ=σ , i.e., samples have been drawn

from two normal populations with the same variance.

Computation of Sample Variances

636 1200

758

600X == 77

10

770Y ==

( ) 90.87

636XXÓ

1n

1S

2

1

21 ==−

−=

( ) 33.1339

1200YY

1n

1S

2

2

22 ==−Σ

−=

Clearly, 22S > 2

1S

Þ 467.18.90

33.133

S

SF

21

22 ===

Notes

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Sample 1 Samples 2

X X-X (X-X)2 Y Y-Y (Y-Y)

2

60

65

71

74

76

82

85

87

-15

-10

- 4

- 1

1

7

10

12

225

100

16

1

1

49

100

144

61

66

67

85

78

63

85

86

88

91

-16

-11

-10

8

1

-14

8

9

11

14

256

121

100

64

1

196

64

81

121

196



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Degrees of freedom F (n2 – 1, n1 – 1) = F (9, 7)

Now, tabulated value for F at d.f 9 and 7 and 5% level = 3.68since

Fcal < Ftable

Þ Null hypothesis is accepted.

Example 5.12

The time taken by workers while performing a job by twomethods m1 and m2 are given as:

m1 : 30 15 29 26 21 25

m2 : 26 30 40 31 34 19 27

Check if the data show that the variances of time distributionin a population from which these samples are drawn do notdiffer significantly.

Solution

Null hypothesis Ho : 22

21 σ=σ ,

There is no significant difference between the variance ofthe time distribution by the workers in performing a job bym1 and m2.

Notes

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M1 M2

X X-X (X-X)2 Y Y-Y (Y-Y)

2

30

15

29

26

31

25

4

-11

3

0

5

-1

16

121

9

0

25

1

26

30

40

31

34

29

27

-5

-1

9

0

3

-2

-4

25

1

81

0

9

4

16

156 172 217 136

266

156X == 31

7

217Y ==

( ) 4.345

172XX

1n

1S

2

1

21 ==−Σ

−=



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( ) 66.226

136YY

1n

1S

2

2

22 ==−Σ

−=

Since, 21S > 2

2S

Þ ===66.22

4.34

S

SF

22

21

Degrees of freedom F (n2 - 1, n1 - 1) = F (6, 5)

Þ Ftable = 4.95

Since Fcal < Ftable

Þ Null hypothesis is accepted.

Example 5.13

Perform a two way ANOVA on the following data:

Use 30 as the code value.

Solution

Since 30 is the code value. So, subtracting 30 from all cellswe have,

Correction Factor (C.F) = 40.515

9

N

T 22

==

Total sum of squares (SST) = O2 + (–6)2 + 32 + 62 + (–3)2 + (–4)2

+……..(0)2 + 32 – C.F.= 271 - 5.4= 265.63

Notes

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T1

I II III

T2

i

ii

iii

iv

v

30

24

33

26

27

26

29

24

31

35

38

28

35

30

33

T1

I II III Total

T2

i

ii

iii

iv

v

0

-6

3

6

-3

-4

-1

-6

1

5

8

2

5

0

3

4

-9

2

7

5

Total 0 -5 18 T = 9



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Sum of squares for variance between T1 (i.e. columns) sample

i.e. SSC = ( ) ( ) 4.55

145O

222 −

+−+

= 38.8

Sum of square of variance between T2 samples (i.e. row)

SSR = ( ) ( ) ( )[ ] 4.5357942222 −++−+

= 52.93

The error sum of squares (SSE)

SSE = SST - SSR - SSC = 265.6 - 52.93 - 38.8 = 173.87

ANOVA Table 5.2

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Source ofVariance

B e t w e e nt r e a t m e n tare samples

B e t w e e ntreatment thesamples

Error

Total

Sum ofSquare

38.80(SSC)

52.93(SSR)

173.87SSE

265.60SST

D.f

2(n – 1)

9(k–1)

8(n–1)(k–1)

19(nk–1)

Mean Squares

19.40

1n

SSCMSC

=−

=

13.23

1K

SSRMSR

=−

=

( )( )21.73

dk1n

SSEMSE

=

−−=

VarianceRatio

1.12

19.40

21.73

MSC

MSCF

C

=

=

=

0.61

21.13

13.23

MSE

MSRF

R

=

=

=

Degree of freedom = (10 – 1) = 9

Now ( ) 919.16avX205.0 ==

Here 2Table

2Cal XX <

So, null hypothesis is accepted.



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Analysis of Co-variance (ANOCOVA)

The object of experimental design in general happens to beto ensure that the result observed may be attributed to thetreatment variable and to no other casual circumstances. Forinstance, the researcher studying one independent variableX, may wish to control the influence of some uncontrolledvariable Z, which is known to be correlated with thedependent variable, y, then he should use the technique ofanalysis of co-variance.

Assumptions in ANOCOVA

1. Various treatment groups are selected at random fromthe population.

2. The groups are homogenous in variability.

3. The regression is linear and is same from group to group.

ANOCOVA Technique

While using ANOCOVA technique, the influence ofuncontrolled variable is usually removed by simple linearregression method and the residual sums of square are usedto provide variance estimate which in turn are used to maketest of significance. In other words, covariance analysisconsists in subtracting from each individual score (Yi) thatportion of it Y: that is predictable from uncontrolled variable(Zi) and then computing the usual analysis of variance onthe resulting (Y-Y)s, of course making the due adjustmentto the degree of freedom because of the fact that estimationusing regression method requires loss of degree of freedom.

Example 5.14

The following are paired observations for three experimentalgroups.

Group I Group II Group III

x y x y x y7 2 15 8 30 156 5 24 12 35 169 7 25 15 32 2015 9 19 18 38 2412 10 31 19 40 30

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Degree of freedom associated with adjusted sums of squarewill be as under:

Between K-1Within N-K-1

Total N-2

Y is the co-variate variable, calculate the adjusted total,within groups and between groups, sums of squares on Xand test the significance of difference between adjustedmeans on X by using the appropriate F-ratio, also calculatethe adjusted means on X.

Solution

We apply the technique of analysis of covariance and workout the related measures as under.

SX = 49+114+175 = 338

Correction factor for X = ( ) ( )

27.76165

338

N

X22

==Σ

SY = 33+72+105=210

Correction factor for Y ( ) ( )

29405

210

N

Y22

==Σ

SX2=9476 SY2=3734 SXY=5838

Correction factor for XY = 4732N

Y.X =ΣΣ

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Group I Group II Group III

x y x y x y

7 2 15 8 30 15

6 5 24 12 35 16

9 7 25 15 32 20

15 9 19 18 38 24

12 10 31 19 40 30

Total 49 33 114 72 175 105

Mean 9.8 6.6 22.8 14.4 35.0 21.0



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Hence total SS for X= SX2-correction factor for X

= 9476-7616.27=18 59.73

SS between for X = ( ) ( ) ( )

++

5

175

5

114

5

49222

– (Correction

factor for X)

= (480.2+2599.2+6125) – (7616.27) = 1588.13

SS within for X = (total SS for X) – (SS between for X) (1859.73)–(1588.13) = 271.6

Similarly we work out the following values in respectof Y:

Total SS for Y = SY2 – correction factor for Y

= 3734-2940 = 794

SS between for Y = ( ) ( ) ( ) −

++

5

105

5

72

5

33222

(Correction factor

for Y)

(217.8+1036.8+2205)-(2940)= 519.6

SS within for Y = (total SS for Y)-(SS between for Y)

794-519.6 = 274.4

We work out the following values in respect of both X and Y.

Total sum of product for XY = SXY - correction factor for XY

5838 – 4732 = 1106

SS between for XY = ( ) ( ) ( ) ( ) ( ) ( )

++

5

105175

5

72114

5

3349 –

correction factor for XY

= (323.4+1641.6+3675)–(4732) = 908

SS within for XY = (total sum of product) – (SS between forXY)

1106 - 908 = 198

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ANOVA Table for X, Y and XY can now be set up as shownbelow.

Source d.f. SS for X SS for Y Sum of product XY

Between group 2 1588.13 519.60 908

Within group 12 Exx 271.6 Err 274.4 Exy 198

Total 14 Txx 1859.73 Trr 794.00 Txy 1106

Adjusted total SS = Txx –( )

Tyy

Txy 2

or 1859.73–( )

794

11062

or

1859.73–1540.6 = 319.13

Adjusted SS within group = Exx– ( ) ( )4.274

19860.271

Eyy

Exy22

−=

= 271.6 - 142.87 = 128.73

Adjusted SS between groups = Adjusted total SS – AdjustedSS within group

(319.13 – 128.73) = 190.4

ANOVA Table for Adjusted X

Source d.f SS MS F-ratio

Between group 2 190.4 95.2 8.14

Within group 11 128.73 11.7

Total 13 319.13

At 5% level the table value of F for V1=2 and V2=11 is 3.98and at 1% level the table value of F is 7.21. Both these valuesare less than the calculated value and according we inferthat F-ratio is significant at both levels, which means thedifference in group means is significant.

Adjusted mean on X will be worked out as follow:

Regression coefficient for X on Y i.e., b =

YforgroupwithinsquareofSum

groupthiniwproductofSum

7216.40.274

198 =

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Deviation of initial group means from

general mean (=14) in case of Y

Final means of group in X (unadjusted)

Group I –7.40 9.8

Group II .40 22.8

Group III 7.00 35.00

\ Adjusted means of groups in X = (Final mean) -b (deviationof initial mean from general mean in case of Y)

Hence,

Adjusted mean for group I = 9.8 – .7216 (–7.4) = 15.14

Adjusted mean for group II = 22.80 – .7216 (.40) = 22.51

Adjusted mean for group III = 35.00 – .7216 (7.00) = 29.95

Summary

This chapter presents the fundamental underpinningsof hypothesis testing methodology. In this chapterparametric and non-parametric tests are available fortesting the hypothesis related to differences. In theparametric case T test is used to examine hypothesisrelated to the population mean. Different forms of T testare suitable for testing the hypothesis based on onesample, two independent samples, or paired samples,in the non-parametric case popular one-sample testinclude chi-square (X2) test. In ANOVA and ANOCOVA,the dependent variable is metric and independentvariables are all categorical 02 combinations ofcategorical and metric variables. One way ANOVAinvolves a single independent categorical variables.Interest lies in testing the null hypothesis that thecategory means are equal in the population. The totalvariation in the dependent variable is decomposed intotwo components – variation related to the independentvariable and variation related to error. The nullhypothesis of equal means is tested by an F statistic,

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which is the ratio of the mean square related to theindependent variables to the mean square related toerror. ANOCOVA includes at least one categoricalindependent variable and at least one interval or metricindependent variable. The metric independentvariables, or covariate, is commonly used to removeextraneous variation from the dependent variable.

Review Questions

1. Why do we use hypothesis testing?

2. Why and how would you use t and z test in hypothesistesting?

3. Why and when would you want to use ANOVA inmarketing research?

4. What will ANOVA test not tell you, and how can youovercome this problem?

5. Which test is used to check for statistical significancein an ANOVA?

6. What are the commonly occurring dependent variablesin marketing applications of ANOVA?

7. Discuss the similarities and differences betweenanalysis of variance and analysis of covariance.

8. What is the relationship between analysis of varianceand the t test?

9. What is the null hypothesis in one way ANOVA? Whatbasic statistic is used to test the null hypothesis in oneway ANOVA? How is this statistic computed?

10. What is the most common use of the covariate inANCOVA?

11. What are the major assumptions of ANOVA?

12. Under what conditions should the t test for the meandifference in two related populations be selected.

13. What is the difference between two independent and

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two related populations?

14. Under what conditions should the F test be selected toexamine possible differences in the variances of twoindependent populations?

15. What are some of the criteria used in the selection of aparticular hypothesis-testing procedure?

16. Under what conditions should the two tests be used toexamine possible differences in the proportions of twoindependent populations?

17. Under what conditions should the X2 test be used toexamine possible differences in proportions of twoindependent populations?

18. What are the similarities and distinctions between theZ and X2 test for differences in populations proportions?

19. Under what conditions should the X2 test ofindependence be used?

Introduction

In carrying out a survey relating to the research, we shouldfirst select the problem and study its implications in differentareas. Selection of the research problem, as has already beenstated, should be in line with the researcher’s interest, chainof thinking and existing research in the same area and shouldhave some direct utility. What is most important in selectinga research problem is that the research topic should be withinmanageable limits.

Secondly, the topic should have practical feasibility. To studyfeasibility, what is important is to prepare a preliminaryabstract on the research topic. Since this chapter is intendedto acquaint the readers with survey procedure, we are notconcentrating on the aspects of research in great detail whichhave in fact already been covered in our earlier discussions.

The first and foremost task in carrying out a survey is toselect the sample. The difference between the population

141

Objectives


y Meaning of sampling.

y Need of sampling.

y Methods of sampling.

y Features of sampling.

y Uses of sampling.

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Unit 6

Sampling Procedures



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and sample has already been discussed earlier. Sampleselection is undertaken for practical impossibility to surveythe population. By applying rationality in selection ofsamples, we generalize the findings of our research. Thereare different types of sampling. We may categorize those inthree major heads as follows:

1. Random sampling

2. Purposive sampling

3. Stratified sampling

Random sampling is not a mere chance selection. Instead, itensures inclusion of each and every sample of the population.The conventional way of selection of samples using randomsampling methods are:

u Lottery method

u Tippett’s number

u Selection from a sequential list

u Use of grid system

Under lottery method, numbers or names of various units ofpopulation are noted on chits and put in a container. Afterthorough mixing, chits are drawn from the container andsurvey of drawn chits is carried out. Since this method ofrandom sampling has some amount of chance in it, this isoften described as a back-dated one.

Tippett’s number which lists 10,400 four digit numberswritten at random is constructed out of 41,600 digits takenfrom census reports by combining them in to fours. Themethod of drawing a sample from Tippett’s number is veryeasy. If we want to draw a sample of 20 persons from a list of6000 persons, for this purpose we shall first number eachunit from 0 to 6000 using Tippett’s four digit codes. Then weopen any page of Tippett’s numbers and select the first 20numbers that are below 6000. Tippett’s numbers are widelyused in sampling techniques and are found to be quite reliablein regard to accuracy and representativeness.

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143UNIT 6 Sampling Proceduresu


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Selection of sample from sequential list requiresarrangement of names under the intended plan according tosome order which may be alphabetical, geographical orsimply serial. Thereafter, out of the list, every 10th orany other number of cases may be taken up. If every 10th

unit is to be selected, the selection might begin from 7th,17th, 27th, 37th, 47th, 57th, etc., or from 5th, 15th, 35th, 45th, 55th,etc.

Grid system is applied for selection of sample from aparticular area. Under this method a map of the entire areais prepared, then a screen of squares is placed on the map.The areas falling within selected squares are taken assamples.

Purposive selection of samples, as the name goes, dependsmore on the researcher’s deliberate choice. Thus, such aselection of samples, in its true spirit defeats the purpose ofresearch as the samples suffer from the character ofrepresentativeness.

Stratified sampling combines the characteristics of randomsampling and purposive sampling. Initially the populationis defined in different numbers of strata or groups. Then fromeach group certain number of items are taken on a randombasis.

Apart from the above sampling procedures, there are othertypes of sampling like:

u Quota sampling (a special type of stratified sampling).

u Multi-stage sampling (where samples are selected froma very large area).

u Convenience sampling (where population is not clearlydefined and complete source of list is not available).

u Self selected sampling, etc.

After deciding over the samples to be surveyed, the next taskis to go ahead with the survey matter.

Survey may be carried out either by directly interviewingthe samples or by sending questionnaire to the samples

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or by mere observation of the characteristics ofsamples.

The Sampling Process

There are seven steps involved in this process:

Step 1 : Define the population: It is the aggregate of allelements, usually defined prior to the selection of thesample. The population is said to be completely defined ifat least the following terms are specified:

i. Elements

ii. Sampling units

iii. Extent

iv. Time

For example, for monitoring the sales of our product, thepopulation might be:

u Element—Our product.

u Sampling units—Retail outlets, super markets.

u Extent—New Delhi, Noida, Faridabad, Gurgaon,Sonepat (Delhi and around).

u Time—May 1-31st, 1999.

Step 2: Identify the sampling frame: The sampling frameshould be so selected which consists of almost all thesampling units. Though it is not possible to have one-to-onecorrespondence between frame units and sampling units,however, we should choose a sampling frame which yieldsunbiased estimates with a variance as low as possible.Popularly known sampling frames are:

Census reports, electoral registers, lists of member units oftrade and industry associations, lists of members ofprofessional bodies, lists of dwelling units maintained bylocal bodies, returns from an earlier survey and large scalemaps etc.

Step 3: Specify the sampling unit: The sampling unit isthe basic unit containing the elements of the targetpopulation.

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Step 4: Specify the sampling method: The samplingmethod indicates, how the sample units are selected. Themost important decision in this regard is to determine whichof the two-probability or non-probability samples is to bechosen.

Step 5: Determine the sample size (n): The decision aboutthe number of elements to be chosen, i.e., number ofobservations in each sample (n) of the target population.

Step 6: Specify the sampling plan: This means that oneshould indicate, how decisions made so far are to beimplemented. All expected pertinent issues in a samplingsurvey must be answered by the sampling plan.

Step 7: Select the sample: This is the final step in thesampling process. A good deal of field work and office workis introduced in the actual selection of the sample elements.However, it depends mainly upon the sampling plan and thesample size required.

Why Sampling?

There are various advantages of sampling, as given below:

i. The ideal solution to know the true or actual values ofthe different parameters of the population would be totake into account the entire population. However, thatis not feasible due to cost, time, labour and otherconstraints, hence sampling is more economical.

ii. As the magnitude of operations involved in a samplesurvey is small, both the execution of the field work andthe analysis of results can be carried out much fasterand hence is very less time consuming. On the otherhand, if we have to gather information about the wholepopulation, in certain cases, we may not be able to havethe information collected timely and the entire studymay become redundant.

iii. In case of destructive testing, for the entirepopulation, we may not be left with anything aftersuch an enumeration, i.e., testing the life of a tube orbulb.

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iv. Relatively very small staff is required for gatheringinformation, analyzing the same and preparation of thereport.

v. A researcher can collect more detailed information inmuch less time than otherwise be possible in a censussurvey. Moreover, we can afford to have a few specialistsfor collection of specialized type of information whichotherwise is not possible for a census study because ofcost and non-availability of specialists.

vi. As the scale of operations involved in a sample surveyis small, the quality of the interviewing, supervision andother related activities can be better than the qualityin a census survey.

vii. In many cases, sampling provides adequate informationneeded for the purpose and sufficiently reliable. Also,the sampling techniques make it possible to quantifythe magnitude of possible error.

Types of Sampling

There are basically two types of sampling methods:

a. Probability sampling method and

b. Non-probability sampling method.

In case of probability sample method:

i. The probability or chance of every unit in the populationbeing included in the sample is known.

ii. Selection of the specific units in the sample dependsentirely on chance.

In case of non-probability sampling method:

i. The probability of inclusion of any unit (of population)in a sample is not known.

ii. The selection of units within a sample involves humanjudgement rather than pure chance.

iii. The maximum information available “per rupee” whichcan be determined from a probability sample is not

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possible in this case and moreover, the degree ofaccuracy is not known.

iv. Although probability sampling is scientific and accurate,however, because of convenience and economy, the non-probability samples are preferred.

v. Many times, samples are selected by interviewers“at random” meaning that the actual sample selectionis left to the choice of the researcher, such sampleare non-probability samples and not probabilitysamples.

Probability Sampling Methods

The major sampling methods under probability samplingare:

u Simple random sampling

u Systematic sampling

u Stratified sampling

u Cluster sampling

Simple Random Sampling

Simple Random Sampling is the simplest type of sampling,in which we draw a sample of size (n) in such a way that eachof the ‘N’ members of the population has the same chance ofbeing included in the sample. A sample selected in this wayis called a simple random sample.

Selection of Random Samples

One way of drawing a simple random sample is to numberevery individual, put the numbers on slips of paper and drawlots. But such a procedure is impracticable in most situations.A more convenient method is to use a table of random digits.Such tables contain lists of digits so chosen that each digitbetween 0 to 9 has an equal chance of appearing at a givenspot in a single column and each two digits between 00 to 99has the same chance of appearing at a given spot in a doublecolumn and so on. Printed tables of random numbers are used



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in practice. For example, if we want to select ten items fromthe item produced during a sift from an automatic machine,which normally produces 500 items in a shift, we needto select 10 random numbers between 001 and 500.The selected 10 numbers arranged in ascending order willgive the serial number of the items to be included in thesample.

We number the individuals from 000 to 499 and proceed toread down same three digits column in a random numbertable:

135ü 283ü

369ü 476ü

387ü 761û

507û 837û

457ü 116ü

077ü 232û

977û 505û

999û 636û

421ü

We continue to write down three-digit numbers until wehave ten different numbers lying between 000 to 499. Here,our simple random sample includes: 135, 369, 387, 457, 077,283, 476, 116, 232, 421

Now put this in ascending order:

077, 116, 135, 232, 283, 369, 387, 421, 457, and 476 (10 Nos.)

0 77

1 16, 35

2 32, 83

3 69, 87

4 21, 57, 76

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Simple Random Sample in Practice

The use of random sampling is made by researchers for thefollowing situations:

u When a small sample is needed from the list of sampleframe (list of universe items).

u The cost per interview is practically independent of thelocation of the sample item.

u Other than a list of items, no other information isavailable.

u In simple random sampling, the sample meanprovides an unbiased estimate of the universe mean.However, the use is severely limited by the followingfactors:

– Cost: Sampling frame is required for a simplerandom sample. In most situations, it is verydifficult to have a frame, if not impossible andmoreover it is very time consuming and hence isuneconomical also.

– Statistical efficiency: One sample designing is saidto be statistically more efficient than anotherwhen the frame is of a small size and a smallerstandard error is obtained. Most large populationsare not homogeneous but can be broken down intomore homogeneous units.

In such conditions, one can have sampling designsuch as stratified sampling which is statisticallymore efficient. Similarly, the use of cluster samplingwhenever we can pick up members fromgeographically closer areas, reduces the costinvolved.

– Supervision: The problem of selecting a sample withthe help of random numbers etc., though appears tobe very simple but in practice it is not so. Suppose,we want to select a sample size of 2,5000 from a listof 2 million, it's a difficult job and errors are bound

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to be there. Moreover, the cost of supervision is alsohigh. As compared to this, systematic randomsampling is much easier.

Systematic Sampling

The systematic sampling also employs the principle ofrandom sampling. However, in this method of sample,selection of a unit depends upon the selection of a precedingunit in contrast to simple random sampling, where theselection of a unit is independent of each other. Systematicrandom sampling in this sense is called quasi-random-sampling.

Systematic Sampling in Practice

The method followed in systematic sampling is simpler ascompared to simple random sampling.

For selecting a sample size of 50 out of 500 the procedure isas follows:

Step I Find simple fraction K = N/x

When N is total of units of population and xis the sample size.

500

50= 10 in this case

Step II Select a number between 1 and 10, atrandom, say 9.

Step III Then, the sample comprises of nos.

9, 19, 29, 39, ...............................489, 499

Only the first unit has to be selected and the selection ofremaining numbers is easy.

Limitations

If the sample frame has any periodicity that parallels thesampling rates, then the possibility of a strong bias is there.For example, in banking transactions if you choose 1/7, 1/14,etc., then you will be having same day of the week for your



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study and hence your study will be a biased study. Be it,Monday or Wednesday or Friday etc.

Similarly, if the frame is arranged in a way-ascending ordescending order of some attribute, then the location of thefirst sample element may affect the result of the study. Insuch cases, one should devise ways to qualify the effect ofbias.

On the other hand, if the frame is so arranged that similarelements are grouped together, then systematic samplingproduces almost a proportional stratified sample.These samples are statistically more efficient as comparedto simple random sampling.

For estimating the precision of the results, systematicsamples are treated as simple random sample and perhapsis the most widely used method among the probabilitysampling designs.

Stratified Random Sampling

Another useful type of sampling procedure is calledstratified random sampling. In this procedure, the membersof the population are first assigned to strata or groups, onthe basis of some characteristic and a simple random sampleis drawn from each stratum. The individuals in all thesamples taken together constitute the sample from thepopulation as a whole, viz.

Stratum Number in stratum Number in sample

1 N1 n1

2 N2 n2

3 N3 n3

4 N4 n4

5 N5 n5

6 N6 n6

7 N7 n7

k Nk nk

Total N n

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If the component sample sizes n1, n2,.................nk are so chosenthat,

=nN

=nN

=- - - - - - - - - - - - -n kN

(n)(N)

1

1

2

2 k

In this way we do proportional stratified randomsampling.

Stratification does not mean absence of randomness. All itmeans is that the population is first divided into certainstrata that are mutually exclusive and collectivelyexhaustive.

Populations divided into three (3) strata s1, s2, s3.

A stratum, as is clear, is a sub-population which is morehomogenous than the complete population. The members ofa stratum are similar to each other.

Example 6.1

Suppose, the population consists of 45,000 households,divided into five (5) strata on the basis of monthly income.This can be illustrating as below:

0 – 1000

1001 – 5000

5001 – 7500

7501 – 10,000

Above 10,000

Then,

a. Find out the number of units from each strata if thesample constitutes 1% of the population.

b. If selection is for 150 items selecting equally from eachstrata, find out the number of sample units from eachstrata.

Solution

a. Proportional stratified sampling

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Stratum No. Population (No of Sample Sampling(i) households) (proportionate) ratio

(ii) (iii) 1%=.01

0-1000 15,000 150 .01

1000-5000 12,000 120 .01

5001-7500 9,000 90 0.01

7501-10,000 6,000 60 .01

> 10,000 3,000 30 .01

45,000 450 .01

b. Equal from each strata:

Total No. of sample units = 150

No. of sample units from each stratum = 150/5

= 30

Sampling ratio = Sample size / Population size

Major Issues

There are three major issues involved in stratified sampling:

i. Bases of stratification: Depends upon the variablebeing studied. Quite often it is desired to have morethan one variable. In marketing research, usuallydemographic characteristics such as age, sex or incomeand geographical distribution such as rural-urbanbreak-up, break-up by region, state or city form the basis.

ii. Number of strata: Since stratification would enhancethe cost of the survey, one would weigh the benefitsresulting from it vs. the cost involved. As a rule of thumb,not more than 6 strata should be used for a single overallestimate.

iii. Sample sizes within strata: Sample size within stratadepends upon the budget and the cost per observation.Suppose in the above example, if the budget is Rs 50,000and the cost per observation is Rs 250, then the samplingsize = 50,000/250 = 200 and not 450. However, thisshould be allocated among the various strata.Researchers can use either a proportional ordisproportional sample.

