qm1 theory notes

8/12/2019 QM1 Theory Notes

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BIET MBA Programme :Compiled by BVN Page 2

Business research is an applied research to find out the solution for business and management problemsfaced by organizations

Determinants of Business research

Time constraint

Availability of dataNature of decisionBenefits Vs Costs

Types of Research

Decision making is the process of resolving a problem or choosing among the alternative opportunities.

Depending on the decision making situation and the information availability in the continuum ofcertainty, uncertainty and ambiguity, the business research is classified into three types.

When the researcher certainly has all information about business problem, it may lead him to choosedescriptive or causal research

Descriptive research seeks to determine the characteristics of the population and answers to who,what, when, where and how questions.

It helps segment and target markets. Descriptive studies are based on some previous understanding of the nature of the research

problem.

For example if researcher wants to study the market penetration of a product, he will try to see thevariables such as sales volume, price competitiveness and other characteristics of a product like

quality, durability, customer satisfaction etc.,.

Researcher resort to causal research when the situation under research is certain and he knows about some

sort of inter-dependency of the variables under study.

Causal research is conducted when there is a cause and effect relationship between the variablesunder study.

Using causal research, one can establish a relationship or dependency of one variable on theother.

For example, if HR manager wants to see the change in productivity as an effect of providingtraining to his employees, training is a cause for change in productivity.

Under the cases of ambiguity, where the nature of the problem to be solved is unclear, objectives vagueand the alternatives are difficult to define, exploratory research is used.

Exploratory research is conducted as a preliminary exercise to analyze the ambiguous situationand to find further direction to the research.

Exploratory research does not provide conclusive evidence to the research. For example if the company wish to launch a product in a new market, it has to study through

exploratory research, the buying behavior of the people in that location.

Completely Uncer

Abso

Descriptive orCausal Research

Exploratory

Research


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Research Process

The stages of the research process are.,

1. Problem defi niti on/formulation: Allows the researcher to set the proper research objectives. Ifthe purpose of the research is clear, the chances of collecting the necessary and relevantinformation will be high. To be efficient, business research must have clear objectives andeffective designs. Exploratory research, Experience survey, Secondary information and literaturereview, pilot studies in the form of focus group interview are some techniques used by theresearcher in precisely defining the research problem with specific objectives.

2. Planning a research design: It is a master plan specifying the methods and procedures forcollecting and analyzing the needed information. It also specifies the sources of information, theresearch method, the sampling methodology, the schedule and cost of the research. Surveys,

experiments, secondary data reviews and observation are the basic tools which help the researcherin selecting appropriate design for the research.

3. Selection of sampling design: It should clearly specify the sampling units of the population,sample size and the most appropriate sampling procedure.

4. Data collection: Once the research design has been finalized, the process of collecting data forthe research begins with pre-determined tools like interviews, questionnaires, schedules etc.,

ensuring minimal sampling error.

5. Data analysis:Once the data is collected, classification, tabulation, editing and coding of the datais done as per the requirement for further analysis. Analysis of the data is determined byappropriate technique as required by the researcher.

6. Conclusion and reporting: The final stage of research is to interpret the information and drawconclusions relevant to managerial decisions. The research report should communicate researchfindings effectively keeping in mind the managerial audience.

Problem Definition / Formulation

Defining a research problem involves the following steps.1. Understand the objectives of the researcher: Research problem should be so framed that it

comprehensively takes care of the existing business problem and finds specific solutions throughfocused objectives.

Iceberg Principle : It is defining the research problem without understanding its depth. Such

business problems are like the submerged portion of the iceberg in a sea, which is neither visibleto nor understood by sailor and hence decisions based on such research are dangerous.Often exploratory research helps researchers to clarify their objectives and decision.

2. Understand the background of the problem : One should always have fair knowledge about thesituation in which the research is being carried out. This can be done by talking to experienced

people in the area of research, going through the past literature which give some clue as to whatneeds to be addressed in the research.


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Business Research Design: Steps involved in a research design.

Research design is the master plan specifying the methods and procedures for collecting and analyzingthe needed information. A well charted research design makes the research process more clear and self

directing.

Following are the steps involved in setting up research design..

Statement of objectives of research Specifying the sources of information Indicating the appropriate research method (i.e., Surveys, experiments, secondary data review or

observation)

Specifying the sampling methodology, schedule and cost of research

Experimental Research

Type of research where the researcher know about the behavior of one variable by having control over theother variables. For example, if the investigator wants to know most efficient complementary offer which

ensure better sales, he has to go on testing the customer response for different offers such as discount, gifthampers, gift coupons, customer cards etc.,.

