Download - 2-1. Data Collection Data Vocabulary Data Vocabulary Level of Measurement Level of Measurement Time Series and Cross-sectional Data Time Series and Cross-sectional

Data CollectionData CollectionData CollectionData CollectionData Vocabulary

Level of Measurement

Time Series and Cross-sectional Data

Sampling Concepts

Sampling Methods

Data Sources

Survey Research

Chapter2222

McGraw-Hill/Irwin © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

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Data VocabularyData VocabularyData VocabularyData Vocabulary

• DataData is the plural form of the Latin is the plural form of the Latin datumdatum (a “given” (a “given” fact).fact).

• In scientific research, In scientific research, datadata arise arise from experiments whose results from experiments whose results are recorded systematically.are recorded systematically.

• Important decisions may depend on Important decisions may depend on data.data.

• In business, In business, datadata usually arise from usually arise from accounting transactions or accounting transactions or management processes.management processes.

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Subjects, Variables, Data SetsSubjects, Variables, Data Sets• We will refer to We will refer to DataData as plural and as plural and data setdata set as a as a

particular collection of data as a whole.particular collection of data as a whole.

• ObservationObservation – each data value. – each data value.

• SubjectSubject (or (or individualindividual) – an item for study (e.g., an ) – an item for study (e.g., an employee in your company).employee in your company).

• VariableVariable – a characteristic about the subject or – a characteristic about the subject or individual (e.g., employee’s income).individual (e.g., employee’s income).

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Subjects, Variables, Data SetsSubjects, Variables, Data Sets• Three types of data sets:Three types of data sets:

Data SetData Set VariablesVariables Typical TasksTypical Tasks

UnivariateUnivariate OneOne Histograms, descriptive Histograms, descriptive statistics, frequency talliesstatistics, frequency tallies

BivariateBivariate TwoTwo Scatter plots, correlations, Scatter plots, correlations, simple regressionsimple regression

MultivariateMultivariate More than More than twotwo

Multiple regression, data Multiple regression, data mining, econometric modelingmining, econometric modeling

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Subjects, Variables, Data SetsSubjects, Variables, Data SetsConsider the multivariate data set with Consider the multivariate data set with

5 variables5 variables 8 subjects8 subjects 5 x 8 = 40 observations5 x 8 = 40 observations

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Data TypesData Types• A data set may have a mixture of A data set may have a mixture of data typesdata types..

Types of DataTypes of Data

AttributeAttribute(qualitative)(qualitative)

NumericalNumerical(quantitative)(quantitative)

Verbal LabelVerbal LabelXX = economics = economics

(your major)(your major)

CodedCodedXX = 3 = 3

(i.e., economics)(i.e., economics)

DiscreteDiscreteXX = 2 = 2

(your siblings)(your siblings)

ContinuousContinuousXX = 3.15 = 3.15

(your GPA)(your GPA)

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Data Data VocabularyData Data Vocabulary

Attribute DataAttribute Data• Also called Also called categoricalcategorical, , nominalnominal or or qualitativequalitative data. data.

• Values are described by words rather than numbers.Values are described by words rather than numbers.

• For example, For example, - Automobile style (e.g., - Automobile style (e.g., XX = full, midsize, = full, midsize, compact, subcompact). compact, subcompact).- Mutual fund (e.g., - Mutual fund (e.g., XX = load, no-load). = load, no-load).

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Data CodingData Coding• CodingCoding refers to using numbers to represent categories to facilitate statistical analysis. refers to using numbers to represent categories to facilitate statistical analysis.

• Coding an attribute as a number does Coding an attribute as a number does notnot make the data numerical. make the data numerical.

• For example, For example, 1 = Bachelor’s, 2 = Master’s, 3 = Doctorate 1 = Bachelor’s, 2 = Master’s, 3 = Doctorate

• Rankings may exist, for example, Rankings may exist, for example, 1 = Liberal, 2 = Moderate, 3 = Conservative 1 = Liberal, 2 = Moderate, 3 = Conservative

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Binary DataBinary Data• A A binary variablebinary variable has only two values, has only two values,

1 = presence, 0 = absence of a characteristic of interest (codes themselves are arbitrary).1 = presence, 0 = absence of a characteristic of interest (codes themselves are arbitrary).