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Proportional Allocation

Under this method each stratum is related to its weight. Inthe Example 6.1, based on relative weight, if we have to havea sample size of 225 then numbers from each stratum wouldbe as follows:

Stratum No of Household For Sample Size n = 225 Sampling Ratio

0-1000 15,000 75 225/45000

1001-5000 12,000 60

5001-7500 9,000 45

7501-10,000 6,000 30

10,001 and 3,000 15

above

45,000 225

Disproportional Allocation

There are circumstances where some form of disproportionalallocation should be considered, i.e., sampling differentstrata at different rates. As a general principle, when thevariability among observations within a stratum is high,‘higher rate for higher internal variation strata and lowerrate for less internal variation strata’ is adopted.

If s12 , s2

2 ,...................sp2 are the variances of the ‘p’ strata

respectively, then the statistical efficiency is highest, when

n

N s=

n

N s=

n

N s1

1 1

2

2 2

p

p p

Example 6.2

Let us consider a case of 3 strata, of income group with givenstratum variance.

Stratum No. of Households Stratum Variance

0 - 5000 300 4.00

5001-10,000 450 9.00

> 10,000 750 2.25

Total 1500

Find out the nos. from each stratum for a given sample sizeof 50?

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Solution

Disproportional stratified sampling

Stratum No No of Strata Stratum Sample Sampling(i) elements/ variance standard size ratio

households deviation (n i ) (n i/N)

0 - 5000 300 4.00 2.0 10 0.033

5001-10000 450 9.00 3.0 22 0.049

> 10,000 750 2.25 1.5 18 0.024

Total 1500 50

n1s1 + n2s2+ n3s3 = (300´ 2.0) + (450´ 3.0) + (750´ 1.5)

= 600 + 1350 + 1125 = 3075

\ n1 = 6003075

50×

n2 = 2213503075

50=×

n3 = 1811253075

50=×

Stratified Sampling in Practice

The main reasons for using stratified sampling for managerialapplications are:

i. It can obtain information about different parts of theuniverse, i.e., it allows to draw separate conclusion foreach stratum.

ii. It often provides universe estimates of greater precisionthan other methods of random sampling say simplerandom sampling.

However, the price paid for these advantages is high becauseof the complexity of design and analysis.

Estimation � statistical Inference

As it is not possible to analyze the entire population andthen draw the conclusion because of limited manpower,money and time factors, we have to draw samples from thepopulation and draw conclusions about the same based uponthe sample result. We draw a sample at ‘random’ of a givensize (say 'n') and compute a statistic – a characteristic of the

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sample ( X , S) and this becomes an estimate of the similarcharacteristic of the population (m, s ).

There are two types of estimates:

u Point estimates

u Interval estimates.

Point Estimation

When we estimate the population parameter (say m or s),we take the help of a simple sample value (m in case of mand s in case of s ). This is called point estimate as we useonly a single value. The point estimator would be the bestestimator if it has the following form of characterization:

u Unbiasedness

u Consistency

u Efficiency

u Sufficiency

An estimator shall be unbiased, if the expected value of thesample average equates the population mean : Sx= m

An estimator is consistent estimator, if the statisticparameter approaches the population as the sample sizeincreases.

As the stratified random sample is a group of simple randomsamples, the estimate of the overall universe mean is simplya weighted average of the stratified sample mean.

Example 6.3

Suppose, we have the following data on consumption ofsample households.

Income strata (pm) Sample mean No of observationpurchase per in each stratum

households (Rs)

1 – 5,000 1000 5000

5001 – 10,000 2500 1500

>10,000 3500 500

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Estimated Population Mean (Mean Monthly Expenditure)

‘X = Â Wi x i [I= 1, 7000

5000 = 0.714]

= .714(1000)+.214(2500)+.072(3500) [I= 2, 7000

1500]= 0.214

= 714 + 535 + 252

= Rs 1501 [I= 3, 7000

5000]= 0.072

Estimation of Confidence Interval with Stratified Random Sampling

For finding the confidence interval, we need the followingdata on sample: variance, sample size and weight for eachstratum.

Let us discuss the following example.

Stratum (i) Sample variance (si2) Sample size Weight of eachin stratum stratum

(n1) ( 2iW )

1. (Rich) 3000 60 0.1

2. (Middle class) 2000 100 0.3

3. (Poor) 1000 250 0.6

Estimation of standard error is given by:

S.E. = ∑in

SiWi 22

= 3

11

2

22

1

11

nSW

nSW

nSW 222222

++∑

= 250(1000)(.06)

100(2000)(.3)

60(3000)(.01)

++

= 2.46.00.50 ++

9.8= = 2.98

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Let us examine with 95% confidence interval,

value of Z = ± 1.96

At an average monthly consumption of say Rs 1500, the valueswill come out to be between

‘ X ± 3s` = Rs 1500 ± 3 (2.98)

= Rs 1500 ± 8.94

= Rs 1508.94 and Rs 1491.06 say Rs 1509 and Rs 1491

It may be noted that in the above calculations, differencesamong strata means has no where been figured and this isthe reason why stratified sampling gives a moreprecise estimate of the population mean than a simplerandom sampling for a given sample size.

Cluster Sampling

In the probability sampling methods, we have seen that eachitem in the sample is chosen one at a time from the completelist of universe elements. However, it would be moreexpedient to select entire groups or clusters at random. Letus take, for example, a residential colony comprising 15Blocks : A to O.

Let us treat each block as a cluster and then select 3 (say)blocks (cluster) out of 15 blocks at random and then collectinformation from all families residing in these 3 blocks(clusters).

Cluster Sampling in Practice

This method is usually convenient for collection of data as acluster is ideally a mini-population and has all the featuresof the population. Clusters are heterogenous withinthemselves and not like the homogeneous strata. Hence,collection of data would be far easy as compared to othermethod. Moreover, apart from cost considerations, such acluster sample would be desirable in the absence of a suitablesampling frame. Frames, for cluster sampling, areneeded for the selected cluster only and hence reduce the

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cost of developing a frame as compared for simple randomsampling or stratified random sampling.

Use of Cluster Sampling in a National Survey

In a national survey, first we’ll select a few districts in thewhole country, (these districts would act as cluster and thenwe would take stratified sampling/simple random samplingso that the survey can be completed with less cost and moreaccuracy.

Area sampling is a special case of cluster sampling.

The question now is how to select a sample in clustersampling?

Following are the number of warehouses in 15 cities:

40,22,15, 33, 75, 30, 21, 24, 57, 32, 63, 27, 46, 51,64

If we want to select a sample of 15 blocks using cities asclusters and then select within clusters proportionate to size,how many stores from each city should be chosen (use 15 asthe start point)?

City # No of warehouse Cumulative Sample Rem arks

1 40 40 15 One sample

2 22 62 55 One sample

3 15 77 Nil

4 33 110 95 One

5 75 185 135 One

6 30 215 175, 215 Two

7 21 236 – Nil

8 24 260 255 One

9 57 317 295 One

10 32 349 335 One

11 63 412 380 One

12 27 439 420 One

13 46 485 460 One

14 51 536 500 One

15 64 600 540, 580 Two

15

600 ¸ 15 = 40

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Multistage and Multiphase Sampling

Multistage sampling, as the name implies, means that theselection of units is done in more than one stages. Thenumber of stages in a multistage sampling is based onconvenience and the availability of suitable sampling framesat different stages. In case of a national survey, it is easierto understand that this can involve the following four stages:

I stage Districts

II stage Cities

III stage Wards or localities

IV stage Households

Example 6.4

Suppose, we want to have 7500 households from all overthe country. In such a case:

I Stage – District: say 30 districts out of 600 are selectedfrom all over the country;

II Stage – Cities: Suppose 5 cities are selected out of each 30districts; and

III Stage – Wards/localities: say 10 wards/localities areselected from each city;

IV Stage – Households: 50 households are selected fromeach ward/locality.

In stage I, we can employ stratified sampling.

In stage II, we can use cluster sampling.

In stage III, we can have simple random sampling.

Thus, the use of various methods shall give individuallycontribute towards accuracy, cost, time, etc. This leads us toconclude that multistage sampling leads to saving of time,labour and money. Apart from this wherever an appropriateframe is not available, the use of multistage sampling hasuniversal appeal.

[Exercise : use of fertilizers in national survey]

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Stratified Sampling : Districts as a sampling unit, averagerainfall in the districts as a criterion for stratification, 20districts).

Cluster Sampling: It may be used to select 10 villages in eachof the selected districts.

Simple Random Sampling: It can be used for selection of 50samples from each village, criterion of stratification beingthe holding of land.

Non-probability Sampling Methods

Though the probability samples give an unbiased sample andthe parameters used for the study can be tested for a givenconfidence internally, still non-probability samplingfinds frequent use in many situations because of difficultconditions such as frame (list of all sampling units), timeand cost involved. Major non-probability sampling methodsare discussed below:

u Convenience sampling: As the name implies, theselection of the sample is left to the researcher who isto select the sample. The researcher normallyinterviews persons in groups at some retail outlet,supermarket or may stand at a prominent pointand interview the persons who happen to be there. Thistype of sampling is also called ‘accidental sampling’ asthe respondents in the sample are included merelybecause of their presence on the spot. The datacollection and sample cost is minimum in this case.However, the method suffers greatly from the quality,i.e., accuracy point of view which can in no way bedetermined. However, this type of sampling is moresuitable in ‘exploratory research’ where focus is ongetting new ideas/insights into a given problem.

u Judgement sampling: In judgement sampling, thejudgement or opinion of some experts forms the basis ofthe sampling method. It is expected that these sampleswould be better as the experts are supposed to knowthe population. However, as the use of randomness isnot there and moreover their is no way to find the

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accuracy of the samples, hence the method has itslimitations and is used mainly for situations requiringextremely small size of samples, i.e., use of rare events,members having extreme positions, etc.

u Quota sampling: This is the most frequently used non-probability sampling method and is used when:

– Employing stratification: i.e., age, sex, income,family size etc. More often compoundstratification is used in groups with sex.

Stratum

Men 21 + 3536 + 45

Women 21 + 3536 + 45

– Sample size, (called quotas) are established foreach stratum. This is done to reduce ‘bias’introduced by sampling.

Let us understand with the help of Example 6.5.

Example 6.5

We have population made up of rich, medium and poorpeople in the ratio of 10% , 40%, 50%, respectively. Usingquota sampling, determine the number of representativesfrom each category in a sample size of 100.

Category I (rich) = 10% of 100 = 10Category II (medium) = 40% of 100 = 40Category III (poor) = 50% of 100 = 50

100

Quota Sample in Practice

u It is economical as travelling costs are reduced.

u It is easy to administer.

u When field work is to be done quickly, this methodprovides the biggest advantage.

u No sampling frame is required.

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However, since the method is not based on random selection,it is not possible to ascertain the accuracy being achieved.Moreover, the sample may not be a representative sample.Also, the quality may suffer if skilled interviewers are notemployed.

In many real life situations, the use of cluster samplingmethod and that of convenience sampling is being mademainly because the cost per observation is much use ascompared to other method. Sophisticated researchtechniques and methods ensuring greater accuracy are notfinding much use.

Characteristics of a Good Sample Design

u Goal orientation: Sample design should be orientedto the research objectives.

u Measurability: The parameters under study should besome how or the other measurable so that accuracy canbe ensured.

u Usability: The sample size should be convenient tocollect and analyze.

u Cost factor: The total cost of sample design, collectionand analysis of the data should be minimum.

Thus one has to weigh the pros and cons of various sampledesigns before selecting the best possible one.

Sampling and Non-sampling Errors

The basic objective of a sample is to draw inferences aboutthe population from which the sample is drawn. Therefore,it is necessary that the sampling technique be a reliableone.

The randomness of the sample is specially important becauseof the principle of statistical regularity which states that asample taken from a population is likely to possess almostthe same characteristics as those of the population.

In the total process starting from data collection to inferringresults, errors are bound to come in. These errors can beclassified into two groups.

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Sampling Errors

Sampling errors are those which arise due to drawing offaulty inferences about the population based on the resultsobtained from the samples. In other words, it is thedifference between the results which would have obtainedif the entire population was taken for such a study and theresults obtained from the samples drawn from it. Thesampling error would be smallest if the sample size is largein relation to the population and vice versa.

Non-sampling Errors

Non-sampling errors are introduced due to technically faultyobservations or calculation during the processing of the data.The faulty methods could be used at different stages:

u Methods of data collection.

u Incomplete coverage of the population.

u Inaccurate information provided by the participants.

u Errors occurring during editing, tabulating andmathematical manipulation of data.

u These errors shall arise even if the entire population istaken understudy.

Both the sampling as well as non-sampling errors must bereduced to a minimum in order to get a representativesample of the population as far as possible.

Some Problems on Sampling Fundamentals

Problem 6.1

From a random sample of 49 colleges of Delhi, the averageexpenditure and its standard deviation were found to be Rs2000 and 450 respectively Construct at 95 percent confidenceinterval average expenditure of a student in Delhi.

Solution

Here, we have n = 49x = 2000Sx = 450

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value of ‘z’ at 95% confidence level = 1.96 (from normal table)

Now SES

z x=

49

450

n

xSSE ==

7

450=

Z.(SE)xì ±=

7

(450)1.962000 ±=

= 2000 ± 126

= Rs 1874 and 2126

Problem 6.2

What should be the sample size for the following case :

Standard deviation being Rs 200 and the estimate within +Rs 40 ?

Solution

Here, e = / 40 /

Let the confidence limit be 95%

Then z = 1.96 (from same table)

New( ) ( )

n

óz

x

óz==l

Where, η

σ=

χ

σ

So,n

2001.9640 =

9.8051.96n =×=

n = 96

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Standard deviation being Rs 100 and the estimate within +Rs 50.

50 = 1.96 n

100

3.8250

1001.96n =

×=

n=15

Problem 6.3

For the following data, calculate the standard error for mean:

Number of motor cycle accidents is 4.1 in a randomexamination of 8 cases out of 2500 with standard deviationbeing 0.9.

Solution

Standard error of Mean= 1N

nN.

n

ó

−

−

When s = std deviation of population = sx = 0.9

N = finite size of population

n = sample size

12500

812500

81

0.9xó

−

−=

=2499

2419

9

0.9

= .96799

0.9×

= 0.1 ´ 0.9839

= .09839

Problem 6.4

For problem 6.3, find the value of mean number of accidentsfor a 90% confidence interest.

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Find the standard error of mean if the population size is“not finite.”

Solution

1. )(zxxl+

n

ó1.645x += (z again 90% confidence interval = 1.645)

81

0.9.1.6454.1 +=

9

.91.6454.1 ×+=

= 4.1 + 1.645 (0.1)= 4.1 + .1645= 4.264 & 3.9355

2. Standard error of mean, when population is “not finite”

3

0.1

9

0.9

81

0.9

n

ó

x ====l

Problems 6.5

The average production of Alloy Steel Plant, Durgapur, for10 shifts taken at random is found to be 100 tones per shiftwith sample standard deviation of 3.2 tones per shift.Construct a 90% confidence interval around the estimate.

Solution

Here, x = 100 tones per shift s x ¯ = 3.2 tones per shift n = 10

As, n < 30, we shall apply ‘t’ test (and not z test),

with degrees of freedom = n – 1 = 10 – 1 = 9

Confidence interval for 90%

= x ± t, n

xó

= 100 ± (2.353) 10

3.2∂

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= 100 ± (2.353). 3.16

3.2

= 100 + 2.383

= 97.617 & 102.383

Review Questions

1. Why is sampling used in marketing research?

2. Define the following terms: population, sampling unit,sampling procedure in a particular marketing researchstudy.

3. What are the major sources of non-sampling errors in amarketing study?

4. Discuss briefly the following sampling techniques andthe merits/demerits of each:

i. Simple random sampling

ii. Systematic random sampling

iii. Stratified random sampling

iv. Cluster sampling.

5. What is a sample size?

6. What features would you consider in designing a samplesize?

7. What are parametric & non-parametric tests? Wherecan each be used more advantageously than the other?

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Types of Data

Once the researcher has decided the ‘research design’, thenext job is of data collection. For data to be useful, ourobservations need to be organised so that we can get somepatterns and come to logical conclusions.

Statistical investigation requires systematic collection ofdata, so that all relevant groups are represented in the data.

To determine the potential market for a new product, forexample, the researcher might study 500 consumers in acertain geographical area. It must be ascertained that thegroup contains people representing variables such as incomelevel, race, education and neighbourhood. The quality of datawill greatly affect the conclusions and hence, utmostimportance must be given to this process and every possibleprecaution should be taken to ensure accuracy, whilegathering and collecting data.

169

Objectives


y Types of data.

y Procedure of data collection–Primary data.

y Procedure of data collection–Secondary data.

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Unit 7

Data Collection Methods



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Depending upon the sources utilised, whether the data hascome from actual observations or from records that are keptfor normal purposes, statistical data can be classified intotwo categories. primary and secondary:

Primary Data

Primary data is one which is collected by the investigatorhimself for the purpose of a specific inquiry or study. Suchdata is original in character and is generated by surveysconducted by individuals or research institutions.

Secondary Data

When an investigator uses the data which has already beencollected by others, such data is called secondary data. Thisdata is primary data for the agency that collects it andbecomes secondary data for someone else who uses this datafor his own purposes. The secondary data can be obtainedfrom journals, reports, government publications, publicationof professional and research organizations and so on. Forexample, if a researcher desires to analyze the weatherconditions of different regions, he can get the requiredinformation or data from the records of the meteorologydepartment.

Table 7.1: Distinction between Primary Data andSecondary Data

Description Primary Data Secondary Data

1. Source Original source Secondary source

2. Methods of data collection Observation method Published data ofQuestionnaire method government agencies

Trade journal etc.

3. Statistical process Not done Done

4. Originality of data Original first time No data are collected by

collected by user some other agency

5. Use of data For specific purpose Data are taken from

data are compiled other sources and used

for decision making

6. Terms and definitions of units Incorporated Not included

7. Copy of the schedule Included Excluded

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Contd...

171UNIT 7 Data Collection Methodsu


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8. Methods of data collection Given Not given

9. Description of sample selection Given Not given

10. Time More Less

11. Cost Expensive Cheaper

12. Efforts More Less

13. Accuracy More accurate Less accurate

14. Training personnel required Experts/trained required Less trained personnel

Data Collection Procedure for Primary Data

Planning the Study

Since the quality of results gained from statistical datadepends upon the quality of information collected, it isimportant that a sound investigative process be establishedto ensure that the data is highly representative and unbiased.This requires a high degree of skill and also certainprecautionary measures may have to be taken.

Modes of Data Collection

There are basically three widely used methods for collectionof primary data:

u Observation

u Experimentation

u Questionnaire

u Interviewing

u Case study method

Observation Process

Information is collected by observing the process at work.The following are a few examples:

i. Service stations: Pose as a customer, go to a servicestation and observe.

ii. To evaluate the effectiveness of display of dunlopillocushions in a departmental store, observer notes.

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a. How many pass by?

b. How many stopped to look at the display?

c. How many decide to buy?

iii. Super market: What is the best location in the shelf?Hidden cameras are used.

iv. Concealed tape recorder with the investigator helps todetermine typical sales arguments and find out salesenthusiasm shown by various salesmen.

By this method, response bias is eliminated.

The method can be used to study sales techniques, customermovements, customer response, etc. However, thecustomer’s/ consumer’s state of mind, their buying motives,their images are not revealed. Their income and educationis also not known. It also takes time for the investigator towait for particular sections to take place.

Experimentation Method

Many of the important decisions facing the marketingexecutive cannot be settled by secondary research,observation or by surveying the opinions of customers orexperts. Experimental method may be used in the followingsituations:

i. What is the best method for training salesmen?

ii. What is the best remuneration plan for salesman?

iii. What is the best shelf arrangement for displaying aproduct?

iv. What is the effectiveness of a point-of-purchase display?

v. What package design should be used?

vi. Which copy is the most effective?

vii. What media are the most effective?

viii. Which version of a product would consumers likebest?

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In a marketing experiment, the experimental units may beconsumers, stores, sales territories, etc.

Factors or marketing variables under the control of theresearcher which can be studied are price, packaging,display, sales incentive plan, flavour, colour, shape, etc.

Competitor’s actions, weather changes, in cooperativedealers, etc. are environmental factors.

To study the effect of the marketing variables in the presenceof environmental factors, a sufficiently large sampleshould be used. Or sometimes a control group is set up.A control group is a group equivalent to the experimentalgroup and differing only in not receiving anytreatment.

The result/response of a marketing experiment will be inthe form of sales, attitudes or behaviour.

Questionnaire Technique

The survey method is the technique of gathering data byasking questions from people who are thought to have thedesired information.

Advantages

One cannot know by observation, why a buyer makesparticular purchases or what is his opinion about a product.Compared with either direct observation or experimentation,surveys yield a broader range of information and are effectivefor producing information on socio-economic characteristics,attitudes, opinions, motives, etc., and to gather informationfor planning product features, advertising copy, advertisingmedia, sales promotions, channels of distribution and othermarketing variables. Questioning is usually faster andcheaper than observation.

Limitations

a. Unwillingness of respondents to provide information:This requires salesmanship on the part of theinterviewer. The interviewer may assure that the

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information will be kept secret. Motivating respondentswith some token gifts often yield result.

b. Inability of the respondents to provide information: Thismay be due to:

i. Lack of knowledge.

ii. Lapse of memory.

iii. Inability to identify their motives and provide‘reasons why’ for their actions.

c. Human biases of the respondents: i.e., ego, etc.

d. Semantic difficulties: It is difficult, if not impossible, tostate a given question in such a way that it will meanexactly the same thing to every respondent. Similarly,two different wordings of the same question willfrequently generate quite different results. Theselimitations can be controlled to some extent by:

i. Careful phrasing of questions.

ii. Careful control of data gathering by employingspecially trained investigators who will observecarefully and report on the subtle reactions ofpersons interviewed.

iii. Cautious interpretation by a clear recognition ofthe limitations of the data and an understandingof what exactly the data represents. This isespecially true of responses to questions like:

What price would you be willing to pay for thisproduct?

iv. Looking at facts in relative rather than absoluteterms. A survey showed that 60% of families inthe middle income group used toothpaste. Takenby itself in the absolute sense, the results of thesurvey are in some doubt because the questionasked encountered an obvious bias. But if this 60%is looked at on a relative basis, viz thecorresponding figure of 60% for upper income

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group families, a more meaningful and significantinterpretation can be made, even though theindividual figure for each group may be slightlyinflated.

Interviewing

Interview on samples may be carried out either with astructured framework or with an undirected approach. Thestructured framework involves use of some pre-determined questions. Such pre-determination enables theresearcher to standardize the responses with some fixedalternatives. The samples here are merely directed tochoose answers/responses from different pre-determinedalternatives. Thus the researcher can or may quantify theresponses in line with his research object. Standardizing theresponses with pre-determination involves great amount ofrisk unless the researcher acquaints himself with theintricacies of the research matter in much greater details.However, this approach is more scientific in nature for itsfeasibility of quantifications with least trouble andapplication of scientific techniques with more rationality.

Unstructured or undirected interview approach enables therespondents or the samples to answer the researcher’squeries with greater amount of flexibility. Since no pre-determined responses here are advised, the researcher mayproceed, keeping in tune with the research matter, withgreater amount of flexibility too. However, quantification ofthe responses from unstructured interviews are difficultunless the researcher fixes the standard of all responses withsome amount of control. If sample characteristics go on rising,enumeration become difficult. Thus unstructured approachmay defeat the purpose and object of research. This approachis resorted to usually in cases where the selected samplesneed to be interviewed in a more intensive way.

There are different types of unstructured interviews:

1. Focussed interview, which is directed to focus theattention of respondents to give some experience andits effects.



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2. Clinical interview, which is somewhat similarto focussed interview but enables the samplesto underlie their feelings or motivations in muchbroader perspectives. This method is usuallyadministered in psychiatric clinics and in prisonadministration.

3. The third method of unstructured interview is non-directive approach. Under this approach the initiativeis left completely in the hands of the respondents.Psychoanalytic research is usually done with a non-directive approach.

Interviewing the subjects or the samples is moreadvantageous than sending questionnaires through mail.Interview method enables the researcher to personally feelthe problems of samples. Moreover interviewer/researcher,being present on the spot, case study certain qualitativevariables like facial expressions and gestures of me samples.For high reliability and feasibility of scoring using testdevices, interview approach is more scientific than mailingquestionnaire.

Structured Study

If a radio manufacturer wanted to find out how many peopleown a radio, what type it is, when they bought it, therespondents could be asked a set of questions in the followinggiven sequence.

Does your family own a radio? Yes/No

(If yes, ask)

What brand is it? Number____________

How many valves? Number____________

When did you purchase this radio? Date________________

This is an example of structured and non disguised study.

Non-structured Studies

More than anything else marketing men want to know whypeople buy or don’t buy their products.

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Reasons for why can be classified as:

1. Those reasons which are a part of the individual ownpurposes or attitudes.

2. Those reasons which are the result of outside influencessuch as advertising.

3. Those reasons which are based on characteristics of theproduct itself.

But questions will have to be aimed at these three categoriesseparately, which makes the approach satisfactory.

Many people will not report motives which might beconsidered biased or socially unacceptable.

To overcome these difficulties, techniques have beendeveloped by psychoanalysts.

Depth Interview (Non-disguised)

Instead of approaching the respondent with a fixed list ofquestions, the interviewer attempts to get the respondentto talk freely about the subject of interest. By doing so theinterviewer hopes to get the respondent at ease and thenencourage him to express any ideas which he has on thesubject. If some idea of interest is passed over too quickly,the interviewer may seek more information by “probing”. Forexample, he may comment “that is interesting. Why do youfeel that way?” This encourages further discussion or thepoint. Various probes can be used to get the respondent toexpand on any particular ideas. Although no formalquestionnaire is used in interviewing of this type, theinterviewer has an outline in mind. If the respondent doesnot get into areas of special interest, the interviewer willinsert questions opening up these topics. The objective ofthese interviews is to get below the respondent’s surfacereasons for particular marketing decisions, and to find theunderlying or basic motives.