Experimental designs

These are the tested models / frameworks which help researcher to carry out experimental research,allowing investigator to control or manipulate some independent variables and study its effect on some

dependent variable so that causal relationship between variables may be evaluated.

Basic issues in experimental design

1. Manipulation of independent variable2. Selection and measurement of the dependent variable3. Selection and assignment of test units4. Control over extraneous variables

Evaluation / Validity of experimental designs

Experimental design is said to be valid if it satisfies the conditions of internal and external validity.

In an experimental research, if observed change in the dependent variable is the sole result of the

independent variables being manipulated, then the experimental design used in such experiment is said topossess internal validity.

If research findings through an experimental design can be generalized/applicable to the externalenvironment, such experimental design is said to possess external validity.


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Extraneous variables affecting internal validity of experimental design.

The variables which are not considered under the experimental design and are likely to influence the finaloutcome of the research without the knowledge of researcher are called extraneous variables. Following

are six major types of extraneous variables which affect internal validity of experimental design.

H istory eff ect: refers to the effect of specific event on respondents which may alter their behavior orresponse to the research tool / questionnaire. Further cohort effect is a special case of history effect whereresponses collected from two group differ because of their exposure to different environments

Maturation eff ect :is an effect on the results of an experiment caused by changes in the responses of therespondents due to the changes in circumstances, taste, behavior, attitude as they get matured in their

thinking during the process of data collection

Pre-testing effect : is the change in the validity of an experiment that occurs when initial testing givesclue about nature of the experiment which in turn may influence the response of the respondent when real

data is collected.

I nstrumentation eff ect : It refers to the effect caused by changing the wordings of the questionnaire,

change in interviewers, or a change in the other procedures to measure the dependent variable.Selection: It is a sample bias resulting from differential selection of respondents for the comparison ofgroups. It is also referred to as sample selection error.

Mortality eff ect :It occurs when respondents start retiring from the experiment due to nay reason causedby the situation or self.

Classification of experimental design

Experimental design is said to be basic if only one variable is manipulated. Otherwise if researcher wishesto investigate effect of more than one variable, the required experimental design is called complex orstatistical experimental design.

Quasi-experimental designs(do not qualify as true experimental designs as they do not adequately account for loss of internal andexternal validity)

1. One-shot design (After -Only Design)Symbolically represented as X O1

Xstands for exposure of a group to an experimental treatmentO1Stands for one observation made after exposing the group to an experimental treatment

Eg. If one want to see the effect of price hike on sales for a product, he/she can test it by exposing

few customers to the new price and observing their buying behavior.

2. One group pretest-posttest designSymbolically represented as O1X O2


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Here two observations of an experimental group are made; one before and one after the

experiment

Eg. If HR manager wants to measure effectiveness of a training program on employeeproductivity, he can do it by measuring productivity before and after exposing the employees to a

training program. (O2-O1) gives measure of effectiveness.

3. Static group designSymbolically represented as Experimental Group : X O1

Control Group : O2

Here one group is exposed to a new treatment and compared against control group, which is not

exposed to any treatment. (O2-O1) gives the effectiveness of new treatment.

Eg. Suppose that an agricultural scientist wants to see the change in yield with application of newfertilizer; he can observe the yield of a crop with (O1) and without (O2) application of new

fertilizer. (O2-O1) tells about the change in yield due to the application of new fertilizer.

Basic Experimental Designs

1. Pretest-Posttest control group designExperimental Group : O1 X O2

Control Group : O3 O4

Stands for randomization of samples. The effect of experimental treatment is (O2-O1) - (O4-

O3).

2. Posttest only control group designExperimental Group : X O1

Control Group : O2

(O2-O1) measures treatment effect.

3. Solomon Four Group DesignExperimental Group 1 : O1 X O2

Control Group 1 : O3 O4

Experimental Group 2 : X O5

Control Group 2 : O6

Compromise designs

RR

R

R

R

R

R

R

R


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In many instances of business research, true experimentation is not possible., then what best the

researcher can do is approximate an experimental design. Such designs are called compromise designs.

Time series designs

When researcher wants to study a variable or phenomenon over a period of time before and afterapplication of an experimental treatment, it is called time series design.