• For example, For example, 1 = employed, 0 = not employed 1 = employed, 0 = not employed 1 = married, 0 = not married 1 = married, 0 = not married 1 = male, 0 = female 1 = male, 0 = female 1 = female, 0 = male 1 = female, 0 = male

• The coding itself has no numerical value so binary variables are The coding itself has no numerical value so binary variables are attribute dataattribute data..

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Binary DataBinary Data

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Numerical DataNumerical Data• NumericalNumerical or or quantitativequantitative data arise from counting or some kind of mathematical operation. data arise from counting or some kind of mathematical operation.

• For example, For example, - Number of auto insurance claims filed in - Number of auto insurance claims filed in March (e.g., March (e.g., XX = 114 claims). = 114 claims).- Ratio of profit to sales for last quarter - Ratio of profit to sales for last quarter (e.g., (e.g., XX = 0.0447). = 0.0447).

• Can be broken down into two types – Can be broken down into two types – discretediscrete or or continuouscontinuous data. data.

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Discrete DataDiscrete Data• A numerical variable with a countable number of values that can be represented by an integer (no fractional A numerical variable with a countable number of values that can be represented by an integer (no fractional

values).values).

• For example, For example, - Number of Medicaid patients (e.g., - Number of Medicaid patients (e.g., XX = 2). = 2).- Number of takeoffs at O’Hare (e.g., - Number of takeoffs at O’Hare (e.g., XX = 37). = 37).

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Continuous DataContinuous Data• A numerical variable that can have any value within an interval (e.g., length, weight, time, sales, A numerical variable that can have any value within an interval (e.g., length, weight, time, sales,

price/earnings ratios).price/earnings ratios).

• Any continuous interval contains infinitely many possible values (e.g., 426 < Any continuous interval contains infinitely many possible values (e.g., 426 < XX < 428). < 428).

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RoundingRounding• Ambiguity is introduced when continuous data are rounded to whole numbers.Ambiguity is introduced when continuous data are rounded to whole numbers.

• Underlying measurement scale is continuous.Underlying measurement scale is continuous.

• Precision of measurement depends on instrument.Precision of measurement depends on instrument.

• Sometimes discrete data are treated as continuous when the range is very large (e.g., SAT scores) and Sometimes discrete data are treated as continuous when the range is very large (e.g., SAT scores) and small differences (e.g., 604 or 605) aren’t of much importance.small differences (e.g., 604 or 605) aren’t of much importance.

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Level of MeasurementLevel of MeasurementLevel of MeasurementLevel of Measurement

Likert ScalesLikert Scales• A special case of interval data frequently used in survey research.A special case of interval data frequently used in survey research.

• The The coarsenesscoarseness of a Likert scale refers to the number of scale points (typically 5 or 7). of a Likert scale refers to the number of scale points (typically 5 or 7).

““College-bound high school students should be required to study a College-bound high school students should be required to study a foreign language.” (check one)foreign language.” (check one)

StronglyStronglyAgreeAgree

SomewhatSomewhatAgreeAgree

Neither Neither AgreeAgreeNor Nor

DisagreeDisagree

SomewhatSomewhatDisagreeDisagree

StronglyStronglyDisagreeDisagree

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Likert ScalesLikert Scales• A A neutral midpointneutral midpoint (“Neither Agree Nor Disagree”) is allowed if an (“Neither Agree Nor Disagree”) is allowed if an oddodd number of scale points is used or number of scale points is used or

omitted to force the respondent to “lean” one way or the other.omitted to force the respondent to “lean” one way or the other.

• Likert data are Likert data are coded numerically coded numerically (e.g., 1 to 5) but any (e.g., 1 to 5) but any equally spaced equally spaced values will work.values will work.

Likert coding: Likert coding: 1 to 5 scale1 to 5 scale

Likert coding: Likert coding: -2 to +2 scale-2 to +2 scale

5 = Help a lot5 = Help a lot4 = Help a little4 = Help a little3 = No effect 3 = No effect 2 = Hurt a little2 = Hurt a little1 = Hurt a lot1 = Hurt a lot

+2 = Help a lot+2 = Help a lot+1 = Help a little+1 = Help a little 0 = No effect0 = No effect1 = Hurt a little1 = Hurt a little2 = Hurt a lot2 = Hurt a lot

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Likert ScalesLikert Scales• Careful choice of verbal anchors results in measurable Careful choice of verbal anchors results in measurable intervalsintervals (e.g., the distance from 1 to 2 is “the same” (e.g., the distance from 1 to 2 is “the same”

as the as the intervalinterval, say, from 3 to 4)., say, from 3 to 4).