Interviewer should have background of social psychology andfield experience of 500 or more interviews.

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Sometimes, a group of 6 to 8 people are called for a discussionwith the interviewer acting as a moderator.

Projective Technique (Disguised study)

Respondent is given an ambiguous situation and asked todescribe it. The description given contains a projection ofthe respondents’ personality and attitudes to the situationdescribed.

Various projective techniques are used but the mostcommonly used are word association, sentence completionand story telling.

In word association, a series of words is read one at a timeto the respondent. After each word, the respondent says thefirst thing that comes into his mind. Sentence completionrequires the respondent to complete partial sentences. Instory telling the respondent is shown a picture or given adescription and asked to tell a story about it.

Major Steps in Conducting a Survey

Deciding on the Research Objectives

Every effort should be made to state the objectives in specificterms. Surveys, in particular, can proceed in an almostunlimited number of directions. To prevent all kinds ofquestions from being asked, clear informational objectivesshould be developed and put in writing, if possible.

Methods of Collection of Data

Following methods are in use for collection of data forquestionnaire technique:

a. Telephone enquiries.

b. Postal or mail questionnaire.

c. Personal interviewing.

d. Panel research.

e. Group interview technique.

f. Special survey techniques.



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Each of this method has its own advantages anddisadvantages. Telephone interviewing stands out as the bestmethod for gathering quickly needed information. It has theadvantage over a mailed questionnaire as it permits theinterviewer to talk to one or more persons and to clarify hisquestions, if they are not understood. The response rate fortelephone interviewing seems to be a little better than formailing questionnaires. The two main drawbacks oftelephone interviewing are that only people with telephonescan be interviewed and only short, not too personalinterviews can be carried out.

The questionnaire mailing may be the best way to reachpersons who would not give personal interviews or whomight be biased by interviewers. It is typically theleast expensive than other major methods. On the other hand,mailing questionnaires require simple and clearly wordedquestions. The response rate to mailed questionnaires istypically low.

Personal interviewing is the most versatile of the threemethods. The personal interviewer can ask more questionsand can supplement the interview with personalobservations. These advantages come at a high cost, however,personal interviewing is the most expensive method andrequires much more technical and administrative planningand supervision. In a real sense, companies turn to telephoneinterviewing or questionnaire mailing as a second choice outof cost consideration.

Construction of a Questionnaire

When information is to be collected by asking questions topeople who may have the desired data, a standardized formcalled questionnaire is prepared. The questionnaire has alist of questions to be asked and spaces in which therespondents record the answers. Each question is wordedexactly as it is to be asked. Also, the questions are listed in aestablished sequence.

Questionnaire construction is discussed the coming in ninesteps. These steps may vary in importance in individualprojects, but each one must be thought through.

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The nine steps are:

i. Decide what information is wanted.

ii. Decide what type of questionnaire (personal interview,mail, telephone) to use.

iii. Decide on the content of individual questions.

iv. Decide on the type of question (open, multiple choice,dichotomous) to use.

v. Decide on the wording of the questions.

vi. Decide on question sequence.

vii. Decide on lay out and method of reproduction ofquestionnaire.

viii. Make a preliminary draft and pretest it.

ix. Revise and prepare the final questionnaire.

Let us discuss each of these steps in detail.

– Basically, a questionnaire must serve two functions;translate research objectives into specific questions andmotivate the respondent to cooperate with the surveyand furnish the information correctly. Therefore, beforea questionnaire can be formulated, a specific statementof the information which is needed must be made. Thecomplete analysis must be anticipated. For example, itis not enough to know that the objective is to find whattype of persons form the market for the product. Thespecific characteristics that are thought to be importantmust be stated. Thus a deodorant soap company wishingto define its market might specify that the surveydetermine the proportion of individuals using the soapwithin the groups shown in Table 7.1. With such alisting the questionnaire framer could develop a seriesof questions that would elicit the information neededfor the proposed analysis. This statement of objectivesis part of the problem definition step. At the risk ofbeing repetitive, it is important here to emphasize thata questionnaire cannot be started until the preciseinformation sought is known.

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Table 7.2

Age Sex Income Geographical Area City Size

Under 20 Male Under $3,000 North-east Over 1,000,00

20-29 Female $3,000-$4,999 North-central 50,000-1,000,000

30-45 $5,000-$7,499 South 2,500-49,999

Over 45 $7,500 and over West Rural

– Determine the manner questionnaire to be used:Questionnaire can be used by personal interview, mail,or telephone. The choice among these alternatives islargely determined by the type of information to beobtained and by the type of respondents from whom itis to be obtained. It is necessary to decide on the type ofquestionnaire at this point since the questions asked,the way, in which they are asked and the sequence inwhich they are asked will all be influenced by thisdecision.

– Determine the content of individual questions: Once thespecific information needed is known and the methodof communication is decided, the researcher is ready tobegin formulating his questionnaire. A first problem isto decide what to include in individual questions. Thefollowing points are in the nature of standards againstwhich to check possible questions; obviously, they leavemuch to the originality of the researcher.

l Is the question necessary?

l Are several questions needed instead of one?

l Does the respondent have the informationrequested?

l Is the point within the respondent’s experience?

l Can the respondent remember the information?

l Will the respondent have to do a lot of work toget the information?

l Will respondents give the information?

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Some respondents do not want to answer particularquestions. It goes without saying that such questions hurtcooperation for the rest of the interview and, therefore,should be eliminated. It is often possible, however, to changesuch questions so as to secure the desired information.

General motors developed a classic questionnaire to getconsumer opinion on car styling. Few consumers coulddescribe the type of car that they liked best, but, if they wereshown pictures of ten cars they could point out the car theyliked best. The pictures made it possible for the respondentto report his answer.

The interviewing situation, as seen by a respondent, is quitedifferent than as seen by the interviewer. The respondenthas no particular interest in the accuracy of the survey assuch. His sees a situation in which a person is asking himquestions; his answers will, in his opinion, influence theinterviewer’s opinion about him. Thus, he may be hesitantto answer accurately if he sees the question as one whichrelates to her social status. Such questions, therefore, willelicit incorrect answers which are useless. A questionnaireon magazine readership, for example, showed relatively littlereadership of pulp magazines in the upper-income groups.On the theory that these people might feel it was degradingto admit reading such “trash,” the study was revised. Peoplewere asked to contribute their old magazines to charity. Acount of these magazines showed that the number of womencontributing certain magazines exceeded the number whoreported reading them by 50 per cent. During the redemptionof war bonds, display of government posters and absenteeismwere points of personal prestige.

Questions of this type should be omitted unless a way canbe found to ask for the information that will obtain correctresponses. In many research studies it is desirableto know the income of respondents. It is commonly believedthat direct questions on this subject may elicit incorrectreplies. The amount spent for housing, however, isusually correlated with income. Furthermore, houses (andincomes) within a block tend to be similar. It is possible inlarger cities, therefore, to obtain estimates of income from

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census data by checking the average rental level of the blocksin which respondents live. In other cases respondents canbe asked how much rent should be for “houses in this block”.Such a question relates less directly to the respondent and,hence, is more apt to obtain an unbiased reply.

Another procedure which seems to reduce the resistance toreporting income data is to use an income card. On the cardvarious income classes are listed. For example:

Class A ...............................under $3,000

Class B ...............................$3,000-$5,000

Class C ...............................over $ 5,000

Interviewers hand over the card to respondents and ask intowhat class their income falls. Respondents seem to find iteasier to say “class A” than to report income of $2,7000.

– Determine the type of question to use: Once the contentof individual questions is decided, the researcher isready to begin framing the actual questions. Before hecan work on the wording of each question, he must decideon the type of questions to use. There are three majortypes from which he may choose: (1) Open (2) Multiplechoice, and (3) Dichotomous.

Multiple choice questions overcome some of thedisadvantages of open questions, but incur some newones. Open questions are subject to interviewer bias inrecording of answers. This is not the problem withmultiple choice questions where answers are in one ormore of the stated alternatives. All that the interviewerhas to do is to check the applicable reply. Thus, themultiple choice questions are faster and less subject tobias.

Also, multiple choice questions simplify the tabulatingprocess. The difficult and time-consuming editingprocess is reduced to a rapid check for mechanicalaccuracy.

Multiple choice questions give a list of alternativeanswers. It is important to point out that this list must

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include all alternatives or there will be a bias againstthose options which are omitted. The alternativesmentioned in a multiple choice questions will bereported by more respondents compared to a situationwhen open questions are used.

Multiple choice questions also tend to bias results bythe order in which the alternative answers are given.

This bias of position can be overcommed by alternatingthe order in which alternatives are listed.

Dichotomous question or two-way question, is anextreme of the multiple choice question. The idea is tooffer only two choices – yes or no, did or didn’t, cash orcredit, railroad or airline, etc. Such questions are themost widely used of the three basic types. The followingare examples of dichotomous questions:

u Would the service proposed by X lines makemotor freight service more useful to you?

u Is any of this discount normally passed on toother?

u Did you buy it or was it a gift?

u Was it new or used when you got it?

To understand the weight of responses, such type ofquestions are used. We have used such questions in oursample questionnaire appended at the end.

u Decide on question sequence: Once the wording of theindividual questions has been determined, it isnecessary to set them up in some order. The orderchosen can change the results obtained. There are threemajor sections in a questionnaire (1) The basicinformation sought, (2) Classification information, and(3) Identification information. Since questionspertaining to these sections tend to be of declininginterest to the respondent, the sections are usually putin the order shown. Questions relating to the basicinformation are place first. To help in analyzing thisinformation, it is usually necessary to be able to classify

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respondents on such bases as age, sex, income, educationand nationality. Questions on these points form theclassification section. The identification sectionidentifies all parties involved. This includes the nameand address of the respondent, and the names of suchindividuals as the interviewer, editor, and card puncher.These are used to permit checking for cheating amonginterviewers and to assign responsibility for the tasksdone.

u Decide on layout and reproduction: The physicallayout and reproduction of a questionnaire can influenceits success. Three major points should be considered inplanning the layout and reproduction of thequestionnaire:

l Securing acceptance of the questionnaire byrespondents,

l Making it easy to control the questionnaire, and

l Making it easy to handle the questionnaire.

u Pretest : Before a questionnaire is ready for the field itneeds to be pretested under field conditions. Noresearcher can prepare a questionnaire perfectly inthe first attempt, improvements can hence be suggestedin field tests. Pretests are best done by personalinterview even if the survey is to be handled by mail ortelephone. Interviewers can note the respondentsreactions and attitudes which cannot otherwise beobtained. After any pertinent changes in thequestionnaire have been made, another pretest can bedone by mail or telephone, if those methods are to beused in the survey. This latter pretest should uncoverany weakness peculiar to the method of communication.

u Revisions and final draft: After each significantrevision of the questionnaire, another pretest shouldbe done. When the last pretest suggests no newrevisions, the researcher is ready to print the actualquestionnaire to be used in the survey.

u Selection of a sample: An elementary unit is anelement or group of elements on which observations canbe made or from which the required statistical

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information can be ascertained according to a welldefined procedure. Elementary units or groups of suchunits which are convenient for purposes of sampling arecalled sampling units.

The totality of all sampling units belonging to the populationto be studied with their proper identification particulars istermed as the sampling frame. Editing would also help toeliminate inconsistencies or obvious errors due toarithmetical treatment.

When the data is to be processed by computers, then it mustbe coded and converted into the computer language. Thiscoding job should be done while editing the data.

Methods for Secondary Data Collection

Secondary data may either be published data or unpublisheddata such as:

u Various publications of the central, state and localgovernments.

u Various publications of foreign governments or ofinternational bodies and their subsidiary organizations.

u Technical and trade journals.

u Books, magazines and newspapers.

u Reports and publications of various associationsconnected with business and industry, banks,universities, economists, etc., in different fields.

u Reports prepared by research scholars, universitieseconomists, etc., in different fields and

u Public records and statistics historical documents, andother sources of published information.

The sources of unpublished data are many; they may be foundin diaries, letters, unpublished biographies andautobiographies and may also be available with scholars andresearch workers, trade associations, labour bureaus andother public/private individuals and organizations.

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Before using secondary data, the researcher must ensurethe reliability, suitability and adequacy of data.

Secondary Data � Internal

Internal records or published records are often capable ofgiving remarkably useful information. Sometimes, theinformation may be sufficient enough to give the desiredresult. However, this preliminary information shall most ofthe time help in developing the overall research strategyand hence must be undertaken before any further researchis contemplated. For a manufacturing industry, for example,the internal production and sales records, if designed andmaintained properly, can help in a big way even forformulating the companies strategies.

Secondary Data � External

External sources of data include statistics and reports issuedby governments, trade associations and other reputableorganizations such as advertising agencies and researchcompanies and trade directories.

In India, some of the major sources of secondary data are:

Indian Council of Agriculture, Central StatisticalOrganization , Army Statistical Organizations, NationalAccounts Statistics, Bulletin on Food Statistics, Handbookof Statistics on Small Scale Industries, RBI Bulletin, AnnualSurvey of Industries, Indian Labour Yon Book, etc.

Schedule Method

Schedule Defined

Schedule may be defined as a proforma that contains a setof questions which are asked and filled by an interviewerin a face to face situation with another. It is a standardizeddevice or tool of observation to collect the data in anobjective manner. In this method of data collection theinterviewer puts certain questions and the respondentfurnishes certain answers.

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The interviewer records as they are given:

Purpose/Objectives of the Schedule

The main objectives of the schedule are as follows:

u Delimitation of the topic: A schedule is always abouta definite item of enquiry. It's subject is a single andisolated item rather than the research subject in general.The schedule therefore delimits and specifies thesubject of enquiry.

u Aids to memorize: It is not possible for the interviewerto keep in mind or memorize all the information thathe collects from different respondents. With our astandardized tool, he might ask different questions todifferent respondents and thereby get confused whenhe requires to analyze and tabulate the data. Thereforeschedule acts as an "aide memoire".

u Aid to classification and analysis: Another objectiveof the schedule is to tabulate and analyze the datacollected in a scientific and homogeneous manner.

Types of Schedules

These are as follows:

Observation Schedule

The schedules which are used for observation are known asobservation schedules. Using this schedule, observer recordsthe activities and responses of an individual respondent ora group of respondents under specific conditions. Themain purpose of the observation schedule is to verifyinformation.

Rating Schedule

Rating schedules are used to assess the attitudes, opinions,preferences, inhibitions, perceptions and other similarelements or attributes of respondent. As evident from the

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term rating in these, schedules the value and the trend ofthe mentioned qualities is measured.

Document Schedule

These schedules are used in exploratory research to obtaindata regarding written evidence and case histories fromautobiography, diary, or records of government etc. It is animportant method for collecting preliminary data or forpreparing a source list.

Institution Survey Schedules

This type of schedule is used for studying different problemsof institutions.

Interview Schedule

Using his schedule, an interviewer presents the questionsto the interviewee and records his responses in the givenspace of the questionnaire.

Merits of Schedule Method

The schedule method has the following merits:

u Higher response: In the schedule, since a researchworker is present and he can explain and persuade therespondent, response rate is high. In case of any mistakein the schedule, the researcher can rectify it.

u Saving of time: While filling the schedule, theresearcher may use abbreviation or short forms foranswers, he may also generate a template. All thesesteps help in saving of time in data collection.

u Personal contact: In the schedule method there is apersonal contact between the respondent and the fieldworker. The behaviour, and character of respondentobviously facilitates the research work.

u Human touch: Sometimes reading something does notimpress as much as when the same is heard or spoken

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by experts as they are able to lay the right emphasis.This greatly improves the response.

u Deeper probe: Through this method it is possible toprobe deeper into the personality, living conditions,values, etc., of the respondents.

u Defects in sampling are detected: If there aresome defects in schedule during sampling it easilycome to the notice and can be rectified by theresearcher.

u Removal of doubts: Presence of enumerator removesthe doubts in the minds of respondent on the one handand avoid from the respondent artificial replies owingto fear of cross checking on the other hand.

u Human elements make the study more reliable anddependable: The presence of human elements makesthe situation more attractive and interesting which helpsin making interview useful and reliable.

Limitations of the Schedule Method

Following are the main limitation of the schedule method:

u Costly and time-consuming: This method is costly andtime consuming due to its basic requirement ofinterviewing the respondents. This becomes aserious limitation when respondents are not found ina particular region but are scattered over a widearea.

u Need of trained field workers: The schedule methodrequires involvement of well trained and experiencedfield workers. This involves great cost and sometimesworkers are not easily available forcing engagement ofinexperienced hands, which defeats the purpose trainedof research.

u Adverse effect of personal presence: Sometimespersonal presence of enumerator becomes an inhibitingfactor. Many people despite certain facts knowingcannot say them in the presence of others.

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u Organizational difficulties: If the field of researchis dispersed, it becomes difficult to organize it.Getting trained manpower, assigning them dutiesand then administrating the research is a very difficulttask.

Characteristics of a Good Schedule

The following are the essentials or characteristics of a goodschedule:

u Accurate communication: It means that the questionsgiven in the schedule should enable the respondent tounderstand the context in which they are asked.

u Accurate response: The schedule should structured insuch a manner so that the required information areaccurate and secured. For this, following steps shouldbe taken.

l The size of the schedule should be precise andattractive.

l The questions should be clearly worded and shouldbe unambiguous.

l The questions should be free from any subjectiveevaluation.

l Questions should be inter-linked.

l Information sought should be capable of tabulationand subsequent statistical analysis.

Suitability of Schedule Method

This method is generally applied in the following situations:

u The field of investigation is wide and dispersed.

u Where the researcher requires quick result at low cost.

u Where the respondents are educated.

u Where trained and educated investigators are available.

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Table 7.3: Distinction between Schedule and Questionnaire

Description Schedule Questionnaire

1. Methodology Direct method of primary Indirect method of data

data collection. collection.

2. Contact with Direct contact exists in this Direct contact may not exist

respondent method between respondent in this method. Response may be

and researcher. through post only.

3. Coverage of area Limited geographical area. Useful for very largely dispersed

geographical area.

4. Reliability of data High degree of reliability Less reliable as personal contact

collection. may not be there.

5. Types of questions Short and to the point answers Lengthy and elaborative

type questions which are of questions: answers required may

yes or no nature. be are detailed and lengthy.

6. Response to the Very high. Low response.

question

7. Clarification It is done during Not possible when questionnaire

questions. direct contact and discussion are

mailed.

8. Distribution Full questionnaire or Full text of question have to be

part there of can be distributed. distributed to the respondents.

9. Persuasion for It is feasible as respondents It is not always feasible to

response motivate can be as respondents

motivated. respondents.

10. Use in sampling Very successful method May cannot be used in sampling

method of research in sampling method of method of research.

research.

11. Instrument design Questionnaire are framed The questions are framed

keeping in view the difficulties keeping in view the educational

of tabulators and field workers. and economic standard of the

respondents.

12. Bias in the data There is great degree of bias in Probability of biasness in data

the collection of data. collection does not exist.

13. Cost and time Very large cost and time Less costly and less time

requirement is required. consuming.

14. Trained staff Trained and qualified staff. Not so trained staff is required.

15. Organization Difficult to organize. Simple to organize.

Questions to be Included in the Schedule

u The questions should be short, simple and easy tounderstand by the respondent.

u The questions should have some direct relation to theproblem.

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u The information collected through schedule should beamendable to statistical manipulation and tabulation.

u The questions must be interrelated and such that crosschecking is feasible.

u Questions should be free from personal bias and shouldnot hurt the feelings of the respondents.

u Questions should be standardized.

u Precise terms should be used in framing the questions.

u They should be subject to pretesting.

Organization of Schedule

1. Selection of respondents: Generally sampling methodis used for selection of respondents. The sample mustbe representative and should contain the biographicaldetails and other relevant information about therespondents.

2. Selection and training of the field workers: In theschedule method, field workers carry out the interviewand collect data. Since there is a shortage of trainedfield workers, they have to be selected carefully.

3. Interviews and correct replies: For a successfulinterview and correct result following steps are to betaken:

u Correct approach: The field worker shouldapproach the respondent in a manner so thatthe respondent understands correctly thepurpose. Generally, the respondent should beapproached when he is not busy and willing tocorporate.

u Proper response: For proper responses theresearcher should be able to convince therespondents.

u Correct reply: For proper response and correctreply the respondent should not be hurt. He shouldbe understood in right perspective and context.

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Testing the Validity of the Results

After receipt of the filled-in schedule it should be subject tocertain tests and checking so that the correctness of thecollected data can be established. It can be done in severalways. The investigator himself may select the respondentand administer the schedule and find out the variation, ifany. If variations are of a large degree then it should be eitherrejected or modified.

Research through Case Study Method

Case study method basically a qualitative research analysispertaining to an organization. In some cases, however, wherequantitative details about the organization are available, casestudy may also provide certain insights to operational detailsof research questions scientifically. Normally case studymethod of research focuses on organization or at best two orthree homogenous or competing organization (forbenchmarking) unless it is a cross-organizational study toauthenticate any management practices or approve ordisapprove any hypotheses framed by a researcher toestablish certain theories. Unlike other methods of research,case study method requires in-depth analysis of somesituations and study on their inter relationship in anorganization. Important characteristics of case study methodof research can be listed as under:

i. In case study method, a researcher can choose to studya single organization or social unit or more. Even bemay confine his focus only on certain areas or situationsof the sample organization. To illustrate if the purposeof research is to review an organization's strategy aresearcher may critically examine, the vision, mission,goals, objectives, strategies, action plan and policies anddocument his observations. Why Reliance can retainmanpower or GE capital not or for that matter evenTCS not, despite the fact that both GE and TCS havepro-active HR policies and Reliance is more traditionalin their approach is something which can be answeredanalyzing their strategies.

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Why HLL is successful in repositioning their 'Lifebouy'brand and why Colgate not again is embedded in theirmarketing strategy?

ii. Case study method research is done very intensivelyfocussing on some limited identified areas rather thanexhaustively. Such study may be longitudinal in naturefor drawing correct inferences.

iii. Even though perennially case study method isconsidered a qualitative analysis, modern researcherscan also do quantitative analysis and interpret theorganizational issues, when such detail are available.For example, a researcher can analyze the resourceallocation strategy of an organization in terms of costbenefit analysis. Similarly efficacy of a compensationstrategy can be studies comparing outsourcing vis-a-visemployment on permanent payroll.

iv. In case study method, a researcher always attempts toestablish a causal relationship between various factorscouching qualitative and quantitative information. Toillustrate effective Customer Relationship Management(CRM) may be co-related with increased market share.Employee motivation may be related to productivity.

v. Case study method of research is direct approach and,therefore, requires analytic rigour and experience.

vi. Case study methods unleash the best managementpractices and therefore significantly contribute inenriching the theories. For example benefit of 'directparticipation', which is a strategy to use collectivewisdom of the people to develop a response capacitytoward some targeted goals of the organization wouldnot have been known to the world, unless the practicesof 'Chevron', the petroleum giant, brought into thelimelight by the researchers. Despite its advantages,research through case study may often suffer from theproblem of generalization and unless properlystructured may also vitiate the purpose of research.Proper structuring requires initial identification of theresearch problem, collection of data, establishing casual

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relationship and also finally developing remedialmeasures. Authors suggest unless researcher hasproper knowledge about business process, one shouldavoid using this method, as strong business and analyticskills are essential prerequisite for the success of suchresearch.

Review Questions

1. What are the various methods of collecting statisticaldata? Which of these are reliable and why?

2. Distinguish between primary and secondary data.

3. What is primary data? What are the advantages andlimitations of the primary data? Describe briefly variousmethods of collecting primary data.

4. Describe the importance of interview method in businessresearch.

5. Define the term schedule. Explain the objectives of theschedule and describe briefly the types of schedule.

6. Explain the case study method of data collection. Whatare the characteristics of case study method? Explainits advantages and limitations.

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APPENDIX-1

INTRODUCTION AND GUIDELINES TO CASE STUDY(with a sample Case Study and its solution)

What is a Case?

A case is a short description, in words and numbers, of an actualmanagement situation. A typical case consists of number of pages ofprose description with some quantitative materials (figures), exhibits,organization charts, graphs or tables.

The use of cases for advanced management education started at HarvardUniversity in 1908.

What is a Case Study?

Case study is a systematic way of helping students to learn fromexperience. Such studies are intended to serve as the basis for classdiscussion and not as an illustration of either good or bad managementpractice. They are not intended to be a comprehensive collection ofteaching material. They provide a useful backbone to a programme ofstudy. In research also we use this method now-a-days.

Steps for a Case Study

1. Read the case carefully and note down all the material facts andidentify the problem(s).

2. Mention the area of management to which the main problemrelates. It is possible that the problem may overlap other area aswell, which may demand simultaneous solution. Total view of thesituation should not be lost.

3. Place yourself in the position of a manager and view the casesituation and the case problem.

4. The analysis should be from a managerial angle – unbiased andobjective.

5. List out various possible alternatives and then prioritize on thebasis of comparative superiority and feasibility.

6. Select the best alternative and state the same as your decision.

7. Indicate an estimate of outcome including the possible side effects,if any.

Important Guidelines

– Note that there is no single correct solution even for a specificmanagement problem. Logical thinking in line with the acceptedbasic principles and practices (processes) of management is whatis judged and assessed by the examiner.

– Questions which are given at the end of each case study suggestthe line of enquiry, hence study the questions carefully.

– Mere restating the facts of a case report without giving any meaningshould be avoided.

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Incident Process/Incident Study

Incidents are a short sketch (within 50 to 100 words) of something whichhas actually happened. This provides students with greater opportunityto learn by doing things for themselves from situational experiences.Often the incident seems trivial but its implications are important. Thoroughinvestigation of the facts of incident is necessary for two-part decision;

– To settle the immediate issue,

– To suggest long-term preventive and remedial action.

Example of a Case Study

The Case Problem

Vinod was the works manager of Laxhmi Engg. Rahul was with thecompany as finance manager and head of the accounts & finance divisionreporting to the works manager.

Rahul’s general attitude was to be tight fisted with financial matters. Hewas always conscious of the need to conform to company policy andprocedures and he firmly opposed any deviation from policy, but wasoften willing to explain the reasons for his view. He prided himself as aman of principles. Vinod, works manager, was the type that wanted totake action regardless of past practice or policy. He considered himself aresult oriented manager.

