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Research design, Sampling

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- 1. Research Design :Research Design :Sampling &Sampling &Data CollectionData CollectionResearch Design :Research Design :Sampling &Sampling &Data CollectionData CollectionABDM4064 BUSINESS RESEARCHABDM4064 BUSINESS RESEARCHbyStephen OngPrincipal Lecturer (Specialist)Visiting Professor, Shenzhen
- 2. 6-2Design in the Research ProcessDesign in the Research Process
- 3. 14-3Sampling DesignSampling Designwithin the Research Processwithin the Research Process
- 4. Sampling DesignSampling Design
- 5. LEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMESLEARNING OUTCOMES1. Explain reasons for taking a sample rather than acomplete census2. Describe the process of identifying a targetpopulation and selecting a sampling frame3. Compare random sampling and systematic(nonsampling) errors4. Identify the types of nonprobability sampling,including their advantages and disadvantagesAfter studying this chapter, you should be able to
- 6. LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)LEARNING OUTCOMES (cont’d)5. Summarize the advantages and disadvantages ofthe various types of probability samples6. Discuss how to choose an appropriate sampledesign, as well as challenges for Internet sampling7. Understand basic statistical terminology8. Interpret frequency distributions, proportions, andmeasures of central tendency and dispersion9. Distinguish among population, sample, andsampling distributions10. Summarize the use of confidence intervalestimatesAfter studying this chapter, you should
- 7. 14-7Small Samples Can EnlightenSmall Samples Can Enlighten““The proof of the pudding is in theThe proof of the pudding is in theeating.eating.ByBy a small samplea small sample we may judge of thewe may judge of thewhole piece.”whole piece.”Miguel de Cervantes SaavedraMiguel de Cervantes Saavedraauthorauthor
- 8. 14-8The Nature of SamplingThe Nature of SamplingPopulationPopulationPopulation ElementPopulation ElementCensusCensusSampleSampleSampling frameSampling frame
- 9. Sampling TerminologySampling Terminology Sample A subset, or some part, of a largerpopulation. Population (universe) Any complete group of entities that sharesome common set of characteristics. Population Element An individual member of a population. Census An investigation of all the individualelements that make up a population.
- 10. 14-10Why Sample?Why Sample?GreaterGreateraccuracyaccuracyAvailabilityAvailabilityof elementsof elementsAvailabilityAvailabilityof elementsof elementsGreaterGreaterspeedspeedGreaterGreaterspeedspeedSamplingSamplingprovidesprovidesSamplingSamplingprovidesprovidesLowerLowercostcostLowerLowercostcost
- 11. 14-11What Is a SufficientlyWhat Is a SufficientlyLarge Sample?Large Sample?““In recent Gallup ‘Poll on polls,’ . . . When askedIn recent Gallup ‘Poll on polls,’ . . . When askedabout the scientific sampling foundation on whichabout the scientific sampling foundation on whichpolls are based . . . most said that a survey ofpolls are based . . . most said that a survey of1,500 – 2,000 respondents—a larger than average1,500 – 2,000 respondents—a larger than averagesample size for national polls—cannot representsample size for national polls—cannot representthe views of all Americans.”the views of all Americans.”Frank NewportFrank NewportThe Gallup Poll editor in chiefThe Gallup Poll editor in chiefThe Gallup OrganizationThe Gallup Organization
- 12. 14-12When Is a CensusWhen Is a CensusAppropriate?Appropriate?NecessaryNecessaryFeasibleFeasible
- 13. 14-13What Is a Valid Sample?What Is a Valid Sample?AccurateAccurate PrecisePrecise
- 14. Why Sample?Why Sample? Pragmatic Reasons Budget and time constraints. Limited access to total population. Accurate and Reliable Results Samples can yield reasonably accurateinformation.information. Strong similaritiesStrong similarities in population elements makesin population elements makessampling possible.sampling possible. Sampling may beSampling may be more accuratemore accurate than a census.than a census. Destruction of Test UnitsDestruction of Test Units SamplingSampling reduces the costsreduces the costs of research in finiteof research in finitepopulations.populations.