O1 O2 O3 X O4 O5 O6

Eg. If fund manager of a financial services company wants to know the investment behavior of his

customers towards a particular mutual fund before and after declaration of dividend; he can do that byobserving the investment pattern at different time points O1, O2, O3before and at time points O4, O5, O6after dividend declaration.

Complex experimental designs

1. Completely Randomized Design (CRD)In this experimental design, effect of one treatment (independent variable) at different levels onthe dependent variable is studied ensuring randomization of samples exposed to the treatmentunder study.

Eg. Effect of application of new fertilizer at varied quantities on yield of the crop can be studiedusing CRD through one-way ANOVA

2. Randomized Block Design (RBD)In this experimental design, effect of two treatments (independent variables) at different levels on

the dependent variable is studied ensuring randomization of samples exposed to the treatmentunder study.

Eg. Effect of application of new fertilizer at varied quantities and type of soil on yield of the crop

can be studied using RBD through two-way ANOVA

3. Latin Square Design (LSD)It attempts to control or block out the effect of two or more confounding extraneous factors. Itmanipulates one independent variable and controls for two additional sources of extraneous

variation by restricting randomization with respect to row and column effects. It assumes thatthere is no interaction effect.

4. Factorial DesignsThese are the most sophisticated experimental designs in which effect of two or moreindependent variables at different levels on the dependent variable can be studied with a scope formeasuring interaction effect and confounding of extraneous variables.


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Module 2 : Sampling and Data collection

Introduction

Sampling design is the crucial part of any business research. It is this phase of research upon which thevalidity of remaining stages rests. As the behavior of the population under research largely depends on the

quality of samples collected, it is very important to see that the samples are collected with utmost care sothat the error due to sampling is as least as possible. In this section, we learn about those various samplingtechniques suited to different situations which ensure collection of best possible samples out of a

population under study.

Sampling

It is a process of collecting samples from the given population using scientific approach, which ensure

minimum sampling error and better estimates of population characteristics.

Sampling distribution

Distribution of sample statistics is called sampling distribution.(detailed explanation will be covered under Module 7}

Sampling Error

The difference between actual value of the population characteristic (eg. mean, s.d etc.,) when compared

to the estimated value based on sample observations.

This error is attributed to sampling fluctuations. This error can not be eliminated completely due to thefact that population parameters are estimated based on only few sample observations. However it can beminimized by applying most suitable sampling technique for data collection.

For example, if the actual value of the average salary of 2000 employees of an organization is Rs. 15000and the estimated value of the average salary based on 100 sample observations is Rs. 14650, then thedifference 15000 - 14650 = 350 signifies sampling error.

Sampling error may creep in due to Faulty selection of the sample (/sampling) Substitution of convenient sample in place of actual sample Faulty demarcation of sampling units Error due to bias in the estimation method

Non Sampling Errors

Non sampling errors in data collection are not attributed to chance and are due to certain causes which canbe traced and may arise at any stage of the enquiry viz., planning, execution, collection, processing andanalysis.

Following are the common reasons for nonsampling errors Faulty planning, vague and imperfect questionnaire, defective methods of data collection Lack of trained investigators, incomplete responses Improper coverage, compiling errors and publication errors


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A good sampling design is the one in which sampling and non-sampling errors are minimized.

Census (Complete) Vs. Sample (Partial) Enumeration

Census Survey Sample Survey1. Here the researcher resort to 100%

inspection of the population2. Provide more accurate and exact

information as the data is collected from

each and every unit of the population.3. Affords to more extensive and detail

study4. Very expensive, time & manpower

consuming.5. Take much time for data analysis if the

population is vast

6. Sampling errors are almost nil.7. Non sampling errors can be controlled

1. It is inspection of representative part of thepopulation

2. Yields near to accurate results whenadministered scientifically

3. Offer quick leads towards the required areaof research

4. Cost effective and less time consuming5. Limited manpower can administer sample

survey

6. Sampling errors are always present.7. Non sampling errors can be controlled

Types of sampling

The choice of an appropriate sampling design is of paramount importance in the execution of a samplesurvey and is generally made keeping in view the objectives and scope of the enquiry and the type of the

population to be sampled. The sampling techniques may be broadly classified as

1. Non-Probability sampling (purposive/convenience/ judgment sampling)2. Probability sampling3. Mixed sampling

Non-probability sampling : In this method, a desired number of sample units are selected purposelydepending upon the object of the enquiry so that only the important items representing the true

characteristics of the population are included in the sample.