The differing attitudes of the works manager and the finance managerhad led to conflicts on past occasion and Vinod had warned Rahul ontwo occasions that if Rahul could not carry out his instructions he wasfree to search for a job elsewhere. Rahul had argued his case with ameasure of success stating that his approach was proper and that infinancial matters policy guidelines had to be observed.

One afternoon Vinod approached Rahul and said, “Here is an incentiveplan for the maintenance group. I am notifying it today and introducing itfrom tomorrow. Have a look at it,” Rahul appeared to be surprised. Hehad not known that an incentive plan was being contemplated formaintenance workers as the company’s policy till then was to payincentives only to direct production workers. Nevertheless he took theplan with him and returned to Vinod a couple of hours later. “You can’tintroduce this plan straightaway”, said Rahul to Vinod, and added, “wehave to give this some more thought. Our maintenance costs are toohigh mainly due to lack of adherence to norms on consumption of spareparts. This incentive plan gives no weightage to consumption of spareparts. Further, it will only add to maintenance costs without any realbenefit to the company.”

Vinod’s reaction was one of anger. “You understand nothing of incentiveplans”, he retorted, and added, “spare-parts consumption is high due topoor quality of spares bought by the materials department. Anyway, Idon’t intend to waste time on this with you. I am notifying this incentiveplan today”.

An altercation followed and the arguments of both Rahul and Vinodbecame so loud that they attracted the attention of others in the hall,outside Vinod’s office. “I am the boss here,” screamed Vinod and added,

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“if you can’t work with me and obey my instructions, you are free to leaveyour job and go elsewhere.”

A few moments later Rahul was back in his office, tired and sullen. Hecalled his secretary and said, “now, I have no option, please write down”.He dictated his letter of resignation.

Questions

1. Discuss the leadership style used by Vinod. How effective is hisstyle? What changes would you advise?

2. To what extent were Rahul’s needs being considered? What kindof organizational climate was being created?

Read the case carefully and analyze the content, i.e., the situation andthe personalities involved before answering the questions. The analysiscould be done mentally after jotting down the salient points arising in thecase:

Analysis of the Case

This is basically a case of restraining leadership but to some extent italso brings out issues relating to motivation of subordinates.

The facts of the case reveal:

i. Difference in the basic approach to leadership between Vinod andRahul. Rahul is conservative in outlook, opposed to deviationsfrom policy and a man of principles whereas Vinod tends to ignorecompany policy and practices in an effort to be result-oriented.

ii. Rahul expects a role whereby he can state his differences with hissuperior. He is also capable of convincing his superior byexpressing his point of view successfully.

iii. Vinod is autocratic in his approach. He appears to be a personwho concentrates authority and decision-making in himself andviews leadership as a matter of issuing orders and believes thatsubordinates must obey them unquestioningly.

iv. The situation as revealed by the facts of the case is one of conflictbetween the subordinate and superior mainly due to the leadershipstyle adopted by the superior.

v. Vinod does not consider it necessary to involve his subordinate indecision-making or explain the rationale of the reasons for whichhe wishes to make changes in respect of the incentive scheme,deviating from company policy.

vi. There is no effort on the part of Vinod to answer the doubts raisedby Rahul on the demerits of the proposed incentive scheme clearlyand cogently.

vii. When Rahul explains his reasons for the need to give some morethought before introducing the change in the incentive scheme,the reaction of Vinod is one of anger. Anger and admonition areexpressed by the superior openly in front of others, thus leavingthe subordinate humiliated and frustrated.

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viii. The conflict leads to a decision by the subordinate to quit theorganization.

Leadership Style Used by Vinod

Vinod’s leadership style is autocratic and authoritarian. An autocraticleader concentrates all authority and decision-making powers on himself.There is no participation by his subordinates in the decision-makingprocess, they simply do what they are told to do.

An autocratic leader believes that his leadership is based on the authorityconferred on him by his position and that his subordinates should followinstructions unquestioningly.

Autocratic leadership leads to lack of confidence and insecurity in thesubordinate and stifles creativity and innovative ability of the subordinate.The autocratic style stifles subordinate development and organizationaleffectiveness.

How Effective is Vinod’s Style?

Vinod’s style is not effective, viewed from the point of view of theleadership that a works manager should provide. In fact it is Vinod’s stylethat has led to a major conflicting situation within the organization betweenhim and the finance manager which has also attracted the attention ofother persons in the organization. This is bound to lead to a sense of fearamong all the persons in the organization and also frustration due tolack of opportunity and fear on the part of subordinates to express a viewdifferent from that of their superior.

Vinod’s style of leadership will lead to resentment and, over a period,resistance to his orders. Further, the style adopted by Vinod will lead tohis subordinates showing no active interest in their job, becoming hesitantin taking initiatives and dependent upon the boss’s, instructions. All thesefactors can defeat the purpose for which Vinod is attempting to modifythe incentive scheme.

What Changes would You Advise?

The facts of the case reveal that Rahul was always cognizant of thecompany’s policies and procedures. He had the ability to argue his viewpoint with a measure of success and where he differs from his superior,he was willing to state the reasons about his differences. In this situationVinod should have adopted a participative style of leadership with trustand confidence in Rahul so that communication with him is open andteamwork is built up.

To be an effective leader, Vinod should have a greater measure ofconfidence and trust in his subordinates, help them in the developmentof methods to achieve organizational objectives and also encourageparticipation.

The facts of the case show that Rahul is willing to explain to his superiorhis points of view on matters where he differs from his superior. He seeksthe freedom to discuss matters. His objective is to interact with his superiorwithout fear bearing in mind organizational goals.

Lack of communication that underlines the leadership style of Vinod andthe sense of insecurity that stems from this leadership style have an

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adverse impact on the feeling of pride that Rahul has. Pride is a powerfuland valuable motivator and when this is stifled, the subordinate feelsfrustrated.

Rahul expects a measure of involvement in decision making. Involvementsatisfies one’s ego and self-esteem. But in the present situation Rahul isdenied the opportunity for involvement in decision-making.

Rahul's needs for motivation are not satisfied to any extent. This is thereason why he decides to leave the organization.

Vinod’s style will lead to a climate where the subordinate refuses toparticipate in the decision-making process. Subordinates will in thissituation become ‘yes men’ and refuse to confidently accept authoritydelegated to them. In this environment, group effectiveness will be lost. Inthe final analysis this adverse climate will not provide a conduciveatmosphere for Vinod to be an effective leader who can functioncomfortably and achieve results competently. Vinod’s claim that he is a‘result-oriented’ manager will be self-defeating if he does not direct theorganization to a participative style of leadership.

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Presentation of Data

All business decisions are based upon evaluation of somedata. Availability of right information is very important formaking right decisions. Once the data begins to flow in,attention turns to data analysis.

It is almost impossible for the management to deal with allthis data in its raw form. Such data must be presented in asuitable and summarized form without any loss of relevantinformation so that it can be efficiently used for decisionmaking.

Whenever there is a need to present numerous figures or todescribe a technical process or procedures, graphic aids canhelp to communicate this information to your audience morequickly. The two graphic aids mostly used in research reportsare tables and graphs. Besides making the report easier toread and understand, graphic aids improve its physicalappearance.

203

Objectives


y Statistical methods of analysis of data.

y Statistical methods of interpretation of data.

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General Guidelines for Presenting Graphic Aids

Normally, it is best to place an illustration within the text ifthe reader needs to refer to it while reading the report. Itshould be placed as close to the discussion as possible. Ifinformation is supplemental or extremely lengthy, it can beplaced in the appendix.

All graphic aids should contain the following elements:

1. Table or figure number: This permits easy location inthe report.

2. Title: The title should clearly indicate the contents ofthe table or figure.

3. Boxhead and subhead: The boxhead contains labelsto the column in a table, while, the subhead containsthe labels for the rows.

4. Footnotes: Footnotes explain or qualify a particularsection or item in the table or figure.

Data can be presented in tabular or graphic form. The tabularform (tables) implies numerical presentation of data. Thegraphical form (figures) involves the presentation of data interms of structures which can be visually interpreted, e.g.,bar charts, pie charts, line charts.

Oral Presentation

Many companies require oral presentation of researchreports. Prior to the presentation follow this checklist:

1. Check all equipment (e.g., light, microphones, projectorsetc.) thoroughly before the presentation.

2. Have a contingency plan for equipment failure.

3. Analyze your audience. How will they react to theresearch findings?

4. Practice the presentation several times. If possible, havesomeone comment on how to improve its effectiveness.

5. Start the presentation with an overview – tell theaudience what you are going to tell them.

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205UNIT 8 Data Analysis-Methodsu


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6. Face the audience directly at all times.

7. Talk to the audience or decision makers, rather thanread from a script or a projection screen.

8. Use visual aids effectively – charts and tables should besimple and easy to read.

9. Avoid distracting mannerisms while speaking.

10. Remember to ask the audience if they have any questionsafter your report is concluded.

Editing

The first step in analysis is to edit the raw data. Editingdetects errors and omissions correct them as far aspossible.

Purpose of Editing

u To ensure accuracy,

u To bring about consistency with other information,

u Make sure that data is uniformly entered,

u It is complete, and

u Arranged to simplify coding and tabulation.

The editor’s responsibility is to decide which of the responsesis consistent with the intent of the question or otherinformation in the survey and is most accurate for itsindividual respondent.

Classification of Data

When the raw data has been collected and edited it shouldbe put into an ordered form (ascending or descending order)so that it can be looked at more objectively. The nextimportant step towards processing the data is classification.Classification means separating items according to similarcharacteristics and grouping them into various classes. Theitems in different classes will differ from each other on thebasis of some characteristics or attributes.

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The classification of data into limited categories specifiessome data detail but is necessary for efficient analysis.

Coding

Coding is the process whereby the data is assigned anumerical code and value so that it can be more easily fittedinto appropriate categories. Coding is necessary wheremachine tabulation is used.

There are four rules that guide coding:

u Appropriate to the research problem and purpose

u Exhaustive

u Mutually exclusive

u Derived from one classification principle.

Data Entry

Data entry convert information gathered by a researcherthrough primary and secondary method to a medium forviewing and manipulation.

Tabulation

Tabulation consists of counting the number of cases whichfall into the established categories. Before tabulation cantake place the plan of analysis must be thought through. Atabulation plan which specifies the precise counts to beobtained needs to be prepared. Tabulation may beaccomplished using manual or machine methods. Bothprocesses have unique advantages and disadvantages.

Machine tabulation is preferable where a large number ofquestionnaires is involved and where cross tabulation isplanned.

After the tabulation step has been completed, it is necessaryto determine whether any differences exist and whetherthese differences are statistically significant. If the resultsfrom a marketing study are to be useful they must beorganised and summarized in such a way as to enable theobjectives of the study to be achieved. This requires the use

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of those summary statistical measures which typify the groupsuch as arithmetic mean and percentages, and the use ofthose measures which indicate dispersion such as standarddeviation. All these measures have their advantages anddisadvantages and the analyst must be competent inselecting the most appropriate measure to use.

Further, since most marketing data are collected using asample, the reliability of the summary estimates must bedetermined. Standard error and confidence limits are twoterms and concepts which are fundamental to the generalsubject of reliability.

To determine the significance of any difference existingbetween a sample estimate and a similar estimate fromanother sample requires the use of tests of significance. Suchtests indicate the probability of the difference having a curedue to random sampling variations. All these tests make useof the standard error and confidence limit concepts.

The next step in the analysis procedure consists in trying toexplain ‘why’ differences exist. This is accomplished byattempting to identify a casual relationship between two ormore variables. To accomplish this, the survey data arearranged to approximate and control the experiment. Casualanalysis requires cross tabulations. This procedureintroduces one or more additional variables into the analysisby dividing the sample into subgroups. This helps to confirmor reject the earlier relationship. In introducing additionalvariables, the analyst must consider the size of the samplein the various subgroups and also be on guard againstspurious correlations.

Statistical Analysis and Interpretation of Data:Non-parametric Tests

Introduction

Theoretical aspects of research have been adequatelydiscussed to enable the readers to understand norms in theirtrue spirit. This chapter is intended to focus on basicstatistical techniques and their applicability in research.

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As has already been pointed out, social science research, orto be more particular, research on commerce andmanagement, mostly deals with qualitative variables. Unlessqualitative impressions are duly quantified, researchfindings may not be clearly understood and may even bequestioned by others as to their authenticity. Statisticaltechniques help the researcher to counter this problem. Infact, it is being increasingly felt that understanding basicstatistical norms is a prerequisite for the success of aresearcher.

Stuart A Rice put forth the following arguments to justifyquantitative expressions of research findings:

u It reduces individual bias to a minimum.

u Permits verification by other investigators.

u Reduces and at the same time makes evident the marginof error.

u Replaces the less exact meaning of descriptive wordswith the precision of mathematical notation.

Data collected from secondary sources may be compiled withgreat ease in the form of tables. Data from secondary sourcesenables us to define the characteristics of phenomena wewhich again try to investigate in the light of our own findingsbased on data collected from primary sources.

In some researches, however, where we do not collect orcompile data from primary sources, we generally base ourarguments by mere analysis of data from secondary sources.For example, an investigation on the ‘structural change ofoccupational pattern in India’ may be made based on analysisof census data over dacades. Similarly, changing pattern ofsectorial distribution of Net Domestic Product (NDP) inIndia may be analyzed in the light of secondary data alone.Use of secondary data in direct form may not always help aresearcher to relate such quantitative trends to his researchproblem. For example, an absolute analysis of wage cost andits shares in total cost of production in comparison with othercountries may certainly lead a researcher to conclude thatlabour wage costs in India are relatively poor. But if a

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researcher, with some amount of inquisitiveness, goes intothe depth of problem and tries to compare the per capitashare of wages as percentage to the per capita share of NDP,the picture will be totally different. In fact, Indian workers,in this respect, are more privileged to gain a higher stakethan workers in UK, USA and Japan. Readers here arerequested to refer the world development reports publishedby the world bank.

Again, while using data from secondary sources, theresearcher should thoroughly check the background of suchdata collection, its methodology and limitations, etc. Themethodology of data collection varies even for same dataprovided by different governmental agencies in India. Forexample, data related to labour matters as made availablein Indian labour year books and annual survey of industrieswidely varies for obvious differences in methodologyfollowed in collection and compilation. Even the same sourcemay use different methodologies in different years ofpublications. The census data is a glaring example in thisrespect.

Collection of data from primary sources involves survey whichmay be carried out either by interviewing the samples inperson or by mailing questionnaires to samples. Since mailingresponse is alarmingly poor, the researchers here are advisedto follow the interview methods for carrying out the survey.In selecting samples, thus, he should be cautious. If he isunable to visit areas widely dispersed, sample should bechosen from those areas where he can afford personal visits.Similarly, he should also consider other constraining factorslike time and money while deciding the number of samples.

Usually in case of structured questionnaire, samples areinterviewed. Structured questionnaire ensures easyquantification.

After necessary collection of data from primary sources, withthe help of tabulation, the researcher arranges these in someconcise and logical order. And for such purpose he or sheneeds to classify the data. The basis of classification dependson the characteristics of data collected. In most cases such



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classification scheme is pre-determined. However, suchscheme may get altered or modified after data collection.

Following criteria are generally considered for statisticalclassification:

u Geographical

u Chronological

u Qualitative

u Quantitative

Under geographical classification, data are organised interms of geographical division as country, state, region, city,village, block, ward etc. Similarly, century, decade, year,month, week, day, etc., is considered while arranging datachronologically. Qualitative attributes such as sex, religion,literacy, occupation, marital status, etc., are also consideredin data classification. Distribution of data by size andmagnitude (frequency distribution as for example) is donethrough quantitative classification. After determining theclassification, the collected data are sorted and counted asper various categories. For handling large data, handtabulation may not always be possible. When mechanicaltabulation is used, data are first transferred to punch cardsby punching holes for each item. Then with the help ofsorting machine and tabulation machine, data are finallyarranged in the form of tables as per the above classification.

But in our country, it is not always possible for a researcherto avail such mechanical facilities and in most casestabulation part is completed manually.

Assigning numerical values to each variable is a difficult taskfor a researcher. Quantitative variables, i.e., variables whichhave a certain number of defined units may either becardinally (explicit) or ordinally (implicit) manipulated bysimple mathematics. But qualitative variables may bemanipulated only by defined characteristics. Similarly, theresearcher should also understand the basic differencebetween continuous and discrete variables while arrangingdata.

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With the help of frequency distribution, variables areclassified according to magnitude or size. After necessarytabulation, the next task of the researcher is to arrange themin statistical tables. There are certain standard norms whichusually are followed in constructing tables.

For simple understanding it should be remembered thatsuch tables should be able to reveal significant relationsamong the data or should be able to emphasize certainfacts.

The frequency distributions may also be presented in theform of graphs. Histogram, frequency polygon, smoothedfrequency curve are the commonly used curves.

After necessary frequency distributions to represent thecharacteristics of entire series by few significant figures, wetake the help of averages. Mean, median and mode are threeof the most commonly used averages.

Here we have discussed various statistical models forresearch.

Hypothesis Testing

Inferences on population characteristics (or parameters)are often made on the basis of sample observations,especially when the population is large and it may notbe possible to enumerate all the sampling units belongingto the population. In doing so, one has to take the helpof certain assumptions (or hypothetical values) aboutthe characteristics of the population if some such informationis available. Such hypothesis about the population istermed as statistical hypothesis and the hypothesis istested on the basis of sample values. The procedureenables one to decide on a certain hypothesis and test itssignificance. “A claim or hypothesis about the populationparameters or values is known as null hypothesis and iswritten as, Ho.”

This hypothesis is then tested with available evidence and adecision is made whether to accept this hypothesis or reject

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it. If this hypothesis is rejected, then we accept the alternatehypothesis.

This hypothesis is written as H1.

For testing hypothesis or test of significance we use bothparametric or standard tests and nonparametric ordistribution free tests. Parametric tests assume withinproperties of the population, from which we draw samples.Such assumptions may be about population parameters,sample size, etc. In case of non-parametric tests, we do notmake such assumptions. Here we assume only nominal orordinal data.

Important parametric tests used for testing or hypothesisare:

i. z – test

ii. t – test

iii. x2 test; and

iv. f – test

When x2 test is used as a test of goodness of fit and also as atest of independence, we use non-parametric tests.

As has been stated earlier all parametric tests used fortesting of hypothesis are based on the Assumption ofnormality, i.e., population is considered to be normallydistributed.

Procedure for Testing of Hypothesis

1. State the null hypothesis as well as the alternatehypothesis: For example, let us assume the populationmean = 50 and set up the hypothesis m = 50. This iscalled the null hypothesis and is denoted as;

Null hypothesis, Ho : m = 50

Alternative H1 : m ≠ 50

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2. Establish a level of significance (prior to sampling):The level of significance signifies the probabilityof committing Type 1 error µ and is generally takenas equal to 0.05. Sometimes, the value µ is establishedas 0.01, but it is at the discretion of the investigator toselect its value, depending upon the sensitivity of thestudy. To illustrates per cent level of significanceindicates that a researcher is willing to take 5 per centrisk of rejecting the null hypothesis when it happens tobe true.

3. Choosing a suitable test statistic: For the purpose ofrejecting or accepting the null hypothesis, a suitablestatistics called “test statistics” is chosen. Thismeans that Ho is assumed to be really true. Obviouslydue to sampling fluctuations, the observed value ofthe statistic based on random sample will differfrom the expected value. If the difference islarge enough, one suspects the validity of theassumption and rejects the null hypothesis (Ho). On theother hand, if the difference may be assumed due tosampling (random) fluctuation, the null hypothesis (Ho)is accepted.

Fixing up the Level of Significance and Defining the Critical rejection)

Regions

Based on the sampling distribution of the statistic, theprobability of obtaining a difference equal to or greater thanthe observed difference is calculated on the assumption thatthe null hypothesis is true.

If we select the value of µ = Level of significance = 0.05,and use the standard normal distribution as our teststatistic for testing the population parameter u, thenthe value of the difference between the assumption ofnull hypothesis (assumed value of the population parameter)and the value obtained by the analysis of the sample resultsis not expected to be more than 1.96 s at u = 0.05.

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This relationship can be shown by the Figure 8.1 givenbelow:

Figure 8.1

z = Observed value of the statistic (x) – Expected value (u)

Standard error of the estimate

Calculated value of z as given by the formula above,

= |Absolute value|

Now find out the critical (or tabulated) value of the statistic(z or t or f, etc).

z-test is used to measure the difference between any variablevalue (x) and the mean of all variable values or'x' values, which is indicated by 'm', divided by the standarddeviation(s). It is based on the normal probabilitydistribution. In following cases, we find the usage of2-test:

i. To judge the significance of statistical measures,particularly the mean. This is done by comparing theobserved value (test statistic) with the probable value(table value) at a specified level of significance.

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12345678123456781234567812345678123456781234567812345678

123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

Acceptance Zone

RejectionZone

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ii. It is used to compare the mean of a sample with somehypothesized mean of the population.

iii. It is also used to judge the significance of differencebetween means of two independent samples.

iv. It can also be used for judging the significance ofdifferent between sample and population proportion orproportions of two independent samples.

v. Finally this test can also be used for measuring thesignificance of medium, mode coefficient of correlationand other measures.

We have illustrated usage of z-tests in testing hypothesis withsome real life examples. In case of small sample and in caseswhen sample variance is constructed as population variance,population variance, being not know, we use t-test based on t-distribution to judge the significance of sample mean orsignificance of difference between two sample means.Normally when sample size is less than 30 we use t-test.

Let us explain the usage of z-test and t-test within flow chart,as Figure 8.2 given below:

Figure 8.2: Flow Chart for 'z' and 't' Tests

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Start

Is sYes Use z test in

computationsStop

StopUse z test incomputations

No

Is n>30? Yes

No

Use t-test incomputations

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Questions

1. A company manufacturing automobile tyres finds thattyre life is normally distributed with a mean of 40,000kms and standard deviation of 3,000 kms. It is believedthat a change in the production process will result in abetter product and the company has developed a newtyre. A sample of 64 new tyres has been selected. Thecompany has found that the mean life of these new tyresis 41,200 kms. Can it be concluded that the new tyre issignificantly better than the old one?

In a problem of this type, we are interested in testingwhether or not there has been an increase in the meanlife of the tyre. In other words, we would like to testwhether the mean life of new tyres has increased beyond40,000 kms.

The various steps in testing the hypothesis are:

i. Null hypothesis and alternative hypothesis are:

H0 : m = 40,000 kms

H1 : m ≠ 40,000 kms

ii. The significance level is taken as 0.05. That is, in5 out of every 100 occasions, there is a risk of beingwrong in accepting or rejecting the hypothesis.

iii. The test criterion is the z-test.

iv. Computations : Substituting the value of standarddeviation, s = 3000 kms in the formula:

σ σx n

=

= 3000

64

= 375

zx

x

= − µσ

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41200 40000

375

−

= 3.2

v. Decision: At 0.05 level of significance, the critical(table) value of Z = ± 1.64.

As the computed value of Z = 3.2 falls in therejection region we reject the null hypothesis thatm = 40,000 kms. That is, the alternative hypothesisthat m > 40,000 kms is accepted. We, therefore,conclude that the new tyre is significantly betterthan the old one.

2. Assuming that the average annual income of low levelgroup is Rs 18,750 at national level with standard,deviation of Rs 2610. A random sample of 100employees of this group was taken and it was found thattheir average salary was Rs 19,240.

At a level of significance a = 0.05 (95% confidencelimit), can we conclude that the average salary ofthis group is representative of the national (salary)average?

Solution

i. Null Hyp. Ho : m = Rs 18,750 n = 100,

Alternative Hyp H1 : m # Rs 18,750 x = Rs 19,240

ii. Level of Significance as given a = 0.05 s = Rs 2,610

iii. Test Statistic Z = x

SE

− µ

SEn

= σ Where, x = Sample mean

m = Population mean

s = Standard Deviation of population mean

Z Calculated

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iv. Since it is a two tailed test,

u The rejection region will be on both sides, i.e., 2.5%on RH and 2.5% on LH.

u Region of acceptance = 95% z = ± 1.96 (FromTable)

z = calculated =19240 18750

2610 1001 877

− =/

.

Since the calculated value of z is lower than thetabulated value, the null-hypothesis standsaccepted.

\ The sample average income is a representative ofthe national average income.

Second Method

What are the limits within which the average salary lies?

m = 18750

z = ± 1.96 at a = 0.05

z

x

n= − µ

σ/

± = −1 96

2610 100.

/

x µ

x = ± FHG

IKJµ 1 96

2610

10.

Hence x1 = 18238

x2=19261

As the value Rs 19,240 lies between x1 and x2, hence thesample average income is representative of the nationalaverage income.

If the sample mean lies within these values, then wecannot reject the null hypothesis.

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One Tailed Test

3. A manufacturer of light bulbs claims that a light bulblasts on an average 1600 hrs. We want to test his claim.Here, we can reject the hypotheses if the average life ofbulb is much less but we cannot reject it if it is greaterthan 1600 hrs. (Whatever big value it may be). A sampleof 100 light bulbs was taken at random and the averagelife was computed to be 1570 hrs with a standarddeviation of 120 hrs. At a = 1%, test the validity of theclaim of the manufacturer.

Solution

As no of observations per sample is very large , we can takes = s

Null hypothesis, Ho : m > 1600Alt hypothesis, H1 : m <1600at 99% confidence limit (a = 0.01)

Z (Tabulated) = – 2.33 on the left tail of the standardizednormal curve

Acceptance Region

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18750 19240 19261

R e j e c t e d

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z=- 2.33 and SEs

n=

120

100=12

z' x m

/ n

1570 1600

12

30

122.5|Z| 2.5=

-=

-=

-=- =

σ

As calculated value of |z| > Tabulated value of |z|

Hence, Ho stands rejected, i.e., management claim is notvalid.

4. The supporters of a party claim that their party has 60%following in Delhi. To test this claim a city paperundertakes a test sample of 400 persons on the Internet,220 people support this claim. Test at 1% level ofsignificance whether the supporters claim is correct ornot.

Solution

It is a one tailed test

H0 : p = 0.6 (or H0 : p ³ 0.6)

H1 : p < 0.6

Sample proportion Px220

4000.55= =

z = 2.33

SEp 1 p

npqn

=−

=b g

= =( )06 04

400. .

0.0245

zPx P

/ n

0.55 0.6

.02452.04=

-=

-=-

σ

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|z| tabulated = -2.33 at 1% level of significance.

As, calculated < tabulated, hence null hypothesis isaccepted.

\ Claim of the party is valid.