• Ratios are not meaningful (e.g., here 4 is not Ratios are not meaningful (e.g., here 4 is not twice 2).twice 2).

• Many statistical calculations can be performed (e.g., averages, correlations, etc.).Many statistical calculations can be performed (e.g., averages, correlations, etc.).

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Likert ScalesLikert Scales• More variants of Likert scales:More variants of Likert scales:

How would you rate your marketing instructor? (check one)How would you rate your marketing instructor? (check one)

TerribleTerrible

PoorPoor

AdequateAdequate

GoodGood

ExcellentExcellent

How would you rate your marketing instructor? (check one)How would you rate your marketing instructor? (check one)

Very BadVery Bad Very GoodVery Good

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Time Series and Cross-sectional Time Series and Cross-sectional DataData

Time Series and Cross-sectional Time Series and Cross-sectional DataData

Time Series DataTime Series Data• Each observation in the sample represents a different equally spaced point in time (e.g., years, months, Each observation in the sample represents a different equally spaced point in time (e.g., years, months,

days).days).

• PeriodicityPeriodicity may be annual, quarterly, monthly, weekly, daily, hourly, etc. may be annual, quarterly, monthly, weekly, daily, hourly, etc.

• We are interested in We are interested in trends and patterns over timetrends and patterns over time (e.g., annual growth in (e.g., annual growth in consumer debit card use consumer debit card use from 1999 to 2006). from 1999 to 2006).

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Sampling ConceptsSampling ConceptsSampling ConceptsSampling Concepts

Sample or Census?Sample or Census?• A A samplesample involves looking only at some items selected from the population. involves looking only at some items selected from the population.

• A A censuscensus is an examination of all items in a defined population. is an examination of all items in a defined population.

- MobilityMobility- Illegal immigrants- Illegal immigrants- Budget constraints- Budget constraints- Incomplete responses or nonresponses- Incomplete responses or nonresponses

• Why can’t the United States Census survey every person in the population?Why can’t the United States Census survey every person in the population?

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Situations Where A Situations Where A SampleSample May Be Preferred: May Be Preferred:

Infinite PopulationInfinite PopulationNo census is possible if the population is infinite or of indefinite size No census is possible if the population is infinite or of indefinite size (an assembly line can keep producing bolts, a doctor can keep (an assembly line can keep producing bolts, a doctor can keep seeing more patients).seeing more patients).

Destructive TestingDestructive TestingThe act of sampling may destroy or devalue the item (measuring The act of sampling may destroy or devalue the item (measuring battery life, testing auto crashworthiness, or testing aircraft turbofan battery life, testing auto crashworthiness, or testing aircraft turbofan engine life). engine life).

Timely ResultsTimely ResultsSampling may yield more timely results than a census (checking Sampling may yield more timely results than a census (checking wheat samples for moisture and protein content, checking peanut wheat samples for moisture and protein content, checking peanut butter for aflatoxin contamination). butter for aflatoxin contamination).

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Situations Where A Situations Where A SampleSample May Be Preferred: May Be Preferred:

AccuracyAccuracySample estimates can be more accurate than a census. Instead of Sample estimates can be more accurate than a census. Instead of spreading limited resources thinly to attempt a census, our budget spreading limited resources thinly to attempt a census, our budget of time and money might be better spent to hire experienced staff, of time and money might be better spent to hire experienced staff, improve training of field interviewers, and improve data safeguards.improve training of field interviewers, and improve data safeguards.

CostCostEven if it is feasible to take a census, the cost, either in time or Even if it is feasible to take a census, the cost, either in time or money, may exceed our budget.money, may exceed our budget.

Sensitive InformationSensitive InformationSome kinds of information are better captured by a well-designed Some kinds of information are better captured by a well-designed sample, rather than attempting a census. Confidentiality may also sample, rather than attempting a census. Confidentiality may also be improved in a carefully-done sample.be improved in a carefully-done sample.