For example, if one wishes to know through sample survey, the customer satisfaction towards EurekaForbes products, he has to collect the needed information only from Eureka Forbes customers.

Non-probability sampling is very subjective in nature and depends entirely on the convenience of theinvestigator. Hence there is a larger scope of bias. Convenience sampling is appreciated when research is

limited to small sample size or in the cases where finding sample units is very difficult and /or expensive.

Probability sampling

Probability sampling provides a scientific technique of drawing samples from the population according to

the laws of probability. The probability sampling scheme will have following characteristics.(i) Each sample unit has an equal chance of being selected(ii) Sampling units have varying probability of being selected(iii) Probability of selection of a unit is proportional to the sample size


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Mixed sampling

Sampling design in which the sample units are selected partly according to some probability laws, andpartly according to a fixed sampling rule (non-probability) is known as mixed sampling.

Some of the mixed sampling schemes are

1. Simple random sampling2. Systematic sampling3. Stratified sampling4. Cluster sampling5. Multistage sampling6. Quota sampling

Simple random sampli ng (SRS): It is a technique in which sample is so drawn that each and every unit

in the population has equal chance of being included in the sample.

If the unit selected in first draw is not replaced back into the population before drawing the next sample, itis called simple random sampling with replacement (srswor)and if it is replaced back before making thenext draw, then the sampling plan is called simple random sampling with replacement (srswr).

Selection of simple random sample can be done by (i) lottery method (ii) use of random number tables.

SRS eliminates bias due to personal judgment. Samples selected using SRS will be more representativethan that of judgment sampling. Samples using SRS will be most reliable at least cost, less time and labor.However if the population is vast, fairly large sample size is required to ensure better estimates of

population characteristics.

Systematic Sampling: Here the population units are numbered in serial order. Samples are collected byfollowing an order such that first sample is randomly selected by randomly assuming a number between 1to 9 and there afterwards required number of samples are selected in a definite sequence at equal spacingfrom one another.

For example, if 10 sample bags are to be selected out of 100 bags of Basmati rice for quality inspection;all 100 bags are numbered serially from 1 to 100. Then first sample is selected as random number

between 1 to 9 say 4. Then bag nos. 4,14,24,34,44,54,64,74,84,94 are the units to be sampled usingsystematic sampling technique.

Stratif ied Sampli ng : When population is heterogeneous with respect to the variable or characteristic

under study, then the technique of stratified sampling random sampling is used to obtain more efficient

results. It involves dividing the population into groups (strata) having homogeneous characteristics. Thenrandom samples are drawn from each stratum according to size of each stratum.

For example, if we are interested in understanding the shopping behavior of people of different age

groups at Big Bazaar, we can stratify the customers according to their age groups and then pickproportionate number of respondents belonging to different age groups randomly according to the size ofeach stratum to study their shopping behavior.


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Cluster Sampling: In this case, total population is divided, depending on problem under study, into somerecognizable sub divisions called clusters and simple random samples of these clusters are drawn.

For example, if one wants to conduct opinion survey of people in an election constituency, the whole citymay be divided into different blocks i.e., clusters of manageable size and then households from each ofthese clusters are selected randomly.

Multistage Sampling : In multistage sampling, instead of selecting all samples from different clusters,clusters are further subdivided to get better and efficient samples.

For example, if we are interested in obtaining a sample of say n households from a particular state, thefirst stage units may be districts, the second stage units may be villages in the districts and third stage

units will be households in the villages.

Quota Sampli ng : Quota sampling is similar to that of stratified sampling with pre-defined sample size

(quota) in each stratum. Investigator has to collect designated number of samples from each stratum.However investigator is given a liberty to choose sample units on his discretion if some sample units are

missing from the stratum at the time of data collection.

Qualitative techniques of data collection.

When the data is qualitative in nature, the usual methods of data collection viz., through observation,interview, questionnaire and schedule can not be used for data collection. In such situations, data may be

collected by:

(i) Structured and direct form of interview(ii) Unstructured and direct form of interview(iii) Structured and indirect mode of interview(iv) Unstructured and indirect way of interview

Structured and direct form of in terview : Here formal questionnaire consists of structured and directform of questions and the respondents are asked to respond to definite questions through direct interviewmethod.

Unstructured and direct form of in terview : In this method, interviewer is given general instructions onthe type of information desired. Interviewer is left to ask direct questions to obtain this information usingthe wording and the order that seems more appropriate in the context of each interview.