5. An educator claims that the average IQ of city collegestudents is no more than 110. To test his claim, a sampleof 150 students is taken and their average IQ was foundto be 111.2 with a standard deviation of 7.2 at a = 0.01.Test his claim.

Solution

Here n = 150 H0 : m £ 110

x = 11.2 H1 : m > 110

s = 7.2

Clearly it is a one tailed test, as we shall reject his claim ofAv value of IQ if found to be significantly higher than 110.

m = 110

zx

SESE

n

s

n

7.2

1500.59=

-= = = =

µ σ

Z calculated111.2 110

0.592.03=

-=

Z tabulated = 2.33 ( at a = 0.01)

As Z calculated < Z tabulated .

Hence, null hypothesis is accepted.

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6. An airline claims that at most 8% of its lost luggage isnever found. A consumer advocacy agency wants to testthe claim at 99% confidence level. Study of 200 randomcases was taken and found that for 22 cases, the luggagewas never found?

Solution

Clearly, it is one tailed test;

H0 : p £ 0.08

H1 : p > 0.08

Px

22200

= 0.11 (Sample proportion)

SEpqn

= =008²92

200. .

= 0.019

zp pSEx=-

=-

=011 008

0019158

. ..

.

Z tabulated =2.33 at a 0.01

Z calculated = 1.58

As calculated value of Z< tabulated value of Z,

Ho stands accepted.

Examples of t-test

Tensile strength of carbon steel samples in kg weight asrecorded by a operator using UTS matrix is given below:

15, 20, 18, 16, 17, 21, 20, 19, 17, 15

At 5% level of significance find out whether the meanbreaking strength of the lot can be considered 18 kg weight.

Solution

Null hypothesis that the population mean is equal tohypothesized mean of 18 kg.

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Weight can be written as under:

Ho:m=mHo=18 kg.

H1:m#mHo

Here sample size being small, we can use t-test assumingnormal distribution, population standard deviation being notknow. Test statistic (computed valve) of 't' is obtained usingfollowing formula.

tx

s nHo= − µ

σ /

To find out x¯ and ss. We make following calculations:Sl. No x i (xi – x¯) (xi – x¯)2

1 15 –2.8 7.84

2 20 2.2 4.84

3 18 0.2 0.04

4 16 –1.8 3.24

5 17 –0.8 0.64

6 21 3.2 10.24

7 20 2.2 4.84

8 19 1.2 1.44

9 17 –0.8 0.64

10 15 –2.8 7.84

n=10 å xi =178 å (xi–x¯)2=41.6

. xx

nkg

i= = =∑ 178

1017 8.

ii. σsx x

nkg

i=

−

−=

−=

∑ d i2

1

41 6

10 12 15

..

iii. t = −17 8 18

2 15 10

.

. /

= –0.294

iv. Degree of freedom = (n-1)

=(10–1)=9

v. At 5 per cent level of significance with 9 d.f. table valueof t-distribution = 2.262.

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vi. As the observed value of t (i.e., – 0.294) is in theacceptance region, we acceptance region, we accept Ho

at 5 per cent level and conclude that the mean breakingstrength of carbon steel may be taken as 18 kg. weight.

Examples of t-test

A company has drawn sample of sales (in units) in two shops,located in two different cities for their new launched product.Data presented as as under:

City Mean of sales Variance Sample size

Delhi 89 6.5 7

Kolkata 82 5.6 4

The company would like to assess the difference in sales intwo cities. Find out at 5 per cent level of significancedifference between the means of two samples.

Solution

Considering null hypothesis that means of two populationsare not different, we can write as under:

Ho: m1=m2

Ho: m1#m2

We can write the given information as under:

Sample from x ns12

189 6 71

= = =σ .5

City Delhi

Sample from x ns22

282 5 6 92

= = =σ .

City Kolkata

As in this case variances of the populations are not knownand sample sizes are small, to measure the differencebetween the means of two samples, we can use t-test to workout the test statistic to as under:

tx x

n n n ns s

= −

− + −× +2

22

21 21 1

1 1

1 2b g b gσ σ

with d.f. = (n1+n2-2)=9

= 89–82

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7 6 4 5 6

7 4 2

1

7

1

4

.5 .a f a f++ −

× +

=1.5973559

observed 't' value, i.e. 1.5973559 is less than table value of 't'at 5 per cent level of significance with d.f. 9, which is 2.262.Therefore difference in sales of two towns is significant at5% level, hence our null hypothesis is rejected.

Chi-square Test

A chi square (x2) test can be used when the date satisfiesfour conditions:

i. There must be two observed sets of data or one observedset of data and one expected set of data (generally, thereare n-rows and c-columns of data).

ii. The two sets of data must be based on the same samplesize.

iii. Each cell in the data contains the observed or expectedcount of five or large?

iv. The different cells in a row or column must havecategorical variables (Gr male, female or younger than25 years of age, 25 year of age, older than 40 years of ageetc).

Examples of situations where chi-square tests can be usedare:

u For a certain product men have a different distributionof comparative rates than women.

u Users of a certain brand in city ‘A’ show a differentincome distribution than users of the same brand in city‘B’.

Application Areas

When tests are undertaken to examine whether the sampledata supports the hypothetical distribution, such problemsare called “test of goodness of fit.”, i.e.,

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u To test whether the sample differences among varioussample proportions are significant or can they beattributed to chance.

u To test the independence of two variables in acontingency table.

u To use it as a test of goodness of fit.

The c2 distribution typically looks like a normal distributionwhich is skewed to the right with a long tail to the right. Itis a continuous distribution with only positive values.

c2 test has the following steps:

i. State the null hypothesis and calculate the numbers ineach category.

ii. Determine the level of significance (i.e., how much riskof type I error) the researcher is prepared to take.

iii. Calculate c2, as follows:

XO E

E

i j

j

2

2

=−

∑d i

Where

Oi = Observed frequency

Ej = Expected frequency in the category.

iv. Find the critical value of c2 against the no of degrees offreedom for the specified level of significance.

v. Compare the calculated value of c2 with the tabulated(critical) value and determine the region of reflection.

NB: Care should be taken to see that the expectedfrequency in the contingency table is not less than 5.

Solved Questions on c2 Test

1. A Company has been engaged in the manufacturing ofice-cream which is sold in three sizes – large, normaland small. It has observed that it sells the ice-cream inlarge, normal and small size in the ratio of 3:5:2.

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The company has been thinking of introducing adifferent flavour and has conducted a test market fortwo weeks in a certain territory. The results of the testmarket show that it has sold 250 large packs, 400 normalpacks and 350 small packs of the newly developed icecream.

The company is now interested in knowing whether theconsumption pattern of new ice-cream is different fromthat of the earlier one. If so, it may have to change thepercentage of three different packs for the newice-cream.

Solution

Ho : Null hypothesis, “consumption is not different fromearlier one”.Packing size Obs freq Expected freq O-E (O-E)2 (O-E)2

E

Large 250 300 -50 2500 8.33

Normal 400 500 -100 10000 20.00

Small 350 200 150 22500 112.50

1000 x2 140.83

Degrees of freedom = (3-1) = 2

At 5% level of significance, value of c2 for df (2) = 5.991

As c2 calculated > c2 tabulated,

We, therefore, reject the null hypothesis, “theconsumption pattern of new ice cream is not different”from the earlier one.

2. In winter season, a study has been made for 10 daysto see whether the distribution of daily reservationis uniform or not, and the results are tabulatedhereunder.

Find whether the distribution is uniform or not.

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Distribution of actual nos of reservations:

S No 1 2 3 4 5 6 7 8 9 10

No of Reservations 65 80 100 98 75 80 82 70 60 90

Solution

Ho: Distribution of daily reservation is uniform in winterseason.

Test the validity of the assumption.

Ho : p1 = p2 = p3 = .................. = p10

H1 : p1 # p2 # p3 #.................... # p10

Average value = 65 80 100 98 75 80 82 70 60 90

10

+ + + + + + + + +a f

= =

=−

=−

+−

+ − − − − −−

∑

800

1080

65 80

80

80 80

80

90 80

802

22 2 2

xo E

E

i j

j

d i a f a f a f

= 19.72

df = (c-1)(r-1) = (2-1) (1-1) = 9

value at 5% level of significance = 16.919

As calculated c2 > tabulated c2

Hence, we reject the null hypothesis, i.e., the reservation inwinter season is uniform.

Calculation of Expected Frequencies

No. of Farmers No.of Farmers who Total

Owned farms Rented farms

Using Fertilizers 100 x 80 = 40

60 100

200

Not Using Fertilizers 40 60 100

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Calculation of c2 :

Row Column Frequency O - E (O -E)2 (O - E)2

O E E

1 1 50 40 10 100 2.50

1 2 50 60 -10 100 1.62

2 1 30 40 -10 100 2.50

2 2 70 60 10 100 1.67

Total 8.34

c2 = 8.34, calculated;

2´ 2 table D f = (2-1) (2-1) = 1 ´ 1 = 1

c2 tabulated at 5% level of significance = 3.84

As c2 calculated >c2 tabulated

Therefore, Ho stands rejected

Hence, there is an association between the ownership offarms and the use of fertilizers.

Test for Independence of Attributes

(contingency table 2´ 2)

a b R1c d R2

C1 C2

R1= a+b C1= a+c

R2= c+d C2= b+d

N= a+b+c+d= R1+R2= C1+C2

Xobserved frequency Expected frequency

Expected frequency

with rees of freedom R C

2

2

1 1

=−

= − −

Σb g

b gb gdeg

Notes

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Yate�s Correction

To improve the approximation result obtained before it isnecessary to apply a correction known as Yate’s correction.The formulae for calculation for c2 becomes.

Xad bc n

R R C Cwith d f2

22

1 2 1 22 1 2 1 1=

− −= − − =

b gn s b g b g. .

The application of this formula is illustrated by an examplegiven below.

Example 8.1

In testing for any relationship between the opinion onnuclear disarmament and the sex of the person, let us assumethat 100 persons including 60 males were asked about theiropinion and their responses were classified into twocategories, yes and no, as follows:

Male Female Total

Favour 35 25 60

Against 25 15 40

Total 60 40 100

Solution

i. Let null hypothesis, H0: there ‘s no difference of opinionbetween male and female.

Then alt hypothesis, H1: there is significant differenceof opinion between male and female opinion.

Method 1. Approximation method with Yates correction.

ii. Calculate c2 =N ad bc n

R R C C

− −a f / 2

1 2 1 2

2

Here, N=100

a=35 R1= a+b=60

b=25 R2= c+d=40

c=25 C1= a+c=60

d=15 C2= b+d=40

Notes

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X22

2

100 35 15 25 25 100 2

60 40 60 40

100 525 625 50

60 40 60 40100 22500

60 40 60 402255760390

=× − × −

× × ×

=− −

× × ×

= ×× × ×

=

=

b gn s

l q

.

iii. Tabulated X2 at 5% level of significance

= 30841

df = (r-1) (c-1)

= (2-1) (2-1)

= 1

iv. As X2 calculated < X2 tabulated

Null hypothesis stands accepted.

i.e., there’s is no difference of opinion between male andfemale

Method II

∑ =−f f

fo e

e

b g2

where, fo= observed frequency

fe= expected frequency

i. Calculate frequencies by this formula; R

Gt C

t

t×

Where Rt = Total of row

Ct = Total of column

Gt = Grand total

Notes

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Male Female

Favour 35 25 60

Against 25 15 40

Total 60 40 100

Expected frequency for cell (1,1) = 60 60

10036

× =

Expected frequency for cell (1,2)= 60 60

10024

× =


10024

× =


10016

× =

ii. Let null hypothesis H0: there is no difference of opinionbetween male and female.

Then alt hypothesis H1: There is significant differenceof opinion between male and female.

iii. Calculate

Xf f

fe

o e2

2

=−

∑b g

= 35 36

36

25 24

24

25 24

24

15 16

16

2 2 2 2−+

−+

−+

−a f a f a f a f

= 0.028 + 0.041 + 0.041 + 0.062

= 0.172

d.f = (c-1) (r-1) = (2-1) (2-1)=1

Tabulated x2 at 5% level of significance

= 30841

df = (r-1) (c-1)

= (2-1) (2-1)

= 1

Notes

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Notes

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iv. As, X2 cal < X2 tabulated

Null hypothesis stands accepted.

i.e., there is no difference of opinion between male andfemale.

Measures of Associations

Research questions in business frequently revolve aroundthe study of relationship between two or more variables.Various objectives may be served by such an analysis. Thestrength, direction, shape and other features of therelationship may be discovered. Or tactical and strategicquestions may be answered by predicting the values of onevariable from those of another.

With correlation, one calculates an index to measure thenature of the relationship between variables calculated. Withregression, an equation is developed to predict the values ofthe dependent variable. Both are affected by the assumptionsof measurement level and the distributions that underlinethe data.

Bivariate Correlation Analysis

Bivariate correlation analysis differs from non-parametricmeasures of association and regression analysis in twoimportant ways. First, parametric correlation requires twocontinuous variables measured on an interval or ratio scale.Second, the coefficient does not distinguish betweenindependent and dependent variables. It treats the variablessymmetrically since the coefficient rxz has the sameinterpretation as ryx.

Linear Regression Equation

The pattern of the scatter diagram, in most cases, is lineallyrelated. The line which runs through most of the points, (ifnot all), is known as the “line of regression”. This lineshould be the most representative of the data, i.e.,most suitable and is thus popularly known as the “line ofbest fit”.



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The best line would be the one which passes through all thepoints. But this is not possible in most situations. The nextstep is to find the line which is closest to all the points, i.e.,the distance between the line and points is minimum. Assome points shall be above the line and some below the line,the distance above line ‘time’ and below ‘we’, therefore, wetake the square of donations (which will be time both cases)and hence the line of best fit would be one which gives theminimum differences

Y = a + b x

where Y = Dependent variables

X = Independent variables

a and b are costants which determine the completed line.

Example 8.2

A researcher wants to find if there is a relationship betweenthe heights of sons and fathers. In other words, do tall fatherhave tall sons?

Their heights in inches is given below in an orderedarrangement.

Father (X) Son (Y)

63 66

65 68

66 65

67 67

67 69

67 69

68 70

a. For this data complete the regression line.

b. Based upon the relationship between the heights, whatwould be the estimated height of the son if the fatherheight is 70”.

Solution

We can solve the problems under:

Let the line be Y = a + b x

Notes

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bn xy x y

n x x

Y bX

=−

−

= −

Σ Σ Σ

Σ Σ

b g b gb ge j b g2 2

X Y X2 XY Y2

63 66 3969 4158 4356

65 68 4225 4420 4629

66 65 4356 4290 4225

67 67 4489 4489 4489

67 69 4489 4623 4761

68 70 4624 4760 4900

å X = 396 å Y = 405 å X2 = 26152 å XY = 26740 å Y2 = 27355

`

b

a

=−−

= −−

= =

= −

= − =

6 26740 396 405

6 26740 396 396160440 16038

156912 156816

6096

0 625

4056

0 625 396 6

675 4125 26 25

b g b gb g b g

b g

.

.

. . .

Hence, the regression line would be

Y = a + b x

= 26.25 + 0.625 x

If fathers height is 70”, height of son will be (X – 70)

Y = 26.25 + .625 (70)

= 26.25 + 43.75 = 70

Expected height of son is also 70".

Standard Error of the Estimate

How good is this fit?

The closer these values are to each other, the better the fit.Accordingly, a measure of the variability of the scatteraround the regression line would determine the reliability

Notes

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of this estimate. The smaller this estimate, the moredependable the prediction will be.

For our problem stand and error of the estimate would be:

Syxy a y b xy

n=

− −

−∑ ∑∑ b g c h c h2

2

27355 26 25 405 0 625 26740

4

− −. .a f a f

11 25

42 8125 1 678

.. .= =

The Coefficient of Determination (r2)

The square of the coefficient of correlation (r) is called thecoefficient of determination (r2).

It is a more precise measure of the straight relationshipbetween the two variables and lends itself to more preciseinterpretation because it can be represented as a proportionor as a percentage. The coefficient of determination can bedefined as a proportion of the variation in the dependentvariable y, that is explained by the variation in independentvariable x, in the regression model.

rExplained iation

Total iation2 = var

var

=+ −

−∑ ∑∑

∑∑a Y b XY Y n

Y Y n

b ga f b g

2

2 2

/

/

For the above example under discussion

r22

2

26 25 405 625 26340 405 6

27355 405 6

10631 25 16712 5 27331 5

27355 27377 56 25

17 5

=+ −

−

= + −−

=

. /

/

. . .

..

.

a f a f a fa f

Notes

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= 0.357 ( 35.7% of Variation in y)

and

r r= =2 0 357.

= 0.597

Rank Correlation

For the two variables x and y whose distribution is unknown,the degree of association between x and y is ascertained bythe Spareman’s rank correlation.

As the name suggests, this method is based on the rank (ororder) of the observations rather than on a specificdistribution of x and y.

In marketing research, the ranking or ordering of alternativepreferences is quite common.

The method is very handy and involves simple calculationsonly.

The rank correlation coefficient is a measure of correlationthat exists between two sets of ranks. In other words, it is ameasure of association that is based on the ranks of theobservations and not on the numerical values of the data. Itwas developed by the famous statistician, Charles Spearman,in the early 1900s and as such, it is also known as Spearman’srank correlation coefficient.

For calculating Spearman’s rank correlation coefficient, firstof all the actual observation has to be replaced by their ranks,giving rank 1 to the highest value, rank 2 to the next highestvalue and following this very order, ranks are assigned forall values.

The second step is to record the difference between ranks(or ‘d’) for each pair of observations. Spearman’s rankcorrelation coefficient, rs, is worked out as under:

rd

n ns = −

−∑

16

1

2

2d i

Notes

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Where n = number of paired observation.

The value of Spearman’s rank correlation will always varybetween + 1 indicating a perfect positive correlation and –1, indicating perfect negative correlation between twovariables.

This is a measure of correlation that exists between two setsof ranks, a measure of degree of association betweenvariables that we would not have been able to calculateotherwise.

This method helps to simplify the process of computingcorrelation coefficient from a very large set of data for eachof the two variables. We can compute measure of associationthat is based on ranks of observations, not the numericalvalues of the data.

These values are rather quick and easy to use and can beapplied to ordinal or nominal scale data.

They do not presuppose any particular distribution andconsequential assumptions.

There are many situations in which the various assumptionsrequired for standard tests of significance cannot be met.We can use this method under such situations as it is easierto explain and understand.

Example 8.3

Suppose 10 salesman employed by a company were given amonth’s training. At the end of the specified training theytook a test and were ranked on the basis of theirperformance. They were then posted to their respectiveareas. At the end of six months they were rated in respect oftheir sales performance. The data are given in the tablebelow:

Salesman Rank obtd Rank on the Difference Differencein training basis of sales squared

performance

# X Y d d2

1 4 5 -1 1

Notes

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2 6 8 -2 4

3 1 3 -2 4

4 3 1 +2 4

5 9 7 +2 4

6 7 6 +1 1

7 10 9 +1 1

8 2 2 0 0

9 8 10 -2 4

10 5 4 +1 1

Here å d2 = 24. Using the formula, we get

rd

n ns = −

−=

−−

−∑1

6

1

1 6 24

10 10 11

144

990

2

2 2d ia f

d i

= 1–.145

= 0.855

This shows that there is a very high correlation betweenperformance in training and the sales performance of theten salesmen.

Analysis of Variance (ANOVA)

Analysis of variance (ANOVA) enables us to infer whetherpopulation from which we have drawn more than twosamples are having the same mean values. By testing thesignificance of difference between more than two samplemeans we make such inferences. To test the equality ofvariances, we use ‘F’ test. By comparing the observed ‘F’ valuewith table value of ‘F’ and analyzing the significance ofdifferences (if any) we test our hypothesis. Before elaboratingon the ‘F’ test, it is important for us to understand theprinciples and techniques of analysis of variance (ANOVA).Only after analysis of variance, we can submit it to ‘F’ test tomake necessary inferences.

Notes

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To test the equality of variances in such cases too,we use ‘F’test, the formula for which is:

2

2s

2

siF

σσ

= =with d.f. (n1–1) for sample 1.

(n2 – 1) for sample 2.

=σ2

1svariance of sample 1

calculated as X X

n 1

li 1

2

1

−∑−

b gb g

We can also use n1 when sample size is 30 or more.

2

2xσ =variance of sample 2

calculated as = X X

n 1

2i 2

2

2

−∑−

b gb g

X1i = is the observed frequencies of sample 1.

X2i = observed frequencies of sample 2. and X1 and X2

are

the respective mean values of samples 1 and 2.

But ANOVA technique is important to compute varianceswhen we want to compare more than two samples to inferwhether the said samples have been drawn from populationhaving the same mean values. Without going into the troubleof considering all possible combinations of populations,ANOVA technique enables the researcher to investigate themean differences of all the populations simultaneously.

We have introduced the term dependent variable andindependent variable with an example earlier. ANOVAenables a researcher to investigate factors which influencea dependent variable. Let us assume productivity rate as adependent variable. We know that productivity usuallydepends on multiple factors like level of technology used inproduction, workers’ skill, incentives and gain sharing,training, supervision and industrial relations. For us allthese factors are independent variables. Now a researchermay be interested in knowing the differences amongst these

Notes

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factors, i.e. which one of the factors is more effective in raisingproductivity (by studying their respective differences atvarious level of significances)or he may be interested ininvestigating the differences amongst various categories ofsame factor (for example various methods on incentive andgain sharing) which influence productivity. When weinvestigate various categories of one factor only, we carryout one-way ANOVA.

But when we are interested in investigating two factors at atime, we carry out two-way ANOVA. Likewise with the helpof ANOVA, we can investigate, in general any number offactors and also various categories within each factor tostudy their respective influences. Thus we find followingsteps are usually involved in analysis of variance:

i. Estimation of population variance based on variancebetween the sample means.

ii. Estimation of population variance based on variancewithin the sample means.

iii. The third step involve is to compare these variances toget F value.

iv. The third step is to compare the obtained F value withthe respective F table value at given degrees of freedomand to judge the differences at desired level ofsignificances.

The formula for computing ‘F’ value takes the following shape

F =MS between

MS within

Now unless the above steps are explained with a practicalexample, it would be difficult for readers without knowledgeof statistics to understand F test in its true spirit. Let usfirst have an example of one-way ANOVA.

In a company there are four shop floors. Productivity ratefor three methods of incentives and gain sharing in eachshop floor is presented in the given table. Analyzewhether various methods of incentives and gain sharingdiffer significantly at 5% and 1% F-limits.

Notes

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Shop floor Productivity rate data for three methods ofincentives and gain sharing

X1 X2 X3

1 5 4 4

2 6 4 3

3 2 2 2

4 7 6 3

Solution

Step 1: Calculate mean of each of the three samples (i.e., x1,x2 and x3, i.e. different methods of incentive gain sharing).

X15 6 2 7

45= + + + =

X24 3 2 3

43= + + + =

X34 3 2 3

43= + + + =

Step 2: Calculate mean of sample means i.e., XX X X

K=

+ +1 2 3

where, K denotes No. of samples

= + + =5 3 3

34 approximatedb g

Step 3: Calculate sum of squares (s.s.) for variance betweenand within the samples.

ss between n x x n x x n x x= − + − + −1 22

2 22

32b g b g d i

ss within x x x x x xi i i= ∑ − + ∑ − + ∑ −1 12

2 22

3 32b g b g b g

Sum of squares (ss) for variance between samples is obtainedby taking the deviations of the sample means from the meanof sample means ( x ) and by calculating the squares of suchdeviation, which are multiplied by the respective number ofitems or categories in the samples and then by obtainingtheir total. Sum of squares (ss) for variance within samples

Notes

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is obtained by taking deviations of the values of all sampleitems from corresponding sample means and by squaringsuch deviations and then totalling the. For our illustrationthen

ss between = 4(5 – 4)2 + 4 (4 – 4)2 + 4 (3 – 4)2

= 4+0+4= 8

ss within =

5 5 6 5 2 5 7 5

4 4 4 4 2 4 6 4

4 3 3 3 2 3 3 3

2 2 2 2

2 2 2 2

2 2 2 2

1 12

2 22

3 32

− + − + − + −

+ − + − + − + −

+ − + − + − + −

∑ −

∑ −

∑ −

b g b g b g b g{ }

b g b g b g b g{ }

b g b g b g b g{ }

b g

b g

b g

x x

x x

x x

i

i

i

1 244444444 344444444

1 244444444 344444444

1 244444444 344444444

= (0 + 1 + 9 + 4) + (0 + 0 + 4 + 4) + (1 + 0 + 1 + 0)

= 14 + 8 + 2

= 24

Step 4: ss. of total variance which is equal to total of s.s.between & ss within and is denoted by formula as follows:

X Xij

2−∑ e j

where

i = 1.23

j = 1.23

for our example, total ss will thus be:

5 4 6 4 2 4 7 4

4 4 4 4 (2 4) (6 4)

4 4 3 4 2 4 3 4

1 4 4 9 0 0 4 4 (0 1 4 1

18 8 6 32

2 2 2 2

2 2 2 2

2 2 2 2

− + − + − + −

+ − + − + − + −

+ − + − + − + −

= + + + + + + + + + + += + + =

OQP

b g b g b g b g{ }

b g b g{ }

b g b g b g b g{ }

b g b gn s

Notes

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We will, however, get the same value if we simply totalrespective values of ss between and ss within. For ourexample ss between is 8 and ss within is 24, thus ss of totalvariance is 32 (8+24).

Step 5: Ascertain degrees of freedom and mean square (MS)between and within the samples. Degrees of freedom (df)for between samples and within samples are computeddifferently as follows:

For between samples, df, is (k–1), where ‘k’ representsnumber of samples (for us it is 3). For within samples df is(n–k), Where ‘n’ represents total number of items in all thesamples (for us it is 12).

Mean squares (MS) between and within samples arecomputed by dividing the ss between and ss within byrespective degrees of freedom. Thus for our example:

i. MS between =ss between

(K 1)−

8

24=

where (K–1) is the df.

ii. MS withinss within

(n k)

24

9=

−=

= 2.67

where (n–k) is the df.