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Situations Where A Situations Where A CensusCensus May Be Preferred May Be Preferred

Small PopulationSmall PopulationIf the population is small, there is little reason to sample, for the effort of If the population is small, there is little reason to sample, for the effort of data collection may be only a small part of the total cost.data collection may be only a small part of the total cost.

Large Sample SizeLarge Sample SizeIf the required sample size approaches the population size, we might as If the required sample size approaches the population size, we might as well go ahead and take a census.well go ahead and take a census.

Legal RequirementsLegal RequirementsBanks must count Banks must count allall the cash in bank teller drawers at the end of each the cash in bank teller drawers at the end of each business day. The U.S. Congress forbade sampling in the 2000 decennial business day. The U.S. Congress forbade sampling in the 2000 decennial population census.population census.

Database ExistsDatabase ExistsIf the data are on disk we can examine 100% of the cases. But auditing or If the data are on disk we can examine 100% of the cases. But auditing or validating data against physical records may raise the cost.validating data against physical records may raise the cost.

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Parameters and StatisticsParameters and Statistics• StatisticsStatistics are computed from a sample of are computed from a sample of nn items, chosen from a population of items, chosen from a population of NN items. items.

• Statistics can be used as estimates of Statistics can be used as estimates of parametersparameters found in the population. found in the population.

• Symbols are used to represent population parameters and sample statistics.Symbols are used to represent population parameters and sample statistics.

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Parameters and StatisticsParameters and Statistics

StatisticStatistic Any measurement computed from a Any measurement computed from a samplesample. Usually, . Usually, the statistic is regarded as an estimate of a population the statistic is regarded as an estimate of a population parameter. Sample statistics are often (but not parameter. Sample statistics are often (but not always) represented by Roman letters.always) represented by Roman letters.

Parameter or Statistic?Parameter or Statistic?

ParameterParameter Any measurement that describes an entire Any measurement that describes an entire populationpopulation. . Usually, the parameter value is unknown since we Usually, the parameter value is unknown since we rarely can observe the entire population. Parameters rarely can observe the entire population. Parameters are often (but not always) represented by Greek are often (but not always) represented by Greek letters.letters.

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Parameters and StatisticsParameters and Statistics• The population must be carefully specified and the sample must be drawn scientifically so that the sample is The population must be carefully specified and the sample must be drawn scientifically so that the sample is

representative.representative.

• The The target populationtarget population is the population we are interested in (e.g., U.S. gasoline prices). is the population we are interested in (e.g., U.S. gasoline prices).

Target PopulationTarget Population

• The The sampling framesampling frame is the group from which we take the sample (e.g., 115,000 stations). is the group from which we take the sample (e.g., 115,000 stations).

• The frame should not differ from the target population.The frame should not differ from the target population.

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NN nn

Finite or Infinite?Finite or Infinite?• A population is A population is finitefinite if it has a definite size, even if its size is unknown. if it has a definite size, even if its size is unknown.

• A population is A population is infiniteinfinite if it is of arbitrarily large size. if it is of arbitrarily large size.

• Rule of Thumb: A population may be treated as infinite when Rule of Thumb: A population may be treated as infinite when NN is at least 20 times is at least 20 times n n (i.e., when (i.e., when NN//nn > 20) > 20)


Here,Here,NN//nn > 20 > 20

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Sampling MethodsSampling MethodsSampling MethodsSampling Methods

Probability SamplesProbability Samples

Simple Random Simple Random SampleSample

Use random numbers to select items Use random numbers to select items from a list (e.g., VISA cardholders).from a list (e.g., VISA cardholders).

Systematic SampleSystematic Sample Select every Select every kkth item from a list or th item from a list or sequence (e.g., restaurant customers).sequence (e.g., restaurant customers).

Stratified SampleStratified Sample Select randomly within defined strata Select randomly within defined strata (e.g., by age, occupation, gender).(e.g., by age, occupation, gender).

Cluster SampleCluster Sample Like stratified sampling except strata Like stratified sampling except strata are geographical areas (e.g., zip are geographical areas (e.g., zip codes).codes).