Depth interview andDelphi technique are the popular methods of data collection through unstructured

and direct form of interview.

InDepth interview, interviewer will continue to ask probing questions to the respondent until the required

information is gathered to his satisfaction. It requires lengthy duration to collect information and dependson the ability and intelligence of the interviewer

In Delphi technique, discussions about a particular issue or business problem is conducted among the

group of experts from respective fields and the necessary information is gathered to sort out the problemor to make better decision using the inputs given by the experts panel on the issue.

I ndirect interviews: Under this method, the respondent is given non-personal, ambiguous situation andasked to describe it. The respondent will tend to interpret the situation in terms of his own needs, motives


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and values. Hence these techniques are also known as Attitude Measurement Techniques. Theseinclude

1. Projective Techniquesa. Association techniques : Here respondents are asked to associate themselves with the

situation and asked to give their inputs. Eg. Group discussionb. Construction techniques : Respondents are given a task of constructing a story or

strategy based on the explained situation with constraints.Eg. If you are selecting a marketing executive for your company, he may be asked to design astrategy for the imaginative problem being faced by the company.

c. Completion techniques : Here respondents are exposed to some incomplete situationsand are asked to respond with their skills and attitude towards meaning solution.

Eg. Students are asked to solve the business cases to assess whether they can apply the theoretical

concepts for solving real life problems.d. Choice of ordering techniques : Here the respondents are asked to place some objects or

constructs in their order of choice, which in turn helps in understanding their attitudetowards a particular goal.

Eg. If you are interviewing a person for HR executive post and wish to assess the value system ofthe candidate: You can ask him to place the values like honesty, sincerity, commitment, loyalty,

integrity, timeliness in his order of preference.e. Expressive techniques : Here, respondents are exposed a situation and asked to respond

to it through their expression. Eg. Play techniques, role playing etc.,.

2. Thematic Appreciation TestIn this method, respondents are exposed to a theme in the form of a story or picture; and asked toreview and respond to the story or situation depicted in the pucture.

3. Focus Group InterviewHere a group of people jintly participate in an unstructured interview conducted by moderator.Moderator attempts to focus the discussion on the problem areas in a relaxed, non-directedmanner. The interaction among the grop members during the interview will possibly lead tospontaneous discussions and the disclosure of attitudes, opinions and information.

Scaling techniques like Likert Scale and Semantic Differential Scale are used to measure attitude.


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Module 3

Measurement and scaling techniques

Scaling Techniques

These are used to measure different psychological aspects such as attitudes, perceptions and preference ofpeople with the help of certain predefined set of stimuli or instructions. The stimuli may be certain brandsof product, alternative advertising themes, package designs and so on. The response may involve howconsumers judge the brands, which brand looks more pleasing for them, which package is more attractiveetc.,.

Scale of Measurement

Scaling procedures can be classified as nominal, ordinal, interval and ratio type.

Nominal Scale: Here symbols/numbers are assigned to objects just for the sake of identification.

Eg.1. Roll numbers are assigned to students just for the sake of identification. These numbers do notreveal strength, rank or superiority of the student./goodness of the student behavior.

2. Numbers are assigned to buses for identification of routes only.

3. Question regarding profession with options like Worker, Businessman, Student, Govt. employee,Pvt. Employee, Former may be assigned numbers 1,2,3,4,5,6 respectively.

Ordinal Scale : In this type of measurement, numbers are assigned to objects to indicate someorderliness based on relative importance of the response to certain question.

Eg.1. Rank list of students show some order in which the number 1 stands for the student who has toppedin the examination results, number 2 stands for the student who has scored II highest marks in the exam

and so on. i.e., in a rank list, the numbers assigned to the student signify students ability/strength in

passing the exam.2. The response to a question, Name the three companies that you would like to join in the order of

your preference. Will generate answers in the form of three Cos in which the first co. has highestimportance, second co. will have importance lesser than that of the first and so on.

Interval Scale : This type of measurement involves comparison between different categories of response.In marketing research, interval scale is often chosen to measure attitude towards brand, culture,

management practice etc.,.

Eg.1. Data regarding Income of people captured on the scale of 10000-15000, 15000-20000 etc.,

Ratio Scale: This measurement consider absolute magnitude of numbers. Typical issues like quantity

sold, number of consumers, probability of purchase are the examples of data recorded on ratio scale.

Methods of scale construction

There are number of ways in which scales may be constructed. They are,

Paired comparison method Ranking Ordered category sorting


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Rating TechniquesIn paired comparison method, respondent has to respond by

comparing two attributes for their desired characteristic.