Step 6: Now we will have to compute F ratio by analyzingour samples. The formula for computing ‘F’ratio is:

MS between

MS within

Thus for our example F ratio

=4.00

2.671.5=

Notes

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Step 7: Now we will have to analyze whether variousmethods of incentives and gain sharing differ significantlyat 5% and 1% ‘F’ limits. For this, we need to compareobserved ‘F’ ratio with ‘F’ table values. When observed ‘F’value at given degrees of freedom is either equal to or lessthan the table value, difference is considered insignificant.In reverse cases, i.e., when calculated 'F' value is higher thantable-F value, the difference is considered significant andaccordingly we draw our conclusion.

For example, our observed ‘F’ ratio at degrees of freedom(V1* & V2**, i.e., and 9) is 1.5. The table value of F at 5% levelwith df 2 and 9 (v1 = 2, v2 = 9) is 4.26. Since the table value ishigher than the observed value, difference in rate ofproductivity due to various methods of incentives and gainsharing is considered insignificant. At 1% level with df 2and 9, we get the table value of F as 8.02 and we draw thesame conclusion.

We can now draw an ANOVA table as follows to show ourentire observation.

Variation SS df MS F-ratio Table value

of F

5% 1%

Between 8 (k–1)= ss between MS between F (v1, v2) F (v1, v2)

sample (3–1)=2 (k–1) MS within =F (2,9) =F(2,9)

=8/2 = 4 =4/2.67 = 4.26 8.02

Within

simple 24 (n–k)= ss.within =1.5

(12–3) (n–k)

= 9 = 24/9

= 2.67

Two way ANOVA technique is used when our data aredivided to both columns and rows and we way to study theeffects. Let us assume that our dependent variableproductivity rate is classified on the basis of incentives and

* v1=d.f. for greater variance (between samples).

** v2=d.f. for smaller variance (within samples).

Notes

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gain sharing and on level of technology used in production(independent variables). To study the effects of independentvariables on dependent variable, under the givenassumptions, we use two way classification of ANOVA.

Again there may be repeated measurements of all categorieswhere we need to study even the interaction variation orthere may not be any such repeated measurement. Based onsuch differences in data collection and presentation, ourcomputational method differs.

When we do not have repeated measurement, we follow thefollowing steps for two-way classification of ANOVA:

Step 1: Calculate total values of individual items in allsamples and indicate it by T. P So T stands for total value ofall samples.

Step 2: Calculate correction factor using following formula:

T

n

2

where n denotes number of samples.

Step 3: Calculate total ss and subtract the correction factorto obtain sum of squares of deviation for total variance. Total

ss is denoted by χ ij

2

2T

n−∑ . Thus our formula for step 3 takes

the following shape.

χ ij

2

2T

n−∑

Step 4: Compute total ss between columns and subtract theresult from the correction factor. Total ss is computed byobtaining the square of each column total and subsequentlydividing such squared values by number of items and totallingthe result. Thus we denote step 4 by following formula

Tj

n

T

n,

j

2FHIK

−∑ ( where j=1,2,3,.....i.e. individual column values

nj denotes total number of items in the column).

= sum of squares of deviations of variance between columns.

Notes

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Step 5: Compute total ss between rows and subtract theresult from correction factor to obtain sum of squares ofdeviation for variance between rows. Total ss between rowsis calculated by squaring each row total by dividing squaredvalues by respective number of items in the row and finallyby taking the total of the results. Thus we can denote step-5by the following formula:

Tj

n

T

n,

j

2FHIK

−∑ where i = 1,2,3 (individual row values) nj

denotes total number of items in the row.

Step 6: Compute sum of squares of deviations for residualor error variance by subtracting the sum of ss betweencolumns and ss rows variance from total variance (s.s total).

SS for residual variance= Total ss – (ss. between columns+ss.between rows)

Step 7: Next task for us is to to ascertain the degrees offreedom and mean square. Mean Square (MS) as we know isobtained by dividing ss values by respective degrees offreedom. In two way ANOVA, we need to compute three MSas under:i. MS between column variance

=−

ss between columns

(c 1)

where (c–1)is the df

C= total number of columns.

ii. MS between row variance

=−

ss between

(r 1)

rows

where (r–1) is the d.f.

r = total number of rows.

iii. MS of residual or error variance

=− −

ssresidual

c r( )( )1 1

where (c–1) (r–1) is the df.

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Step 8: This step involves computation of F ratio. Here alsofor two-way ANOVA, we will have to compute two F-ratiosas under for having two independent variables to measurethe significance of differences for each independent variableon dependent variable.

F ratio for column independent variation

=MS between columns

MS residual

F-ratio for row independent variation

=MS between r s

MS residual

ow

To compare table value of F with our observed F ratios fordrawing necessary conclusion at defined level of significance,we consider respective df of SS between columns and df ofMS residual to find out table value of F for columnindependent variation and df of SS between rows and df ofMS residual for row independent variation.

Let us now frame a problem to study the effects of incentiveand gain sharing and level of technology (independentvariables) on productivity rate (dependent variable).

Productivity Rate Data of Workers of M/s. XYZ & Co.

A B C

W 4 3 3

X 5 3 2

Y 1 1 1

Z 6 5 2

Solution

1. Total values (T) of individual item = 36, n = 12

2. Correction factor = (T)

n

36 36

12

2

=×

= 108

Level oftechnology

Incentives andgain sharing

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3. Total ss = (16+9+9+25+9+4+1+1+1+36+25+4)

= 140 – 108 =32

4. ss between columns:

=×

+×

+×

−LNM

OQP

16 16

4

12 12

4

8 8

4108

5. ss between rows:

=×

+×

+×

+×

−

+ + + −

LNM

OQP

LNM

OQP

10 10

3

10 10

3

3 3

3

13 13

3108

=100

3

100

3

9

3

169

3108

= [33.33 + 33.33 + 3 + 56.33] – 108

= 126 – 108

= 18 (after adjusting fraction)

6. ss residual:

= Total ss – (ss between column + ss between rows)

= 32 – (8+18) = 6.

Now we need to set up ANOVA table

Variation source SS d.f M.S F ratio 5% 1%

Between columns 8 (c–1) 42

8= 4

1

4= F (2, 6) F (2, 6)

= 2 = 5.14 = 10.92

Between rows 18 (r–1) 63

18= 6

1

6= F (3, 6) F (3, 6)

= 3 = 4.76 = 9.78

Residual 6 (c–1) x 16

6=

(r–1)= 6

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From the ANOVA table, we find that differences related tovarieties of incentives and gain sharing are insignificant at5% level as the calculated F-ratio, i.e., 4 is less than tablevalue of F, which is 5.14. However differences are significantfor different levels of technology at 5% level as the observedF ratio is higher than table value of F. At 1% level, however,differences are insignificant.

Now coming to the problem of two-way classification ofANOVA in cases of repeated measurements apart from theearlier steps, we need to calculate interaction variation alsoas it enables us to measure the interrelationship among thetwo different classifications. For example, we may classifyour productivity rate data in two groups of workers, assumingour company is having two separate production units.

We follow upto Step-5, as elaborated earlier for two-wayANOVA without repeated measurements. Rest of the stepsare as follows:

Step 6: For having two different classifications of data (forus productivity rate), apart from computing total SS, SSbetween columns and between rows, we need to work out sswithin samples, i.e. sum of squares of deviations betweentwo samples classifications.

Step 7: Our next task is to compute ss for interactionvariation (within sample error). For this we subtract totalss from the sum of ss between columns, ss between rows andss within samples.

Step 8: In this step, we need to calculate degrees of freedomand Mean Squares (MS) For this ANOVA too we shouldcompute three mean squares as under:

i. MS between column variation =−

ss between columns

(c 1)

Where c represents total number of column and (c–1)represent degree of freedom.

ii. MS between rows =−

ss between r s

(r 1)

ow

where ‘r’ represents total number of rows and (r–1)represents degree of freedom.

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iii. MS for interaction variation

=ss interaction variation

(c - 1)(r - 1)

where (c–1) and (r–1) are the degrees of freedom.

iv. MS for within samples variation

=ss within samples

(n - k)

where ‘n’ is the total number of samples (all observationsare included ) and ‘k’ represented total number of samplesgroup.

Step 9: This final step involves calculations of ‘F’ ratio. Forhaving repeated values, in addition to measurement ofsignificance of differences for each independent variableson dependent variable, we need to measure significance ofsuch differences between groups, i.e., how different groupsof people (based on our sample observations) are affecteddifferently (it terms of variation in productivity rate for ourexample) for independent variables. Thus we computefollowing F ratios :

i. ‘F’ ratio for column independent variation

= sampleswithinMS

rowsbetweenMS

ii. ‘F’ ratio for row independence variation

= sampleswithinMS

rowsbetweenMS

iii. F ratio for interaction variation

= sampleswithinMS

variationninteractioforMS

We then compare the observed ‘F’ ratios with table valuesof ‘F’ at given df and draw our conclusions. Degree offreedom is determined by same principles followedearlier.

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Multivariate Analysis

Definition of Multivariate Analysis

Multivariate analysis or multivariate techniques may bedefined as the collection of methods for analysing data inwhich a dependent variable is represented in terms ofseveral independent number of observations which areavailable to define such relationship. In brief, techniques thattake account of the various relationships among variablesare termed multivariate analysis or multivariate techniques.Mathematically, multivariate analysis was defined byTakeuchi, Yanai and Mukherjee as, “forming a linearcomposite vector in vector space, which can be representedin terms of projection of a vector on to certain specifiedsubspaces.”

Notes

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A multivariate method

Are some of the variablesdependent on others?

Dependencemethods

Yes No

Interdependencemethods

How many variablesare dependent?

Are inputs metric?

One Several

Is it metric Are theymetric?

Yes No Yes No

Multipleregression

Multivariateanalysis ofvariance

Multiple discriminantanalysis Canonical analysis

NoYes

Factoranalysis

Clusteranalysis

Metric multi-dimensional

scaling

Non-metricscaling

Conjointmeasurement

Latent structureanalysis

Figure 8.3



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Objectives of Multivariate Analysis

The basic objectives of multivariate analysis are:

(i) To represent the collection of large set of data in asimplified way, by transforming large number ofobservations into smaller composite scores.

(ii) To predict the variability of the dependent variablebased on its covariance with all the independentvariables.

(iii) To classify individuals or objects into one of the two ormore mutually exclusive and exhaustive groups on thebasis of a set of independent variables.

Advantages of Multivariate Analysis

The main advantage of multivariate analysis is that since ittakes into account more than one factor/element ofindependent variables which affect the variability ofdependent variable, the conclusions drawn are moreaccurate. The conclusions are more realistic and nearer tothe real life situation.

Disadvantages of Multivariate Analysis

(i) It requires rather complex computations to arrive at asatisfactory conclusion.

(ii) Due to the above fact that a large number ofobservations for large number of variables need to becollected and tabulated, it is a rather time consumingprocess.

(iii) Obviously due to (i) and (ii) above, at times multivariateanalysis proves to be an expensive proposition, in termsof cost.

(iv) Specialized trained staff is required to process andanalyze the complex data utilizing multivariatetechniques.



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Applications of Multivariate Analysis

These techniques are successfully employed in the followingareas:

(a) Econometrics or decision-making in economics:Such as impact of inflation, money circulation, loweringof tariffs, etc., on price rise.

(b) Sociological decision-making: Such as divorce rates,and their cause-effect relationships, with marriage,social demographics and income levels.

(c) Agrarian predictions: Such as impacts of rain,fertilizers and mechanization on agricultural yields peracre.

(d) Drug testing: Such as impact of new drugs on the maindisease and other side effects.

(e) State fiscal decision-making: Such as impact of taxstructure, duties, penalty rates, etc., on the governmentrevenues.

(f) Industrial decision-making: Such as plant locationwhich depends on infrastructure, availability of rawmaterials, distribution channel, etc.

Factor Analysis

It is one of the more popular "analysis of interdependence"techniques. In studies of interdependence, all the variablesare on an equal footing, and the analysis is concerned withthe whole set of relationships among the variables thatcharacterize the objects.

Unlike regression or discriminant analysis, factoranalysis would focus on the whole set of interrelationshipsdisplayed by the variables. At the conceptual level, afactor is a qualitative dimension of the data that attemptsto depict the "way in which entities differ, much as thelength of an object or the flavour of a product defines aqualitative dimension on which objects may or may notdiffer."



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Factor analysis is a procedure that takes a large number ofvariables or objects and searches out factors in common whichaccount for their inter-correlation. For example, we canattribute the high association between grades in computercourses to the factor of intelligence or the associationbetween certain attributes of coffee and factor of acidity.

Application of Factor Analysis in Marketing Research

There are a number of applications in marketing research.These includes data reduction, structure identification andscaling.

Data Reduction: Factor analysis is used for reducing a massof data to a manageable level. For example, the marketingresearcher who has collected data on 40 attributes of abrand. This analysis and understanding of this data maybe aided by reducing 30 attributes and having only 10attributes.

Factor analysis has been employed to “purify” original setsof scale items by isolating those items that do not reflect acommon core and also to name the dimensions captured bymeasure. It is also used in the study of lifestyles andpsychographic research problems in which it is used todevelop consumer profiles that reflect people’s attitudes,activities, interests, opinions, perceptions and preferences,so as to better predict their consumption and purchasebehaviour. One of the major impetuses of lifestyles andpsychographic research has been the generally inadequatenature of market segments defined using traditionaldemographic measures.

Structure Identification: Factor analysis may be used tounderstand the basic structure underlying a set of measures.For example, the above 30 attributes may be reduced to tenfactors identified by the researcher.

Scaling: A marketing researcher may develop a scale on aresearch topic. One problem that may occur in developingany scale is in weighing the variables being combined to formthe scale.



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Limitations of Factor Analysis

(1) The factor analysis is not strongly supported bystatistical methods.

(2) The different results can be obtained by using loadingfactors in different manners.

(3) A large number of attributes are required to study factoranalysis.

(4) In some cases, complex factors are used whichrespondents find difficult to understand.

14 coffee flavours – Unpleasant flavourStagnant, muggy taste – Sparkling, refreshing taste

Mellow taste – Bitter tasteCheap taste – Expensive taste

Comforting, harmonious, smooth, friendly taste – IrritatingDiscordant, rough, hostile taste

Dead, lifeless, dull taste – Alive, lively, peppy tasteTastes warmed over – Tastes just brewed

Hearty, full-bodied, full flavour – Watery, thin, empty flavourPure, clear taste – Muddy, swampy taste

Raw taste – Roasted tasteFresh taste – Stale taste

Overall preference: Excellent quality – Very poor quality

Note: Ten blank boxes separated each set of opposing statements. Subjects checkedthe position that came closest to describing how they felt towards the product.

Figure 8.4: Coffee Attributes and Intercorrelations AmongAttribute Ratings

* The 10 scale categories were assigned successive integers, beginning with 1 at the favourable side of the scale. Thus,ratings could vary from 1 (very good) to 10 (very bad) on an attribute.

Source: Updated to 1995 from Bishwa Nath Mukherjee “A Factor Analysis of Some Qualitative Attributes of Coffee”,Journal of Advertising Research, Vol. 5, p. 36, March ’95. Used with permission.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1. Pleasant flavor 1.00 .76 .81 .79 .83 .81 .74 .66 .65 .71 .76 .65 .71 .75

2. Sparkling taste 1.00 .78 .85 .77 .87 .83 .65 .70 .78 .85 .69 .74 .83

3. Mellow taste 1.00 .77 .85 .81 .77 .60 .65 .64 .75 .69 .69 .74

4. Expensive taste

1.00 .78 .87 .83 .76 .69 .81 .81 .64 .71 .87

5. Comforting taste

1.00 .82 .77 .66 .60 .69 .82 .69 .69 .74

6. Alive taste 1.00 .88 .70 .74 .80 .81 .65 .77 .87

7. Tastes like real coffee

1.00 .67 .76 .75 .79 .62 .76 .87

8. Deep distinct flavour

1.00 .51 .84 .70 .54 .59 .70

9. Tastes just brewed

1.00 .67 .65 .67 .80 .75

10. Hearty flavour 1.00 .83 .65 .72 .76

11. Pure clear taste

1.00 .83 .65 .72 .76

12. Roasted taste 1.00 .78 .61

13. Fresh taste 1.00 .73

14. Overall preference

1.00

4.5 4.3 4.4 4.6 4.4 4.2 4.2 4.3 4.3 4.2 4.3 4.4 4.6 6.9 Mean rating*

Standard deviation 1.6 1.3 1.4 1.4 1.3 1.4 1.6 1.5 1.5 1.5 1.4 1.2 1.4 2.7

Table 8.1: Intercorrelations Among Attribute Ratings



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Four factors underlying the 14 attributes. The elements inthis matrix listed under the factors are called unrotatedfactor loadings. The loadings measure which variables areinvolved in which factor pattern, to what degree and in whatdirection. They can be interpreted as correlation coefficients.The square of the loading equals the proportion of thevariation that a variable has in common with an unrotatedfactor.

Another way to conceptualize this relationship is toremember that a loading is a correlation coefficient betweena variable and a factor. In essence, when we square a loadingwe are calculating a coefficient of determination, h2, betweena variable and a factor. Thus, the squared loading representsthe amount of shared variation between a variable and afactor.

The h2 measures are called communalities. Communality isthe proportion of a variable’s total variation that is involvedin the factors. Mathematically h2 equals the sum of thesquared loading of a variable on all factors. For example, forattribute 1:

h2 = (.86)2 + (-.01)2 + (-.20)2+ (.04)2 = .78

Communality may be interpreted as a measure of uniqueness.By subtracting h2 from 1.0 the degree to which a variable isunrelated to the others may be calculated. Here we note that78 per cent of the variation in scores on attribute 1 can bepredicted from the other variables, leaving 22 per centuniquely related to this attribute.

To get the percentage of total variance in the data explainedby the four factors, we simply calculate H where

H=sum of all h s

numberof variables100

=11.61

14100

=83%

2

×

×

This value is called the common variance explained by thefactors.



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To calculate the amount of variation in the data accountedfor by a factor, we square each loading for a factor, add andthen divide the result by the number of variables. Forexample, for factor 1 the value is

(.86)2 + (.91)2 + (.86)2 + ......... + (.90)2 = 10.42

This value is called an eigen value in the vocabulary of factoranalysis. Thus, the percentage of total variance explainedby factor 1 is 10.42/14 = 74.4 per cent. The percentage ofcommon variance explained by this factor is then 10.42/11.61= 90 per cent. We note that the percentages of both commonvariance and total variance are presented in Table 8.2.

In order to obtain an interpretation of the result, we examinethe rotated factors.

Table 8.3 presents one such interpretation. There the factorshave been placed with high-loading variables and each givena creative name by the author of the study. Note that thereis no unique definition of the meaning of any factor; it is upto the creativity of the researcher.

Table 8.2: Factor Loadings

Principal factor matrix Rotated (varimax) matrix Oblique factor matrix

I II III IV h2 A B C D A B C D

1 .86 -.01 -.20 .04 .78 .63 .38 .36 .34 .34 .01 .07 -.03

2 .91 -.01 -.01 -.09 .83 .48 .43 .53 .38 .14 .04 .23 .04

3 .86 .11 .28 .002 .83 .70 .26 .38 .36 .36 .13 -.003 -.01

4 .91 .15 -.001 -.10 .87 .46 .53 .54 .29 .16 -.05 .34 -.07

5 .87 .002 -.31 .10 .87 .74 .38 .30 .32 .47 .01 -.004 -.08

6 .93 .03 -.02 -.16 .90 .49 .43 .59 .35 .12 .07 .30 -.01

7 .90 -.02 .04 -.21 .86 .42 .38 .64 .37 .03 .11 .33 .04

8 .77 .36 .11 .16 .77 .31 .74 .27 .22 .24 -.40 .32 -.10

9 .79 -.28 .24 -.09 .76 .23 .24 .52 .62 .15 .11 .14 .37

10 .87 .25 .22 .17 .89 .28 .75 .33 .39 .14 .38 .31 .07

11 .89 .11 .05 .10 .82 .51 .55 .36 .36 .28 -.15 .17 -.01

12 .76 -.29 .04 .27 .74 .43 .28 .16 .67 .18 -.08 .18 .38

13 .84 -.27 .19 .12 .83 .33 .32 .36 .70 .01 -.03 -.001 .41

14 .90 .04 .08 -.23 .86 .38 .43 .65 .34 .002 .08 .39 .01

90.0 4.1 3.3 2.6 Percent common variance

Percent total variance 74.4 3.4 2.7 2.6

Source: Adapted and updated to 1995 from Bishwa Nath Mukherjee. “A Factor Analysis of Some Qualitative Attributesof Coffee”, Journal of Advertising Research, Vol. 5, p. 37, March 1965. Used with permission.



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Unfortunately, researchers can all too easily fool themselveswith wonderful sounding interpretations. Great care mustbe taken in this regard.

The presentation of factor analysis has concentrated on thenature of the input and output. There are many more issueson all aspects of factor analysis not covered here. You shouldconsult a more advanced reference if you are interested.

Difficulties, Problems and Cautions

Cost: Factor analysis involves the study of various factors.To study a large number of factors, the researcher hasto spend a lot of time. Therefore, it is considered an expensiveanalysis. But now, we can use computers to get fasterresults.

Reliability: A factor analysis starts with a set of imperfectdata. Data change because of changes in the sample, changesin data gathering procedures or any of the numerous kinds

Table 8.3: Table Interpretation of Factors

Variable Attribute V arimax Oblique

Factor A (comforting quality)1 Pleasant flavour .625 .3403 Mellow taste .698 .3595 Comforting taste .736 .46511 Pure clear taste .512 .283Factor B (heartiness)8 Deep distinct flavour .742 .39610 Hearty flavour .745 .380Factor C (genuineness)2 Sparkling taste .524 .2324 Expensive taste .541 .3346 Alive taste .594 .3017 Tastes like real coffee .636 .3288 Deep distinct flavour .268 .32310 Hearty flavour .332 .31014 Overall preference .653 .387Factor D (freshness)9 Tastes just brewed .621 .35912 Roasted taste .670 .46513 Fresh taste .698 .238

Source: Updated to 1995 from Bishwa Nath Mukherjee, “A Factor Analysis of SomeQualitative Attributes of Coffee”, Journal of Advertising Research, Vol. 5, p. 37, March1965. Used with permission.



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of measurement errors, the results of any single analysisare, therefore, always less than perfectly dependable.

Cluster Analysis

Cluster analysis is used by the researcher to place variablesor objects into subgroups or clusters. These clusters are notdefined by the researchers but are formed by the clusteranalysis procedure itself. The following factors areconsidered for cluster analysis:

1. They form subgroupings and assign variables or objectsto these groups.

2. They take as input a matrix of association betweenvariables or objects.

3. They assume that natural clusters exist within the data.

Example of Cluster Analysis

A two-dimensional perceptual Figure 8.5 has been drawnon the basis of data relating to 15 individuals A to O, on thebasis of (i) Number of vacation days (ii) Expenditure onvacations during a given year.

I

C M

H

F L

Num

ber o

f vac

atio

n da

ys

II

N

K

I

O

G DIII

B A

J E

Figure 8.5: Cluster Analysis

It will be seen that there are three distinct clusters. Thefirst cluster comprising five individuals C, F, H, L and Mshows that although these individuals take too manyvacations, they do not spend much on their vacations. The



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second cluster comprising six individuals D, G, I, K, N andO shows that they take vacations moderately and also spendmoderately. Finally, the third cluster comprising threeindividuals A.B. and J shows that they have relatively fewvacation days but spend substantially more on theirvacations.

Discriminant Analysis

Discriminant analysis is a technique that is appropriate witha nominal dependent variable and interval independentvariables. Nominal dependent variables are very common inmarketing. For example, a satisfied customer, an unsatisfiedcustomer, service seeker customer, non-service seekercustomer. This is the reason why discriminant analysis hasreceived extensive application in marketing research.

The basic idea is to find out the linear combination of theindependent variables that make the mean scores acrosscategories of the dependent variable on this linearcombination maximally different. This linear combination iscalled the discriminant function. It can be represented inthe following way:

DF = V1 X1 + V2 X2 + ... Vm Xm

The criterion used to decide when group means are maximallydifferent is the familiar ANOVA (F-Test) for the differencesamong means thus, the V’s are derived such that

FSS between

SS within= is maximised

Confusion matrix for customer satisfaction.

Actual category Satisfied Unsatisfied

Satisfied 400 20

Unsatisfied 30 50

Table 8.4: Predicted Category



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The output of discriminant analysis includes the values ofthe V’s plus what is called a confusion matrix. This matrixcompares the category of the dependent variable that thediscriminant functions predict a subject will be in with thecategory involved in it. The example of pain relieversexplains the complete analysis of discriminants.

Discriminant Analysis in Marketing: This analysis hasbeen used quite extensively in marketing. The followingaspects can be studied by this type of analysis:

1. Identification of new buyer group.

2. Consumer behaviour toward new products or brands.

3. Brand loyalty study.

4. Relationship between variables.

5. Checklist of properties of new products.

The targeting strategy of various pain relievers needs to bediscriminant targeting different characteristics as perceivedby consumers. The survey of 1000 consumers have beenmarked on a 5 point scale. The pain relievers characteristicsneed to be grouped and marketed accordingly.

I II III IV V VI VII

Moov Iodex Zandu Amrutanjan Medicream Relaxyl Spray

1. Joint Pains 4.2 3.4 3.3 3.3 4.3 5.0 2.3

2. Muscular Pain 3.3 4.3 3.0 2.0 4.3 4.3 4.5

3. Backache 4.2 4.2 3.0 1.5 3.2 5.3 3.3

4. Sciatica (Nerve) 3.1 3.1 2.1 2.0 3.2 4.3 4.5

5. Headache 1.0 0.0 4.2 4.0 0.0 0.0 0.0

6. Cold (Coryza) 0.0 0.0 3.3 3.0 0.0 0.0 0.0

7. Rheumatism 2.1 1.0 1.2 1.1 3.2 4.0 1.5

8. Arthritis 2.1 1.0 1.2 1.2 3.2 4.0 1.5

9. Gout 3.2 2.0 1.5 1.2 2.5 4.0 1.0

10. Smell/Aroma 4.5 1.0 2.0 2.0 4.0 4.0 3.5

11. Non Greasiness 4.0 1.0 1.5 1.5 4.0 5.0 5.0

12. Ease of Application 4.5 2.0 2.0 2.5 4.0 4.5 5.0

13. Cooling/Warming 4.0(W) 2.0(W) 3.0(C) 3.5(C) 4.0(W) 3.5(W) 5.0(C)

Pain RelieversCharacteristics

Table 8.5



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Discriminant analysis technique can be used by themarketing manager who wants to have an idea about themarket in terms of certain profile of pain relievers from adata about particular types of pain relievers. The methodderives the relative weights to the different types of painrelievers needs. Thus, the discriminant functions show thecommon patterns of pain relievers for various types of painrelievers. In this example, the market is initially segmentedon the basis of product types and then we attempt todiscriminate each of the products on the basis of the specificcombination of pain relievers needs that they may be serving.