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Nonprobability SamplesNonprobability Samples

Judgment Judgment SampleSample

Use expert knowledge to choose Use expert knowledge to choose “typical” items (e.g., which employees “typical” items (e.g., which employees to interview).to interview).

Convenience Convenience SampleSample

Use a sample that happens to be Use a sample that happens to be available (e.g., ask co-worker opinions available (e.g., ask co-worker opinions at lunch).at lunch).

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Simple Random SampleSimple Random Sample• Every item in the population of Every item in the population of NN items has the same chance of being chosen in the sample of items has the same chance of being chosen in the sample of nn items. items.

• We rely on We rely on random numbersrandom numbers to select a name.to select a name.

=RANDBETWEEN(1,48)=RANDBETWEEN(1,48)

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Random Number TablesRandom Number Tables• A table of random digits used to select random numbers between 1 and A table of random digits used to select random numbers between 1 and N.N.

• Each digit 0 through 9 is equally likely to be chosen.Each digit 0 through 9 is equally likely to be chosen.

Setting Up a RuleSetting Up a Rule• For example, NilCo wants to award cash prizes to 10 of its 875 loyal customers.For example, NilCo wants to award cash prizes to 10 of its 875 loyal customers.

• To get 10 three-digit numbers between 001 and 875, we define any consistent rule for moving through the To get 10 three-digit numbers between 001 and 875, we define any consistent rule for moving through the random number table.random number table.

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Setting Up a RuleSetting Up a Rule• Randomly point at the table to choose a starting point.Randomly point at the table to choose a starting point.

• Choose the first three digits of the selected five-digit block, move to the right one column, down one row, and Choose the first three digits of the selected five-digit block, move to the right one column, down one row, and repeat.repeat.

• When we reach the end of a line, wrap around to the other side of the table and continue.When we reach the end of a line, wrap around to the other side of the table and continue.

• Discard any number greater than 875 and any duplicates.Discard any number greater than 875 and any duplicates.

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82134 14458 66716 54269 31928 46241 03052 00260 32367 25783

07139 16829 76768 11913 42434 91961 92934 18229 15595 02566

45056 43939 31188 43272 11332 99494 19348 97076 95605 28010

10244 19093 51678 63463 85568 70034 82811 23261 48794 63984

12940 84434 50087 20189 58009 66972 05764 10421 36875 64964

84438 45828 40353 28925 11911 53502 24640 96880 93166 68409

98681 67871 71735 64113 90139 33466 65312 90655 75444 30845

43290 96753 18799 49713 39227 15955 46167 63853 03633 19990

96893 85410 88233 22094 30605 79024 01791 38839 85531 94576

75403 41227 00192 16814 47054 16814 81349 92264 01028 29071

78064 92111 51541 76563 69027 67718 06499 71938 17354 12680

26246 71746 94019 93165 96713 03316 75912 86209 12081 57817

98766 67312 96358 21351 86448 31828 86113 78868 67243 06763

37895 51055 11929 44443 15995 72935 99631 18190 85877 31309

27988 81163 52212 25102 61798 28670 01358 60354 74015 18556

19216 53008 44498 19262 12196 93947 90162 76337 12646 26838

28078 86729 69438 24235 35208 48957 53529 76297 41741 54735

34455 61363 93711 68038 75960 16327 95716 66964 28634 65015

53510 90412 70438 45932 57815 75144 52472 61817 41562 42084

30658 18894 88208 97867 30737 94985 18235 02178 39728 66398

Table of 1,000 Random DigitsTable of 1,000 Random DigitsStart HereStart Here

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With or Without ReplacementWith or Without Replacement• If we allow duplicates when sampling, then we are sampling If we allow duplicates when sampling, then we are sampling with replacementwith replacement..

• Duplicates are unlikely when Duplicates are unlikely when nn is much smaller than is much smaller than NN..

• If we If we do notdo not allow duplicates when sampling, then we are sampling allow duplicates when sampling, then we are sampling without replacementwithout replacement..

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Systematic SamplingSystematic Sampling

• For example, starting at item 2, we sample every For example, starting at item 2, we sample every k k = 4 items to obtain a sample of = 4 items to obtain a sample of nn = 20 items from a list of = 20 items from a list of NN = 78 items. = 78 items.