Eg. If six tyre brands are to be compared on road grip quality

by comparing two at a time, the following tables give pairedcomparison responses.

1 implies that row brand is better than column brand0 implies that column brand is better than row brandX implies invalid comparison

In Ranking method, respondent is given an option to rank the objects according to the desired

characteristic of the object.

Eg. For the above example, if the respondent is asked to rank the tyre brands according to their road grip

quality, the resulting response in terms of brands being ranked as 1,2,3.represent ranking method.MRF(1), Ceat(2), Dunlop(3) etc.,.

In Ordered category sorting method, respondent will be instructed to give his response by placing theobjects in desired categories as per his experience and perception.

Eg. For the same example of tyres, respondent may be asked to categorize the tyre brands as Top class,

Average class and Poor class

Rating Techniques are the most widely used scaling techniques in marketing research. They are mostpopular as they allow easy flow of data collection. In all rating scale researchers devise a number ofstatements that relate to the product, attribute or service quality. Respondents have to indicate their

response with the help of numerical, graphical or verbal scale values. Likert scale and SemanticDifferential Scalesare the popular rating techniques used in all social / marketing research.

Likert scale: Here, respondents are asked to indicate on a five point numerical scale their degree ofagreement of disagreement with some pre designed set of statements. The researcher is free to choose his

own way to label the agree/disagree response. Care has to be exercised in labeling the response categoriesfor favorable vis--vis unfavorable statements. That is obviously for unfavorable statements direction of

response scores will be opposite that of a favorable statements.

Eg. Give your opinion about voting rights to the shareholders in choosing Managing Director of the PSU.

on the five point scale as Highly Important(5), Important(4) Neutral(3), Not important(2), Not at allimportant(1).

Semantic Differential Scale (SDS) : It is also one of the mostly used rating techniques in corporateproduct and brand image studies. In SDS, the respondents are asked to indicate their choice among a setof bi-polar phrases for adjectives that best describe their feelings towards an issue or object. A set ofstatements are constructed and the responses consisting set of opposite meaning phrases at the two

extreme ends of the scale. Semantic scale assumes that the centre position of the response is somewhatneutral and the intermediate positions are defined by two extreme poles.

Brand A B C D E F

A X 0 1 1 1 1

B 1 X 1 1 1 1

C 0 0 X 0 0 0D 0 0 1 X 0 0

E 0 0 1 1 X 1

F 0 0 1 1 0 X


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Eg. In a study of a brand of two cough drops viz., Vicks and Halls, the following form of semanticdifferential scale was developed.

Cooling effect : Weak - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -StrongStrength of flavor : Mild - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - StrongColor : Not pleasing - - - - - - - - - - - - - - - - - - - - - - - - - - Pleasing

Clears Blocked nose : Ineffective - - - - - - - - - - - - - - - - - - - - - - - - - - - EffectiveWrapper : Bad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - GoodAfter effect : Short Lived - - - - - - - - - - - - - - - - - - - - - - - - - - - Long Lasting

Source: Marketing Research Authored by Ramanuj Majumdar, New Age International Publishers, 1e, 2005.


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Module 6

Probability & Theoretical Probability Distributions (Covered for B & C Sections)

Probability in statistics is a measure of chance associated with activities which are random in nature. Thefollowing few examples make us understand the necessity of probability in our day to day life / making

better business decisions.

Eg. It may rain today ; production of wheat this year will be high ; we may experience steep drop inrecruitments due to US recession ; Capital requirement to start a new business will be roughly more thanRs. 2 bn in the next year.

In all the above examples, no information or expression is certain to happen but it is an estimate based onthe chance factor associated with respective situations. If we could explore and quantify this chance

factor, it is remarkable in making better decisions.

In this module, we try to learn about basic concept of probability and probability distributions which helpus to apply probability rules in solving business problems for better decision making under uncertainty. It

is for this reason, probability finds its wide space in statistics, serving various needs in the fields ofscience, social science as well as business.

In order to understand probability concepts , knowledge of following terminology is essential.

Random Experiment (r.e.) : An experiment resulting in random outcomes

Eg., Tossing a coin results in two random outcomes Head & Tail

Trail: Each repetition of a random experiment is called trialEg., Tossing coin for two times means 2 trials of tossing a coin

Event: It is an outcome of a random experiment

Eg., In tossing a coin, H & T are the two events

Sample Space (S): Set of all outcomes of a random experimentEg., When a coin is tossed, S ={H,T}; When two coins are tossed, S ={TT, HT, TH, HH}

Mutually exclusive events: Two events are said to be mutually exclusive when happening of one eventprevents the happening of the other.