Figure 8.6: Pain Reliever Needs for Moov

Figure 8.7: Pain Reliever Needs for Iodex

5.0

4.0

3.0

2.0

1.0

0.0

J MP BA S H C R A G S NG EA C/W

J=Joint Pains MP=Muscular Pain BA=Backache S=Sciaticia (Nerve)H=Headache C=Cold (Coryza) R=Rheumatism A=ArthiritisG=Gout. S=Smell/Aroma NG=Non Greasiness EA=Ease of ApplicationC/W=Cooling/Warming

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Figure 8.8: Pain Reliever Needs for Zandu

Figure 8.9: Pain Reliever Needs for Amrutanjan

5.0

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3.0

2.0

1.0

0.0


J=Joint Pains MP=Muscular Pain BA=Backache S=Sciatica (Nerve)

H=Headache C=Cold (Coryza) R=Rheumatism A=Arthritis

G=Gout S=Smell/Aroma NG=Non-Greasiness EA=Ease of Application

C/W=Cooling/Warming

5.0

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Figure 8.10: Pain Reliever Need for Medicream

Figure 8.11: Pain Reliever Needs for Relaxyl



G=Gout S=Smell/Aroma NG=Non Greasiness EA=Ease of Application

C/W=Cooling/Warming

5.0

4.0

3.0

2.0

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6.0

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Figure 8.12: Pain Reliever Needs for Spray

6.0

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C/W=Cooling/Warming

❤





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0

1

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MOOV

IODEX

ZANDU

AMRUTANJAN

MEDICREAM

RELAXYL

SPRAY


Figure 8.13



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Conjoint Analysis

Conjoint analysis is concerned with the measurementa combination of two or more attributes that are importantin marketing decisions from customers point of view. Inthis analysis, marketing research suggests a new combinationon the basis of existing attributes. For example: A bankwould like to know which is the most desirablecombination of attributes to frequent borrowers – rateof interest, instalment amount, date of payment ofinstalment.

Conjoint analysis is useful for products which can be offeredin different combinations for which the consumer has tomake a trade-off.

As such it is more useful for products which require a longerbuying process for consumers.

The attributes for which the different levels are to be testedmight not be the ones that the consumer considers importantwhile making a choice. It is not always right to add the utilityscores across respondents unless the researcher is sure thatthey belong to a homogenous group.

Numerical Example

Consider a situation in which a manufacturer differentcolours of paints is interested in measuring consumers’ tradeoffs among the following attributes:

*Brand *PriceAlpha 50 per litreGamma 60 per lireBeta 70 per litre*Life *Colours3 Years Pink4 Years Green5 Years

Potential replacement paint purchasers are recruitedand presented with the 18 alternatives. Each respondentis asked to rate each of the alternatives on a 0-10scale, where 0 indicates absolutely no interest in



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purchasing and 10 indicates extremely high interest inpurchasing.

Illustratively, Figure 8.13 shows the 18 evaluations made byone respondent. Although a total of 3x3x3x2 = 54combinations of attribute levels could be made up, therespondent needs to evaluate only 18 of these. However, thisspecific set of 18 should be selected in a particular way, aswill be noted later.

Figure 8.14 shows graphs of the implied values for each ofthe attribute levels; these can be obtained from an ordinarymultiple regression program using dummy variable coding.All one needs to do to estimate the respondent’s originalevaluations is to add each separate value (The regression’sintercept term may be added in later if there is interest inestimating the absolute level of purchase interest.) Forexample, to obtain the respondent’s estimated evaluation ofcard 1, one reads off the part worths:

Value of alpha = 2.4

Value of 3 years = 0

“Value” for Rs 50 per litre (a Rs 20 cost saving) = 1.6

Value for green colour = 1.2

= 55.2

In this instance we obtain an almost perfect prediction ofthe person’s overall response to card 1. Similarly, we canfind the estimated total evaluations for the other 17 optionsand compare them with the respondent's originalevaluations.

The regression technique guarantees that the (squared)prediction error between estimated and actual response willbe minimized.

The information also permits the researcher to findestimated evaluations for all combinations including the 54–18=36 options never shown to the respondent. Moreover,all respondent’s separate part-worth functions as illustratedfor person can be compared in order to see if various types



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of respondents (e.g. high versus low income respondents)differ in their separate attribute evaluations.

In short, while the respondent evaluates complete bundlesof attributes, the technique solves for a set of part-worths–one for each attribute level that are computed from theoverall trade offs. These part-worths can then be combinedin various ways to estimate the evaluation that a respondentwould give to any combination of interest. It is this highleverage between the options that are actually evaluated andthose that can be evaluated (after the analysis) that makesconjoint analysis a useful tool.

Card 1

Brand Alpha

Life 3 Years

Price Rs 50

Colour Green

Respondent's Rating....5.2

Card 2

Brand Alpha

Life 4 Years

Price Rs 60

Colour Green


Card 3

Brand Alpha

Life 5 Years

Price Rs 70

Colour Green


Card 4

Brand Gamma

Life 3 Years

Price Rs 60

Colour Green


Card 5

Brand Gamma

Life 4 Years

Price Rs 70

Colour Green


Card 6

Brand Gamma

Life 5 Years

Price Rs 50

Colour Green


Card 7

Brand Beta

Life 3 Years

Price Rs 70

Colour Green


Card 8

Brand Beta

Life 4 Years

Price Rs 50

Colour Pink


Card 9

Brand Beta

Life 5 Years

Price Rs 60

Colour Green


Contd...



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Card 10

Brand Alpha

Life 3 Years

Price Rs 70

Colour Pink


Card 11

Brand Alpha

Life 4 Years

Price Rs 50

Colour Green


Card 12

Brand Alpha

Life 5 Years

Price Rs 60

Colour Green


Card 13

Brand Gamma

Life 3 Years

Price Rs 50

Colour Green


Card 14

Brand Gamma

Life 4 Years

Price Rs 60

Colour Pink


Card 15

Brand Gamma

Life 5 Years

Price Rs 70

Colour Green


Reliability and Validity Checks

In carrying out a conjoint analysis it is useful to include thefollowing ancillary analysis: (1) Test-retest reliability,(2) A comparison of actual utilities with those of randomrespondents and (3) An internal validity check on model-based utilities.

The test-retest reliability can be conducted by including afew replicate judgements at a later stage in the interview.The purpose here is to see if the judgements are highlycorrelated, on a test-retest basis, to justify the analysis ofthe respondent’s data.

Card 16

Brand Beta

Life 3 Years

Price Rs 60

Colour Green


Card 17

Brand Beta

Life 4 Years

Price Rs 70

Colour Pink


Card 18

Brand Beta

Life 5 Years

Price Rs 50

Colour Pink


Figure 8.14: Product Descriptions for Conjoint Analysis



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Random-respondent utilities are obtained by running asample of pseudo subjects. The pseudo subjects input dataconsist of random ratings or rankings as the case may be. Asthe sample size increases we would expect, on an average,equal utilities within each set of factor levels. However, anyspecific pseudo subject would depart from this expected valuethrough sampling variability alone. By analysing a sampleof 100 or so pseudosubjects the researchers can develop acrude type of confidence interval around each set of averagedpart-worths with which to compare real respondents results.

Guidelines for use of Multivariate Analysis inMarketing Research

There are a large number of applications of multivariateanalysis which can performed by multivariate analysis.

4

3

2

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0Alpha Gamma Beta

Brand

(2.4)

(3.3) 4

3

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Life

(2.7)

(3.5)

4

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1

050 60 70

Price

(1.7) (1.5)

4

3

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0 Pink Green

Colours

(1.2)

Figure 8.15: Part-worth Functions Obtained from ConjointAnalysis (Hypothetical Data)



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Jagdish N. Sheth, in "seven commandments for uses ofmultivariate methods", multivariate methods for market andsurvey research offers a number of guidelines to themarketing researcher who intends to use multivariatemethods.

1. The marketing researcher should not try to betechnique-oriented. If he develops a fancy for one or twoparticular techniques and uses them indiscriminatelywithout checking their suitability in a given case, it willharm the interests of marketing research. It may alsobring about the downfall of multivariate methods.

2. He should not be carried away in building models,disregarding the fact that multivariate models areinformation inputs to facilitate management in theprocess of decision-making.

3. He should remember that multivariate methods are notsubstitutes for his skills and imagination in the designof research. These are necessary in conceptualizing theproblem.

4. He should not overlook the need for lucidcommunication with the management. A first rate studyusing sophisticated techniques may go to waste if themanagement is unable to understand it.

5. He should not make statistical inferences about theparameters of multivariate models. Such inferences arenot possible on account of the sizeable existence of non-sampling or measurement errors in the data in the socialsciences. Such techniques should be seen as descriptivestatistical techniques for reducing large data to asummarized and meaningful form.

6. Sometimes, the researcher may be carried away by arandom relationship among the variables and putsubstantive meanings into the data, which may not betrue. This is especially true of some multivariatemethods such as cluster analysis, multidimensionalscaling and conjoint measurement as there is nosampling theory behind them. Therefore, these are



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heuristics. To guard oneself against this error, it maybe advisable to use at least two different techniques.

7. Finally, he should exploit the complementaryrelationship inherent in the structural and functionalmultivariate methods. In other words, he shouldsubstantiate a number of judgements which he has tomake with structural multivariate analysis of data. Forexample, it is advisable to use cluster analysis first tospecify mutually exclusive groups before using amultiple discriminant analysis.

Summary

Multivariate analysis procedures involve simultaneousanalysis of data measured on two or more variables.Multivariate techniques are largely empirical and dealwith the reality; they possess the ability to analyzecomplex data. The basic objective underlyingmultivariate techniques is to represent a collection ofmassive data in a simplified way.

It transfers a mass observation into a smaller numberof composite scores in such a way that they reflect asmuch information as possible contained in the raw dataobtained concerning a research study. Multivariateanalysis is specially important in behavioural sciencesand applied researches for most of such studies involveproblems in which several response variables areobserved simultaneously.

Review Questions

1. What do you mean by multivariate techniques? Explaintheir significance in the context of research studies.

2. What is the significance of using multiple discriminantanalysis? Explain in brief the technical details involvedin such a technique.

3. Write short notes on:

(a) Cluster analysis



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(b) Conjoint analysis

(c) Factor analysis

(d) M.D.S

4. Name the important multivariate techniques andexplain the important characteristics of each one of suchtechniques.

5. Differentiate between bivariate and cluster analysis.

6. Explain in brief the ‘correspondence analysis’ technique.

7. Differentiate between univariate and multivariateanalysis.

Introduction

The formal marketing research proposal can be viewed as aseries of steps called the research process. To effectivelyconduct a research process it is essential to anticipate allthe steps and recognize their interdependence. In researchproposal, the researcher should get the details of sponsor.The research proposal could be framed up for one’s owncompany as an aid to marketing decisions, for a client forcommercial purpose or by a student of marketing as anacademic exercise. In all the three cases, a researcher has toobtain certain details, which would facilitate the researcherto design the market research proposal. The researcher cancollect the following information from the sponsor:

1. The main objective of research and the detailedobjectives of the study and how the relevant informationwill be used by the sponsor.

2. The inhouse information available to assist inpreparing the research plan. It should include thedetails on marketing mix, marketing strategies andsales data.

275

Objectives


y Discuss a market research proposal.

y Understand cost elements in a market research proposal.

y Discuss-how to prepare a research proposal.

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Unit 9

Report Writing



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3. The market competition and industry conditions in themarket.

4. The time framework for the completion of the project.

5. Cost considerations, if any, which may have implicationson the mode of operations and the area to be covered.

6. Any other special considerations.

After collecting the above information and also personaldiscussion with sponsor, the research agency/researcher canprepare a proposal for carrying out the research work. Thefollowing Example will help in understanding detailsrequired from the Hero-Honda company regarding marketsurvey on “psychographic analysis of Hero-Honda splendorowners”.

Example 9.1

Details from M/s Hero-Honda Ltd. for the market survey ofHero-Honda splendor owners:

1. Product details: __________________(technical aspects). __________________

2. Give details on the __________________exact product mix that is __________________to be covered for the __________________market survey. __________________

3. List all present dealers __________________of the product. __________________

4. List all facilities __________________available to the customers. __________________

5. Which are the different __________________market segments available for __________________the product? __________________

6. Which are the known competitive __________________products available in the market __________________which fulfil the same needs _________________of the users? _________________

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277UNIT 9 Report Writingu


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7. Who are the major known _________________competitors at present in _________________the market? _________________

8. What is main objective of _________________this market survey? _________________

9. What coverage is desired _________________for this market survey? _________________

10. What assistance will be provided _________________by your company? _________________

— Past sales records _________________

— Industry demand _________________

— Sales literature _________________

— Sales display _________________

Research Proposal

The research organization will require a team depending onthe scope of the research project. An organization set-up asgiven below could normally be used.

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Research Organization

Research Project Incharge

Research Officers

Research Assistants

Field Staff

Figure 9.1



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The following Table shows job description at each level couldbe as under:

Table 9.1

Research Research Officer Research Assistants Field StaffProject Incharge

He is Research officer The main job They will carryin-charge will select the would be the out the actualof the samples, will supervision over the field work forresearch design the field staff. They data collection andproject. questionnaire will also help in will conductHe is and will provide compilation of all personaldirectly the necessary the data in a discussions withinvolved with the training to systematic manner, the samples.sponsor and assistants and properly segmentedthe research team. field staff. and in tabularHe will do He is also forms for easy analysis.the costing, involved in thepreparation analysis of the dataof time-schedule collected, arrivingand report writing at conclusions

and preparingthe draft of the report.

Costing

The following headings are to be covered in market researchproposal:

1. Man-hour costs ___________________(Man-hours × cost + per hour) ___________________

2. Travelling costs ___________________

3. Daily allowances ___________________

4. Cost of stationery, postage, ___________________telephone, fax, internet, etc. ___________________

5. Typing, binding ___________________

6. Admn–charges(Normally taken as 7.5% of 1-5) ___________________

7. Profit Margin ___________________(Normally taken as 25% of 1-6) ___________________Total cost proposed to client ___________________

The Research Proposal

After several weeks of preparation, a research proposal isdeveloped and sent to the sponsor for review. At a subsequent

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meeting with the research firm and after a few changes, theproposal is approved. The following is the summary of thefinalized proposal submitted to M/s Electrolux by Admar on“market mapping study of washing machine”.

Rationale for the Study

The rationale is to have an in-depth understanding of theoverall durable market as well as that of the washing machinemarket. This will aid in identifying opportunity segmentsand the need gaps present in the market.

Based on this, they will be able to develop appropriatepositioning strategy for Electrolux. Moreover, it will help inproviding specific inputs for development of an effectivecommunication strategy and plan.

Research Objectives

(a) To understand consumer psychographics with respectto ownership and purchase of durables in general andwashing machines in specific.

(b) To understand existing habits and beliefs that influencethe needs and expectations with respect to ownershipand purchase of washing machines, its type and brandsin specific.

(c) To map positions of different brands of washingmachines in the consumer’s mind by perceived strengthsand weaknesses of each of its contributors.

(d) To gauge the existing equity of Electrolux and itsvariance across different levels of familiarity.

Research Methodology

u The research design will be an exploratory-cum-diagnostic qualitative research study.

u It will involve personal, face-to-face and in-depthinterviewing technique with the help of an interviewguide.

u The research is to be conducted by the field staff.

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Target Respondents

To give the premium pricing strategy of Electrolux range ofwashing machines the following could be our target groups:

u Monthly household income of Rs 10,000 plus or owninga new generation car and air-conditioner at home.

u Potential buyers on active search.

u Recent buyers (within 3 months) of washing machines.

u Households having a high level of education as well ashigh income.

u Either replacement or first time buyers of washingmachines.

Research Centres

The centres, we have chosen by contrasting weather andbuying habits are two of the largest cosmopolitan cities andthe most potential markets in India.

Mumbai — Humid and high monsoon market. A city ofmiddle-class earners.

Delhi — Dry and low monsoon market. A cityconstituting mostly of business-class earners.

Sample Size and Sample Composition

Delhi Mumbai Total

Recent Buyers 15 15 30Potential Buyers 15 15 30Total 30 30 60

u A quota of about 10 to 15 buyers of front loading washingmachines.

u 60:40 split between replacement and first time buyer.

u 50:50 split of executives/professionals and businessmen.

Sampling Procedures

u The procedure adopted for this project is purposivesample method.

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u The listing of respondents from both households anddealers outlets is spread across 6-8 areas within eachcity.

u Appointments will be fixed during listing andrespondents interviewed at home.

Research Project Execution

u The entire recruitment is carried out and managed bythe general field force of Admar.

u Research executives carry out all interviews.

u Usual norms of quality are followed both at therecruitment as well as before the interviewing stage toensure data integrity.

u Research executives analyse all response contents.

Research Units

u Most of the houses surveyed were nuclear families livingin flats with 4-6 members.

u Out of them 2-3 were families with school going children.

u The living room wears a functional look with a sofa orsofa-cum-bed, a centre table, wall paintings/hangings,bronze plates, wall paper decorations.

u The flats usually have attached dining and drawingrooms.

u The television and music systems are normally kept inthe living room (in Mumbai) and in the bedroom (inDelhi). Normally there is a trend of multiple televisionownership in Delhi.

u Washing machines are normally kept in the toilet ordining area.

Samples

u Life revolves around the house and family.

u In Delhi, mainly full-time housewives, whereas inMumbai, it’s the reverse.



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u Cooking–she does it herself.

u Bartan dhona, jharru-pochha and dusting-the maid/servant does it.

u Kapra dhona–she does it herself.

u Bartan dhona, jharru-pochha and dusting–the maid/servant does it.

u Kapra dhona–she does it herself in Delhi but not so inMumbai.

Research at a Glance

u Typically the middle class and a few upper middle classfamilies have a functional outlook.

u The housewife almost always holds the rein of the familywith the husband as the financier.

u Most of the families apparently seem quite content withwhat they own.

u Household entertainment and kitchen gadgets form thebasic possessions everywhere.

u There is wide variation evident across cities surveyedfor items like car, cooler, air-conditioner, oven, vaccumcleaner.

u Washing machine—emerging as a necessity.

Example 9.2

Research Project SynopsisConsumer Behaviour of Titan Quartz Watch

1. Introduction

A business firm comes into being because of the existence ofconsumers who have unfulfilled needs and wants. To fulfilconsumers’ needs, organizations are created. The consumerbehaviour can be defined as, “the decision process andphysical activity engaged in when evaluating, acquiring,using or disposing of goods and services”. The term consumeris a far wider term as it comprises of not only the actual

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buyer or consumer but also users, i.e., customers. There aretwo situations when this distinction between consumers andcustomers may occur:

(a) When the service or product is provided free.

(b) When the customer is not the actual user of the productor is only one of the many users.

2. Objectives of the Study

The objectives of the study are:

(a) To find out the consumers of Titan watches.

(b) To find out why do these consumers buy this brand andnot the competitors’ brands.

(c) To analyse as to how watch consumers perceive Titanproducts to fulfil their needs.

(d) To evaluate whether they feel satisfied after havingbought Titan product.

(e) To study the feelings of the consumers as reflected intheir behaviour as consumers.

3. Research Methodology used for Carrying out the Study

(a) Data collection: The study conducted is exploratory innature. The data will be collected for 100 people–bothmales and females.

(b) Data analysis: The technique of sampling used isstratified random sampling. Here the sample is basedon three groups. First group is upto post graduates,second group is employees and third group is above 45years of age.

(c) Statistical analysis: Consumer behaviour of usersof Titan’s Quartz watch is analyzed by gettinginformation from friends, newspapers, magazines,television and hoardings about the price and quality ofthe watch.

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4. Application of Consumer Behaviour in Marketing

Marketing is defined as ‘human activity directed at satisfyingneeds and wants through the exchange process’. Consumerbehaviour and marketing go hand in hand. Consumerbehaviour has a number of applications in the area ofmarketing as given below:

(a) Analysis of market opportunity.

(b) Selection of the target market.

(c) Determination of the product mix.

(i) Product

(ii) Price

(iii) Distribution

(iv) Promotion

(d) Non-profit and social marketing.

(i) Analysis of market opportunity: The study ofconsumer behaviour helps in identifying needs andwants which are not fulfilled. This is done byexamining income status, consumers’ lifestyle andemerging influences. Its rapidly rising sales graphis an indication of how well the product hassatisfied the consumers’ needs.

(ii) Selecting the target market: The study ofconsumers’ trend would reveal distinct groups ofconsumers with very distinct needs and wants.Study of potential consumers for wrist watchesreveal that there is a class of consumers whoprefer Quartz watches on special occasions anduse normal watches in their daily routine.

(iii) Determining the product mix: Having identifiedthe unfulfilled needs slot and having modified theproduct to suit heterogenous consumers tests, themarkets now have to get down to the brass tacksof marketing. They have to determine the rightmix of product, price, promotion and advertising.



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(a) Product: The marketer has the product thatsatisfies hitherto unfulfilled consumerneeds, but he must decide the size, shapeand attributes of the products. Titanmust figure out conspicuously to havepredominant quality over other products tochoose from. Does the product require anyspecial kind of packaging? Does it need anyguarantee or after sales services? The studyof consumer behaviour also guides themarketer in making decisions regardingpackaging.

(b) Price: Titan company has already fixed theprice the marketer should charge for theproduct. Should it be the same as that ofthe competing product or lower orhigher? Should the price be market on theproduct or left to the discretion of theretailer?

(c) Distribution: Having determined theproduct size, packaging, shape and price, thenext decision the marketer has to make isthe distribution channel. What type of retailoutlet should sell the products? Does theconsumer look for the nearest convenientlocation or is he willing to travel somedistance for buying the product?

(d) Promotion: The marketer here is concernedwith finding the most effective methods ofpromotion which make the product standout amongst the clutter of so many otherbrands and products which help increasethe sales objective and yet be within thebudget.

(iv) Use in non-profit and social marketing: Theknowledge of consumer behaviour is also usefulin the marketing of non-profit or social orgovernmental service or institution.

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5. Contribution from the Study

Consumer behaviour comprises the entire spectrum ofactivities and processes in which individuals engage whenbuying, using, acquiring or disposing of goods and services.The purchase is only one part of this range of activities. Anunderstanding of consumer behaviour is of paramountimportance to all persons engaged in a marketing activity.Its importance can be measured from the fact that:

(a) Behaviour of consumers can be understood.

(b) Behaviour can be influenced.

(c) The marketer can manipulate the influencing variablesto his advantage. Having understood the behaviour ofconsumers and knowing that their behaviour can beinfluenced, the company can initiate a number of stepsto do so.

Research Report Writing

The last step in the research process is the preparation andpresentation of the research report. The best of researchefforts will be of little value unless the result can besummarized and communicated to marketing managementin a form that is both understandable and useful.Preparation and presentation of the research report isthe most important part of the research process. If thereport is confusing or poorly written, all the time and effortspent on gathering and analysing data would not bring anyresult.

The purpose of this chapter is to give guidance in preparinga research report, which is simply the presentation ofresearch findings to a specific audience. We will discusstwo vital ingredients of this communication process: (1) Thewritten research report, and (2) The oral presentationtypically provided for those who occupy executivepositions. Along the way, we will review some of themore popular devices for graphical and visual supportand how statistics can be used or misused to suit yourneeds.

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Types of Research Reports

Depending on its intended audience, the research report mayby either technical or popular in orientation. While bothapproaches describe the research study, its methodology,findings, conclusions and recommendations, they can differconsiderably in terms of detail, writing style, use of technicalterms and length. In general, the higher the executive statusof the audience, the shorter the report will tend to be.

Technical Report

The technical report is generally intended for otherresearcher, or for research managers. The report shouldenable another researcher to be a critic of methodology, checkcalculations and accuracy and to follow everything which isdone on a step-by-step basis. A brief definition of anytechnical term should be given.

The Popular Report

The popular report is intended for a more general audience,one that is not conversant with the details of researchmethods and terminology. Compared to the technical report,the presentation will be a bit more lively with increasedattention to headlines, flow diagrams, charts, tables andoccasional summaries for the purpose of stressing majorpoints.

Because different kinds of audience may be interested inthe results of the same marketing research study, it issometimes necessary to write both a technical report and apopular report.

Guidelines for Writing a Report

Researchers who are effective in report writing agree thatthere are a series of guidelines which should be followed.

Consider the Audience: Make the report clear; use onlywords familiar to the readers and define all technical terms.To make the comparison of figures easier, use percentages,rounded off figures, ranks or ratios; put the exact data in atable within the text or in the appendix. Use graphic aids

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(charts, graphs, pictures, etc.) wherever they help clarify thepresentation of data.

Address the Information Needs: Remember the researchreport is designed to communicate information to decisionmakers. Make sure it clearly relates the research findingsto the objectives of management.

Be Concise, Yet Complete: Most managers will notwant to read about the details of a research report.Knowing what to include and what to leave out is aconfusion.

Steps in Report Writing Process

Two main attitudes must be cultivated while preparing towrite a project report:

Attitude 1: Adopt the fresh mind approach (FMA).

Attitude 2: Adopt the kiss approach (keep it short andsimple).

Fresh-Mind Approach (FMA)

Normally we proceed with a preoccupied mind as if thesolution is available and the report is to be made suitingthat solution. It is essential that a researcher must clearhis mind of all preoccupations about the solution to theproblem. If the data collection, investigation and analysisare done properly, the interpretation and recommendationsmay be quite different from what the researcher expected.Developing the fresh mind approach will help in avoidingthe mindset about a situation, which is too commonwhen dealing with a familiar work situation. We arealways able to find fault with someone else’s work, whilewe fail to see what is wrong with our own. In light of this,the person who is going to assess your work will adopt theabove strategy of evaluating your work if sufficientoriginality, genuineness and a fresh approach has not beadopted by you. The project assessor certainly possesses theskills of assessing whether the work is done with FMA orotherwise.

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Kiss Approach (Keep it Short and Simple)

Your project work is going to be read and evaluated bysomeone who:

u Maybe outside your organization.

u May not be quite familiar with the field of study.

u May not be conversant with technical terms.