• Note that Note that NN//n = n = 78/20 78/20 4. 4.

• Sample by choosing every Sample by choosing every kkth item from a list, th item from a list, starting from a randomly chosen entry on the list.starting from a randomly chosen entry on the list.

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Systematic SamplingSystematic Sampling• A systematic sample of A systematic sample of nn items from a population of items from a population of NN items requires that periodicity items requires that periodicity kk be approximately be approximately N/nN/n..

• Systematic sampling should yield acceptable results unless patterns in the population happen to recur at Systematic sampling should yield acceptable results unless patterns in the population happen to recur at periodicity periodicity kk..

• Can be used with unlistable or infinite populations.Can be used with unlistable or infinite populations.

• Systematic samples are well-suited to linearly organized physical populations.

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Systematic SamplingSystematic Sampling• For example, out of 501 companies, we want to obtain a sample of 25. What should the periodicity For example, out of 501 companies, we want to obtain a sample of 25. What should the periodicity kk be? be?

k = Nk = N//n n = 501/25= 501/25 20. 20.

• So, we should choose every 20So, we should choose every 20 thth company from a random starting point. company from a random starting point.

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Stratified SamplingStratified Sampling• Utilizes prior information about the population.• Applicable when the population can be divided into relatively homogeneous subgroups of known size (strata).

• A simple random sample of the desired size is taken within each stratum.

• For example, from a population containing 55% males and 45% females, randomly sample 120 males and 80 females (n = 200).

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Stratified SamplingStratified Sampling• Or, take a random sample of the entire population and then combine individual strata estimates using Or, take a random sample of the entire population and then combine individual strata estimates using

appropriate weights.appropriate weights.

• For a population with For a population with LL strata, the population size strata, the population size NN is the sum of the stratum sizes: is the sum of the stratum sizes: NN = = NN11 + + NN22 + ... + + ... + NNLL

• The weight assigned to stratum The weight assigned to stratum jj is is wwjj = = NNjj / / nn

• For example, take a random sample of For example, take a random sample of nn = 200 = 200 and then weight the responses for males by and then weight the responses for males by wwMM = = .55 and for females by .55 and for females by wwFF = .45. = .45.

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Cluster SampleCluster Sample• Strata consist of geographical regions.Strata consist of geographical regions.• One-stageOne-stage cluster sampling – sample consists of all elements in each of cluster sampling – sample consists of all elements in each of kk randomly chosen subregions randomly chosen subregions

(clusters).(clusters).

• Two-stageTwo-stage cluster sampling, first choose cluster sampling, first choose kk subregions (clusters), then choose a random sample of elements subregions (clusters), then choose a random sample of elements within each cluster.within each cluster.

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Cluster SampleCluster Sample• Cluster sampling is useful whenCluster sampling is useful when

- Population frame and stratum characteristics are- Population frame and stratum characteristics are not readily available not readily available- It is too expensive to obtain a simple or stratified- It is too expensive to obtain a simple or stratified sample sample- The cost of obtaining data increases sharply with- The cost of obtaining data increases sharply with distance distance- Some loss of reliability is acceptable- Some loss of reliability is acceptable

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Judgment SampleJudgment Sample• A nonprobability sampling method that relies on the expertise of the sampler to choose items that are A nonprobability sampling method that relies on the expertise of the sampler to choose items that are

representative of the population.representative of the population.

• Can be affected by subconscious bias (i.e., Can be affected by subconscious bias (i.e., nonrandomnessnonrandomness in the choice). in the choice).

• Quota samplingQuota sampling is a special kind of judgment sampling, in which the interviewer chooses a certain number of is a special kind of judgment sampling, in which the interviewer chooses a certain number of people in each category.people in each category.

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Convenience SampleConvenience Sample• Take advantage of whatever sample is available at that moment. A quick way to sample.Take advantage of whatever sample is available at that moment. A quick way to sample.

• Sample size depends on the inherent variability of the quantity being measured and on the desired precision Sample size depends on the inherent variability of the quantity being measured and on the desired precision of the estimate.of the estimate.

Sample SizeSample Size

Download - 2-1. Data Collection Data Vocabulary Data Vocabulary Level of Measurement Level of Measurement Time Series and Cross-sectional Data Time Series and Cross-sectional

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