Eg., When a coin is tossed, H & T are called mutually exclusive events; i.e., if Head turns up, it is to

understand that head is preventing Tail to turn up or vice-versa.

Equally Likely events : Two events are said to be equally likely, when chance of occurrence of those

events are same.

Eg., : In tossing a coin, chance of getting Head = = chance of getting tail

Exhaustive events : Two events are said to be exhaustive, when total chance of their occurrence is 1.Eg. When a coin is tossed, total chance of (occurrence of head + occurrence of tail) = + =1


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Mathematical Definition of Probability

Let there be a random experiment with n mutually exclusive, equally likely and exhaustive events. Let

m of these outcome be favorable for happening of event A. Then probability of event A is given by,P(A) = (No. of favorable outcomes of A) / (Total No. of outcomes)

= m/nFor example, if we wish to find probability of getting Head out of tossing a coin, P(H) =

Similarly, in rolling a dice experiment, if we wish to get only even nos. P(getting even nos.) = 3/6( as there are only 3 even nos. out of 6 numbered faces of a dice. i.e., 1,2,3,4,5,6)


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Numerical Examples on Z Test (Solved in all 3 sections)

(Equal ity of mean in single population)

1. A random sample of 100 students have mean weight of 58 kg and s.d. 4 kg. Test the hypothesisthat the mean weight in the population is 60 kg at 5% and 1% level of significance (l.o.s.).

2. Daily sales figures of 40 shop keepers showed that their average sales and s.d. were Rs. 528 andRs. 60 respectively. Can you conclude that daily average sales is Rs. 400 at 5% l.o.s.

3. An educator claims that the average IQ of American college students is at most 110, and that in astudy made to test his claim, 150 students, selected at random had an average IQ of 111.2 with astandard deviation of 7.2. Use l.o.s. of 0.01 to test the claim of the educator.

(Equal ity of two means in two populations)

4. The average number of articles produced by two machines per day are 200 and 210 with standarddeviations 20 and 15 respectively. On the basis of records of 25 day production, can we regard

both machines equally efficient?

5. A company claims that its light bulbs are superior to those of a competitor on the basis of a studywhich showed that a sample of 40 of its bulbs had an average life time of 628 hours with s.d. of27 hours, while a sample of 30 bulbs made by the competitor had an average life time of 619

hours with s.d. 25 hours. Check at 5% l.o.s. whether this claim is justified?

6. The mean scores of two samples of 1000 and 2000 students are 67.5 and 68 respectively. Can thesamples be regarded as drawn from the same population of standard deviation 2.5 inches?

(Equality of proporti on in single population)

7. A candidate at an election claims 90% of support of all voters in a locality. Verify his claim, if arandom sample of 400 voters from the locality, 320 supported his candidature. Use 5% l.o.s.

8. In a city, 325 men out of 600 men were found to be smokers. Does this information support theconclusion that the majority of men in this city are smokers?

(Equal ity of proportions in two population)

9. In a year there are 956 births in town A, of which 52.5 % were males, while in town B 450 birthsresult in 43.4% males. Is there any significant difference in the proportion of male births in two

towns?

10. In a days production, 16 out of a random sample of 500 bolts were found to be defective. Afterfine tuning the machine, another sample of 100 bolts contained 2 defective bolts. Is there anysignificant difference in the proportion of defectives produced? 5% l.o.s..


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t-test

Applicable when sample size is small (i.e., n


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Chi-square Test

(2

- Test)

Application

1. To test goodness of fit2. To test independence of attributes3. To test the equality of variance These applications out of syllabus4. To test the equality of several proportions

Conditions for the validity of 2 - Test

1. The total frequency N should be large (> 50)2. The sample observations should be independent3. Theoretical frequencies / cell frequencies should be more than 5 (otherwise pooling to be done).