Therefore, you must write the project study such that:

u It is understandable.

u It is simple.

u It provides sufficient background information.

u It creates a clear picture in the mind of your workenvironment.

u It helps him understand the problem under study.

For the above you must:

1. Use short sentences.

2. Use simple language.

3. Use logic.

Short sentences will help in avoiding grammatical mistakes,thus creating a good impression of the researcher. Avoid useof technical jargon. This may cause harassment to theassessor. If the use of technical terms in unavoidable, it isdesired to include glossary of terms in the project report.Sometimes the researcher uses abbreviations. It isrecommended that a page explaining the full form ofabbreviations may also be included. In a nutshell, shortsentences and simple language should be used throughoutthe report.

Tips to be followed.

u Use a friendly and informal tone.

u Explain things clearly.

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u Avoid overloading with information.

u Use relevant anecdotes.

u Keep sentences, and paragraphs, short.

u Choose simple and familiar words.

u Avoid long phrases. Say although’ rather than "inspiteof the fact that”.

u Explain jargon and technical terms clearly.

Size Report

Size of report will depend upon the subject matter and whatis involved in the study.

All India Management Association, Centre for ManagementEducation, suggests that the report should be coveredbetween 60 to 100 typed pages (double space). Eachpage must be typed only on one side leaving a widemargin.

School of Management Studies, Indira Gandhi National OpenUniversity (IGNOU) suggests that the length of the reportmay be about 50 to 60 double spaced typed pagesnot exceeding 18000 words (excluding appendices andexhibits). However, 10 per cent variation on either side isadmissible.

Faculty of Management Studies, University of Rajasthansuggests an average size of the report is between 100 -150typed pages in 3/2 space.

Bearing in mind the time available to students to completethe report, and to facilitate the understandable anxiety ofstudents who are doing this exercise for the first time, thesize of the report is fairly good.

In practice, there is no mandatory length and the studentsshould be guided by their project guides on this matter,in fact, the researcher should deal with the report withoutregard to its length ensuring that all the information isrecorded and the report produced conforms to therequirements of the objectives of the study.

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Check list

1. Check whether all essential information is included.

2. Check for proper structure.

3. Check for clarity.

4. Check for completeness.

5. Check there is no unnecessary pending.

6. Check that it essentially contributes to the objectives.

7. Check if anything can be curtailed if it is too voluminous.

In other words, write everything about the subject understudy and structure it with the help or your guide. It isdesirable to get the first draft typed in double space with atwo inch margin on the right hand side of the page. This willgive the opportunity to see:

u What the report looks like?

u What modifications are necessitated?

The margin and the spacing helps in entering correctionsand additional information if desired. This also facilitatesediting of the report.

Steps in Writing Report

The method of carrying out the study, assembling of dataand compiling of a report should be carried on in the followingeight stages:

1. Preparation

2. Gathering the information

3. Sorting, selecting, arranging and recording the material

4. Writing the introduction

5. Recording inferences

6. Writing recommendations

7. Preparing the report presentation

8. Typing the report.

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Preparation

Ready yourself mentally for the task of project writing asexplained in Fresh Mental Approach (FMA).

Be sure you accurately understand the purpose of yourreport and its objectives as defined in the project synopsisor terms of reference.

Put yourself in the position of the evaluator and ask yourselfthese questions:

1. What information, i.e., evidence and justification, wouldI require to arrive at a logical inference and make theright decision?

2. As an evaluator, how much, if anything, do I alreadyknow about this subject? Decide on the following issues:

u Method of study.

u What information do you need?

u Who is going to be involved?

u With whom you going to carry out your study?

u When are you going to carry out your study?

u Project plan–time schedule to complete the task.

It is extremely useful to relate the plan to a time scheduleso that you know what to do and when, in order to completethe report by the required deadline. (Prepare a CPM bybreaking down the project activities into sub-tasks andallocate a duration to each sub-task).

Gathering the Material

At this stage, don’t attempt to write the report. Collect allthe information i.e., facts, figures and ideas, about the subjectby whatever means available. Some of the means used ingathering the information are briefly given as under:

By Observation

Don’t rely on your memory. While observing an operation orcoincidence or a situation, record the sequence in detail. Lookat it, watch it, time it and record everything you see.

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By Reading

Published work of other researchers on similar issues, factualdocumentation produced within the organization (if the studyis about an organization), documentation of professionalbodies will often provide enough information relative to yoursubject. Give credit in your report to the source of suchinformation.

By Interviews

Interviews can be formal or informal depending upon theirnature and the person being interviewed. Keep the followingpoints in mind:

u Plan your interview

u Give your interviewee notice of your subject

u Prepare your questions beforehand

u Don’t rush an interview

u Focus on substance

u Be accurate.

By Discussion

Hold discussions with your colleagues, guide, and anyinterested person in the subject. Respect their views.

By Surveys

Surveys are carried out to assess customer opinion andreaction. These are also useful in understanding people’sattitudes. Questionnaires are useful instruments in carryingout surveys. Care must be taken in preparing thequestionnaire and, if in doubt, seek the advice of your guide.Include copies of the questionnaires and of their analysis inyour report.

By Enquiries

Enquiries can be made from manufacturing or serviceindustry through letters, fax or telephone.

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Explain

u Who you are?

u Purpose of your enquiry.

Be polite while asking for their help. Generally you willreceive a favourable response and these sources ofinformation can be most valuable. Give credit to suchinformants and always thank them for their help.Acknowledge their support in your report. Use yourknowledge and experience

By experiment

Try something and see if it works. Record the details andverify the results. If there is any doubt about the accuracy ofthe information, try and check and verify it from anothersource.

If it is not possible to verify the information, discard it orquote it as uncorroborated. Always be sure of the facts.

Make liberal use of visuals, i.e., diagrams, maps, charts,photographs, statistical tables. Even sometimes it may beappropriate to attach sample products to illustrate andexplain your text. This will make your report visuallyattractive and interesting.

Avoid using memory and prejudice. These can often lead todistorted facts. As a report writer always carry a notebookwith you and note down pieces of information or ideas orthings to do at the time they come to you, instead of relyingupon the memory. Once you have written it down you canconcentrate on something else.

At this stage you will have sufficient information in the formof notes, collections from various published data, survey dataand so on. The next step is to sort it all out.

Sorting, Selecting, Arranging and Recording Material

Having assembled all your material, check to ensure thatyou have all you need to support your arguments. Arrangeit in logical sequence, start to finish, ensuring a natural flow.

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The questionnaires, surveys and any other similar documentshould be explained properly. To ensure clarity to thereaders adequate notations should be used for visuals, i.e.,diagrams, maps, charts, photographs, statistical tables.

If illustrations are used to explain a particular part of thetext and are not going to be referred to several times, insertthem in the appropriate position in the text.

If the evaluator needs to refer to these illustrations severaltimes or if they form a supportive material it should be putin the appendices section at the end of the report.

At this stage, clear your mind and go through what you havewritten. Put following questions to yourself:

1. Is it clear?

2. Does it make any sense?

3. Does it clearly specify or indicate problem areas?

4. Does it lead you to the “conclusion” section logically?

Writing the Introduction

While writing the introduction take following points intoconsideration:

1. Create a background of the organization and worksituation for which the project work is being done.

2. Describe the purpose of study.

3. Describe the method of study.

4. Explain difficulties encountered in the preparation ofreport.

5. Introduce yourself, your institution/organization briefly.

6. Ensure continuity between all sections.

Recording Inferences

The conclusions or findings should flow from the outcome ofthe investigations. These findings should lead to concreterecommendations. While writing conclusions, the objectivesof the study should be kept in mind. This will facilitate in

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understanding the quality of investigations and gauge thesuccess of work. Summary of the problem areas followed byexplanation of the various alternative solutions to theproblem should be undertaken and the reason for acceptingor rejecting the possible alternative should be explainedlogically.

Writing Recommendations

While writing recommendations you must adopt a positiveattitude and enlist those points first, which you really wantto be done. You must adopt a constructive approach. Thissection may be started as follows.

It is recommended that (provide a list of recommendationsor action you feel should be taken):

1.

2.

3.

4.

5.

6.

7.

-

-

-

If the recommendations involve financial figures ofstatements, these should be shown against each item. Don’trepeat what you have written. In conclusion, you may give across reference of a relevant paragraph if you want to includesomething in this section.

Give your Report a Positive Ending

At this stage the text of the report is complete and you areready to go the next stage i.e. presentation of the report.

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Report Presentation

Stitch together all the different threads of information intoa coherent whole. Present the data in the form as suggestedin the chapter plan. Write the first draft. Discuss with yourguide and incorporate the suggested modifications. Revisethe document and type it finally. The graphics play asignificant role in report image and care must be taken aboutthe visual aspects of the report.

Visual Aspects of the Report

Many reports require communication of voluminous andcomplex information. It is not possible to do this job withwords only. Graphics portray things that would take volumesto explain through words. Technical reports, in particular,cannot be completed without use of graphics. The main roleof graphics in a report is:

u To support text to communicate report content. Toemphasize key points.

u To make the report attractive.

u To add interest.

u To save time.

u To increase credibility.

u To add variety.

u To create impact.

u To help the reader to remember main points.

Before organizing the report, you must think and plan:

u What graphics are to be used?

u How many graphics are to be used?

u Where to use graphics in the text?

The graphics used in reports are normally:

u Charts

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u Graphs

u Photographs

u Maps

How many graphics are to be used

Each graphic should be selected such that it serves tocommunicate a specific point of the report. Random use ofgraphics should be avoided. There is no set rule to determinethe number of graphics. However, plan what is required tobe communicated effectively through graphics and includethese graphics only.

Where to use graphics in the text

The graphics should be placed in such a position that theyare likely to be there where they are required to be seen.

Consider following points while placing graphics:

1. Place them close to the related text.

2. If the graphic is large, and is of full size, place it on thepage following the text.

3. If the graphic is small, place it appropriately andsurround it with the related text.

4. Graphics which are not discussed in the main reportbut support the discussion should be appended.

5. Always make reference of the graphic in the text to inviteto reader to refer it.

6. Always use rules and borders to enhance presentability.

7. Use colour if you have access to colour printers.

8. Number graphics and title appropriately.

Types of Visual Aids/Graphics

The common type of visual aids used in communicating dataare:

1. Bar charts

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2. Line or area charts

3. Pictogram

4. Pie charts

5. Pictorial diagrams

General Points about Charts

Your illustrations should include

u Appropriate title and units

u Scales or labels on axes

u Key

u Source of data (if from outside source)

u Caption to the chart

Bar charts

Bar charts are:

u Easy to draw

u Familiar to all

u Good for making comparison

While using bar charts ensure:

u The order of categories should be logical and match anytallies of the same data.

u The width of all the bars should be kept same.

u Start the vertical axis at zero (0), if possible.

u If it is unavoidable to start at other than zero (0), indicatethis clearly by a break in each bar or in the vertical axis,with a zig-zag or wavy stroke across each end of thebreak.

Stacked Bar Chart

These charts show the total well. It is difficult to compareheights of the sections with stack bar charts. The stackedbar charts should not be used if the total height has nomeaning.

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Line or Area Chart

Line and area bar charts are used when there is logical orderof points. The order of North (N), South (S), West (W), andEast (E) could be changed giving a completely differentpattern to the graph so it is not a good chart for this data.

Pictograms

A picture or symbol standing for a word or group of words Achart on which symbols are used to represent values.

Pie Charts

Pie charts are the commonly used visual aids. Thedisadvantage of pie chart is that it is not possible to showany category that has zero (0) frequency.

Use a pie chart when you want to compare a number ofelements to each other and in relation to a whole. If youcompare the same information expressed as regularrectangular blocks to a pie graph, you see that the bars aremore precise in comparing elements to each other, but thatthe pie graph is much more effective comparing elements tothe whole. One of the fundamental rule of using pie chart is“never include more than 6 elements.” If you have more thanthis number only show six main elements and include theothers under a diverse heading. If necessary break down thediverse category into a second pie graph.

The pie graph can be made more attractive by:

u Adding pattern to each part

u Using colours

u Adding depth

Two Variables Diagrams

These diagrams are very important when illustration of morethan one variable is needed. It is of great significance todetermine, which variable should be put on which axis.

They illustrate the total number of each sex respondentsquestioned, but this may not be what you want to illustrate.

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They also illustrate the total number people of in eachcategory clearly.

It is more logical to have ‘sexes’ on the horizontal axis fora percentage stacked bar chart where the response ofsexes are being compared. Illustrates a percentagestacked bar chart where responses of the sexes arecompared.

For showing the comparison, multiple bar charts areconstructed. Always provide a gap between the bars forclarity.

Area Charts

Area charts illustrate how it stacks the data like a stackedbar chart and so indicates total record data.

Typing the Report

For report typing, A4 size of paper is recommended. It is ofa standard size and will present no difficulty with covers,binding, photocopying and dividing cards between thesections. The margins should be kept as suggested earlier inthis chapter.

Make sure:

1. Each section of the report starts on a new page.

2. Indicate where capitals, italics and underlining arerequired.

3. If using DTP indicate bold, capital, front type and fontsize required.

4. All headings and sections and subsections are clearlyindicated.

5. Indicate where any indentations of the text are requiredfor the ease of reading.

It is recommended that a clear system of identification isissued for sections, subsections and paragraphs for the speedof reference.

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A typical example is as follows:

Section Headings 1 2 3

Sub-sections 1.1 2.1 3.1

1.2 2.2 3.2

1.3 2.3 3.3

Paragraphs 1.1.1 2.1.1 3.1.1

1.1.2 2.1.2 3.1.2

1.1.3 2.1.3 3.1.3

1.2.1 2.2.1 3.2.1

1.2.2 2.2.2 3.2.2

Sub-paragraphs 1.1.1(a) 2.1.1(b) 3.1.1(a)

(b) (b) (b)

(c) (c) (c)

Important Note

The sample reports given in the book, the main reports withappended parts. These are only typical reports to supportthe report writers in understanding the principles of reportwriting. Each report will be unique depending upon the topicof research.

To submit the report, the prefatory parts should be addedin the main report. The typical sample of a prefatory part isgiven in the book at appropriate places.

Check List for project report before final binding (Typical)

Ensure the prefatory parts are enclosed in the following sequence after

the tittle page:

1. Approved project proposal proforma

2. Synopsis

3. The certificate of originality of work

4. Letter of authorization

5. Letter of transmittal

6. Acknowledgements

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Ensure the main report contains:

1. Table of contents

2. Table of illustrations, glossary of terms, abbreviations, executive

summary, introduction, main report with chapter plan

recommendations and limitations.

Ensure appended parts contains:

1. Bibliography

2. Appendix

3. Any other source of information.

Final Remarks

As soon as your project has been typed, read it carefully andcorrect any errors. Consider following questions about yourreport.

1. Does it look a presentable document?

2. Does it make sense?

3. Does it meet objectives of study?

4. Is it clear and understandable?

5. Is it factual, logical, conclusive?

6. Will the evaluator/reader be stimulated to read it?

7. Are you satisfied with it?

8. Is your guide satisfied with it?

The researcher should get the report signed by the guide.Determine the number of copies required before going forphotocopying. It is preferable, but not necessary, to reproducephotographs and other illustrations in original. The originalcopy which goes to the assessor and the copy which goes tothe library must be presentable. The library copies in allprobability may be referred by your juniors.

A Bit of Advice

Your guide is the person who is supposed to be with youthroughout the preparation of the report. Don’t hesitate tobring your problems to his notice. Seek his advice. Be guidedby him. Respect him. Involve him.

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Documentation and Bibliography

While writing your report you are likely to use theinformation which is not your own information. Theinformation which is developed through secondary sourcesmust be foot-noted. It should also be listed in thebibliography. It is always advisable to acknowledge thereferred material when it is not a general knowledge. Foracknowledging the sources a standard (e.g., BIS, Harward,APA, Chicago, MLA) reference system should be selected. Itshould be followed throughout the report consistently. Sometypical examples of recording informations are discussedbelow:

Guidelines for Getting Information

Determination is a major word to keep in mind when lookingfor facts. If you don’t find what you need in one reference,look for other sources. Never give up and stop with one ortwo attempts.

Guidelines for Getting Information

u Scan material to find out if it is relevant to your project study.

u Check the credibility of the material by considering its text:

Source

Publisher;

Author; and

Current data

u Everything in print is not necessarily true. Check for genuineness.

u Look for several viewpoints on a subject. Don’t depend on one.

Guidelines for Recording Information

Although you may find considerable information ona subject, the real test of your research ability comesin getting the important facts down in a form thatis easily understandable. Volumes of inconsistentinformation do not yield adequate information for preparingreports.

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Follow these guidelines when taking notes:Guidelines for Recording Information

u Use separate sheets of paper or help cards for each source.

u Make a tentative bibliography by writing down the titles whichappear to offer the information you require.

u Keep the papers or help cards in alphabetical order.

u Write in ink.

u Use a consistent bibliographical form.

u Prepare an outline that will give direction to your investigation.

Note: Usually, bibliography material is recorded on 3 × 5 inch helpcards, and notes are made on 4 × 6 inch help cards. Cards are madefrom thick sheets of paper.

u Place a heading, keyed to your outline, on each help card.

u Use direct quotations only when they are significant. Enclose quotedmaterial in quotation marks, taking care to copy each word exactlyas written.

u Use footnotes to give credit for another person’s idea which you areusing.

u Arrange your notes in the order of the outline to facilitate their usefor the basis of the report.

Preparing Footnotes

Footnotes are single spaced and indented five spaces withfootnote typed slightly above the line. The names of authorsare given in normal order. Commas are used to separate mainitems. Each footnote ends with a period.

These examples will guide the author to write footnotes:

Books

(One author)1. Robert Cameron, Statistics for Business (New York:

Oxford Press, 1971), p. 35.

(Two authors)2. M.K. Rampal and S.L. Gupta, Cases and Simulation in

Marketing (New Delhi: Galgotia Publishing Company,1999), p. 101.

(Three authors)3. Ruth Goldhammer, Arthur McGille, and Clyda Bailey,

Marketing Ideas for Today (Columbus: UniversityPrinters, 1973), p. 44.



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(More than three authors)4. Carla samples et al. Survey Methods for Business (New

York: Capital Publishers, 1970), p. 58.

(An editor)5. M.K. Rampal, Cases in Service Marketing (New Delhi:

Galgotia Publishing Company, 2000), p. 84.

(Corporate authorship)6. S.R. Lubeck Committee, Administrative Techniques for

Corporations (San Francisco: American AdministrativeAssociation, 1970), p. 223.

Magazines and Newspapers

(Article in a weekly magazine with no author given)

1. “Trends in Office Equipment,” Office Equipment,January 1977, pp. 88-90.

(Article in a weekly magazine with author given)

2. Rajni Rampal, “Motivating Executives”, “MarketingNews, 20, No.5 (1999),52.

(A news story with author given)

3. Ashok Galgotla, “Current Legislation AffectingBusiness,” Delhi Monitor, 16 Feb, 1998, p. 8, col. 4.

(A news story with no author given)

4. “Coping with Income Taxes,” The Daily News, 4 July1995, p. 3, col. 1.

Encyclopedias

(An article in reference work with author given)

1. “Facts About the Bureau of the Census,” TrinityEncyclopedia, 1970, VII, 493.

(An article in a reference work with no author given)

2. Ben Miller, “Secretarial Skills for the Seventies",Modern Encyclopedia, 1972, X, 477.

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Bulletins and Pamphlets

Guidelines for managers (Washington, D.C.: AssociatedManagers of the United States, 1977), p. 17.

Highlights of the Annual Meeting of the PersonnelManagement Association, Personnel ManagementAssociation Publication No. A-22 (Washington, D.C.:Washington University Press, 1970), p. 35.

Footnote Pointers

Acknowledgments

u Footnotes are used to acknowledge and documentmaterial taken from sources. Failure to give credit forborrowed material is plagiarism.

Placement

u Footnotes may appear at the bottom of the page on whichthe quoted material is used or at the end of each chapteror at the end of an entire work.

Numbering

u Footnotes may be numbered consecutively throughoutthe entire work or numbered consecutively by chapter.

Printing

u Footnotes appear in print as single spaced with doublespacing separating one footnote from another. However,in manuscript copy, footnotes are double spaced withtriple spacing separating one footnote from another.

Referencing the Same Source

u Use ibid., (in the same place), to indicate that the sourceis exactly the same one as in the immediately precedingfootnote.

Example 9.3

(First reference)

1. Rampal M.K., Industrial Marketing (New Delhi: GalgotiaPublishing Company, 2001), p. 80.

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(Repeated reference)

2. Ibid., p. 70.

Note: If the page number is not different, simply use Ibid.

Preparing Bibliography

Bibliography is a list of publications or works which theresearcher has used in the preparation of the report. In otherwords, this should be a list of acknowledgements of sourcesof information other than personal contacts.

The need for referencing is two fold:

1. It enables the researcher and the evaluator to identifythe source of the information or argument, they mayconsult that source directly when the need arises.

2. It helps you to avoid plagiarism, the effects of whichmay be the payment of a severe penalty.

Referencing Guidelines

Reference is required whenever you:

u Quote anything. If the quotation is taken from a bookor article by a third person, then you need to makethis clear in your reference; thus you would citethe original source, indicating that it has beenquoted by that third person–identifying also thatsource.

u Refer explicitly to the work of a particular writer, evenwhere no direct quotation is involved.

u Say something which is the most important element inyour argument, for which a reference can be given.

No reference is required to support:

u Factual Information or general statements which areclearly common knowledge.

u An argument that derives from large number ofdifferent sources.

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The Reference Form

Once again there are no common rules that all researchersfollow, but there are two key principles which every effectiveform of citation follows:

1. Whatever system of citation you employ in a particularpiece of work, it is crucial that you are consistent. Thus,once you have decided on the set of conventions you aregoing to follow, make sure that you follow it rigorouslyand consistently throughout the piece of writing.

2. References should always be full enough to enable thereader to follow them up with a minimum of difficulty.Thus, it is essential that every reference identifies theparticular page number(s). A reference that leaves thereader to find his or her own way to the appropriatepart of the book is of very little value, unless of courseit is in fact the whole book to which you want to refer.

Books

(One author)

Singh Harpal, Indian Company Law’, New Delhi: GalgotiaPublishing Company, 1999.

(Two authors)

Bailey, Clyda, and John O’Donnell, The Economic World,American Economists Association, Chicago: CronkitePublishing House, 1979.

(Three authors)

Gupta Nirmal, Jain R.K. and Malik R.K., Elements ofAccounting. New Delhi: Galgotia Publishing Company, 1998.

(More than three authors)

Griffith, Donna Jean, et al, Problems in Editing. Boston:Hartcourt and Company, 1976.

(An editor)

Cammero, T.J., ed. Corporations and OrganizationalPsychology. New York: Wilson Publishers, 1979.

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(Corporate authorship)

Committee on Business Research. Research Design forBusiness. Pittsbugh: University Press, 1974.

Magazines and Newspapers

(Article in a weekly magazine with no author given)

“Today’s Stocks,” Business World, 2 April 1977, pp, 21-23.

(Article in a weekly magazine with author given)

Kristen, Dorothy. “Women in Personnel Management.”American Management Association, 12 March 1978, pp. 18-20.

(A news story with author given)

Clee, Peter, “Financial Trends.” New York Daily, 26 April1973, p. 4, cols. 3-4.

(A news story with no author given)

“The Rampage of Inflation.” The Cleveland Monitor, 16December 1972, p.5. cols. 1-2

Encyclopedias

(An article in 8 reference work with author given)

Johnson, Samuel T. “ The Design of Organizations."Encyclopedia Britannica, 1970, X, 776.

(An article in a reference work with no author given)

“Career Guidance.” The Modern Encyclopedia, 1975, XII, 456-51.

Bulletins and Pamphlets

Organizations Planning, Washington, D.C.: AmericanAssociation of Administrators, 1978.

Motivating Employees. Dept. of Health, Education, andWelfare. Washington, D.C.: U.S. Government Printing Office,1971.

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Citing Electronic References

This is a relatively new area and stilt in a state of fluxhowever, the basic components of the reference citation are:

u Author [surname comma first initials].

u Title of work.

u Title of complete work.

u Protocol and address.

u Path.

u Date of message or visit.

Abbreviations

cf. Compare. Also abbreviated cp.

Et. Al, And others [et al l aliae].

e.g. for example [example gratial]. Not in italics;preceded by comma.

etc. And so forth. Should never be used in formal writing

ff. following

ibid in the same place [ibidem]. Used to refer to thebook, chapter, article or page cited just before. Notin italics.

Idem the same as; as mentioned before. Used to indicatea reference previously mentioned, is generally usedto refer to the author’s name while ibid. refers tothe book title.

i.e. that is [id est). Not in italics and preceded by acomma.

inter alia among other things. In italics.

loc. cit. in the place cited [loco citato]. Not in italics.

op. cit. in the work quoted (opere citato). Not in italics.

sup. above [supra]. In italics.

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[sic] thus; so. Used to indicate that a surprising or dubiousword, phrase, or fact is not a mistake and is to readas it stands. With brackets.

Ivde see.

vide infra see before. In italics.

see supra see above. In italics; abbreviated v.s

vis – a – vis face-to-face. With hyphens.

viz. namely. Not in italics.

Summary

A good marketing research report possesses of adheringto the study objectives. A marketing researchreport must ensure that it has covered all theissues. The marketing researcher should logicallyjustify their choice of data, presentation of data andfindings.

The standard format of the research report may also beused for report purpose. Deviations from this areallowed to make it interesting and informative to thereader by incorporating the nature of the product andhighlights of the research findings. The user must alsohave an inherent understanding of the research processused, the assumptions made and limitations of theresearch, to rule out being taken for a ride on statisticalfigures which are distorted at times to meet therequirements of the marketer.

1. A research report is the presentation of theresearch findings for a specific purpose. Thepresentation can be written or given orally or both.

2. The guidelines for written and oral reports are(a) consider the audience (b) be concise yet completeand (c) be objective yet effective.

3. The main elements of the written report are (a) thetitle page (b) the table of contents (c) the

Contd....

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management summary (d) the body of the report(e) the conclusions and recommendations and (f) theappendix.

4. The research data can be presented in tabular orgraphic form. The three types of graphic forms are(a) the pie chart (b) the bar chart and (c) the linechart.

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mb-207 research methodology

Documents