F- Test

Application

1. To test equality of several population means using ANOVA2. To test for equality of population variances3. To test the significance of observed sample multiple correlation These applications out of syllabus4. To test the significance of observed sample correlation ratio

Assumptions for F-Test

1. Samples are drawn randomly2. Samples are independent of each other3. Samples are drawn from normal population


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Steps in the Procedure of Testing Hypothesis

1. State the Null and alternative hypothesis2. Choose desired level of significance3. Choose the most suitable test statistic (i.e., Z, t, 2or F)4. Obtain the sample statistics and other information about known population parameters5. Calculate the value of the test statistic6. Decide about acceptance or rejection of hypothesis afer comparing the calculated value of the test statistic

with the table value(critical value of the test statistic)

Module 8

Non Parametric Tests

Statistical tests that are learnt in the previous module are parametric tests, which assume that the form of the

population distribution is known and the test concerning a parameter is to be made. However there are many

situations where one or more assumptions made in the case of parametric tests can not be met. In such cases we

make use of non-parametric tests.

Non-Parametric testsare those, for which the distribution from which samples are drawn is not known and testing

of hypothesis is not concerned with parameters.

Advantages of Non-Parametric tests

1. No or less stringent assumptions are required in non-parametric tests as compared to parametric tests2. More suitable when data is ranked, scaled or rated.3. Easier to perform as they involve simple calculations.

List of some non-parametric tests

1. Sign test for paired data2. Runs test for randomness3. Mann-Whitney U-test4. Signed rank test (Wilcoxon Matched Pairs Test)5. Kruskal-Wallis Test

Multivariate Analysis (Write a note on Multivariate Analysis techniques.)

Multivariate analysis techniques are applicable when two or more variables are considered under study. These are

usually applied to analyze the dependence or interdependence between two or more than two variables.

Dependence multivariate techniques are

ANOVA

Multiple regression

Discriminant analysis,

Conjoint Analysis,

MANOVA and


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Canonical correlations.

Interdependence multivariate techniques include

Factor analysis,

Cluster analysis and

Multi-dimensional scaling

Multiple regression is used when dependence of one variable on many other variables to be studied. For example

yield of a crop depends on weather condition, fertilizer used, amount of rain, fertility of land, care of farmer etc.,.

Using Multivariate analysis, one can understand the extent of dependence of these variables for one variable under

study that is yield.

ANOVA is used when two or more variables/factors are to be studied for their equality under controlled situations.

For example, if sales efficiency of 4 salesmen are to be studied on new marketing locations during the same time,

one can make use of ANOVA, which compare between two sets of data using the variance explained between and

within each group of data.

Discriminant Analysis is used to establish a linear relationship between one dependent and many independent

variables. For example if one wants to predict the sale of insurance policies based on Income, savings, psychological

and demographic factors of the respondents, discriminant analysis gives a linear function to estimate sales using the

relationship between sales of insurance with income, savings and given psychological and demographic factors.

Conjoint Analysis is used when an investigator makes respondents preference judgment about a new concept and

test it using the actual response of the respondant.

Canonical Correlation is applicable when an experimenter wishes to relate two factors determined by two linear

models (constructed with interdependence of many variables), which generate canonical variables in two sets;

further they are tested for correlation.

Factor analysis is carried out when the investigator wants to define those factors which influence a change in

dependent variable, based on the data collected using likert scale for many questions framed on attitudes andbehaviors of the respondents.

Cluster analysis helps in separating the population of data into different homogenous groups based on common

characteristics suited to each group. For example if investigator wants to classify the customers into different

categories of brand loyalty using sales, frequency of visit, duration of relationship etc., one can make use of cluster

analysis.

Multidimensional Scaling(MDS) is used when liking towards different brands are studied based on the perceptions

of customers towards their brands.


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Report Writing (Write a note on various steps of report Writing). Elaborate on the following steps(*****)

1. Title2. Executive Summary

Major findings, conclusion and recommendations as a summary in one paragraph3. Problem Definition

Background of the problem

Literature review Statement of the problem with specific objectives

4. Research Design Type of research, Data collection methods, Scaling techniques used, Questionnaire, Sampling,

Fieldwork

5. Data collection, Analysis6. Results7. Conclusions and Recommendations

Answer to Qn 4b in model paper. (it is based on Harmonic Mean)

Airplane covers distance of first 100km with speed 100kmph, Second 100km with 200kmph, third 100km with

300kmph and fourth 100km with speed.

We know that velocity = Distance/time

Time taken = distance/velocity

= (100/100)+(100/200)+(100/300)+(100/400)=1+0.5+0.33+0.25=2.08

Therefore Avg. Speed = total distance/total time taken = 400/2.08 = 192.08kmph

Do not neglect theory part of your paper.. i t is hardly about 20 pagesAl l the best.

qm1 theory notes

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