- 15. A Photographic Example of How Sampling WorksA Photographic Example of How Sampling Works
- 16. 16–16Stages inStages inthetheSelectionSelectionof aof aSampleSample
- 17. 14-17Types of Sampling DesignsTypes of Sampling DesignsElementSelectionProbability Nonprobability•UnrestrictedUnrestricted • Simple randomSimple random • ConvenienceConvenience•RestrictedRestricted • Complex randomComplex random • PurposivePurposive• SystematicSystematic • JudgmentJudgment•ClusterCluster •QuotaQuota•StratifiedStratified •SnowballSnowball•DoubleDouble
- 18. 14-18Steps in Sampling DesignSteps in Sampling DesignWhat is the target population?What is the target population?What is the target population?What is the target population?What are the parameters ofWhat are the parameters ofinterest?interest?What are the parameters ofWhat are the parameters ofinterest?interest?What is the sampling frame?What is the sampling frame?What is the sampling frame?What is the sampling frame?What is the appropriateWhat is the appropriatesampling method?sampling method?What is the appropriateWhat is the appropriatesampling method?sampling method?What size sample is needed?What size sample is needed?What size sample is needed?What size sample is needed?
- 19. 14-19When to Use Larger Sample?When to Use Larger Sample?DesiredDesiredprecisionprecisionDesiredDesiredprecisionprecisionNumber ofNumber ofsubgroupssubgroupsNumber ofNumber ofsubgroupssubgroupsConfidenceConfidencelevellevelConfidenceConfidencelevellevelPopulationPopulationvariancevarianceSmall errorSmall errorrangerange
- 20. Practical Sampling ConceptsPractical Sampling Concepts Defining the Target Population Once the decision to sample has been made,the first question concerns identifying thetarget population. What is the relevant population? In many casesthis is easy to answer, but in other cases, thedecision may be difficult. At the outset of the sampling process it isvitally important to carefully define the targetpopulation so that the proper source fromwhich the data are to be collected can beidentified. To implement the sample in the field, tangiblecharacteristics (e.g. age, gender etc) should beused to define the population.
- 21. Practical Sampling ConceptsPractical Sampling Concepts(cont’d)(cont’d) The Sampling Frame In practice, the sample will be drawn from alist of population elements that often differssomewhat from the defined target population. A sampling frame is a list of elements fromwhich the sample may be drawn. The sampling frame is also called the workingpopulation, because these units willeventually provide units involved in theanalysis. The discrepancy between the definition of thepopulation and a sampling frame is the firstpotential source of error associated withsample selection.
- 22. ExampleExample Target population: Students inMalaysia between 18 years old and 22years old. Sampling frame: students from ahigher education institution.
- 23. Practical Sampling ConceptsPractical Sampling Concepts(cont’d)(cont’d) The Sampling Frame A sampling frame error occurs whencertain sample elements are excluded orwhen the entire population is notaccurately represented in the samplingframe. Population elements can be either under-or overrepresented in a sampling frame.
- 24. Sampling UnitsSampling Units Sampling Unit A single element or group of elementssubject to selection in the sample. Primary Sampling Unit (PSU) A unit selected in the first stage of sampling. Secondary Sampling Unit A unit selected in the second stage ofsampling. Tertiary Sampling Unit A unit selected in the third stage of sampling.
- 25. EXAMPLETarget population: Students in Malaysiabetween 18 years old and 22 years old.Sample frame: students from a highereducation institution.Sampling units: Advanced Diploma students only (primarysampling unit) School of Business Studies only (secondarysampling unit) ABU only (tertiary sampling unit)16–25
- 26. Random Sampling andRandom Sampling andNonsampling ErrorsNonsampling Errors If a difference exists between the valueof a sample statistic of interest and thevalue of the corresponding populationparameter, a statistical error hasoccurred. Two basic causes of differencesbetween statistics and parameters:random sampling errorssystematic (nonsampling) errors
- 27. Random Sampling and Nonsampling Errors (cont’d)Random Sampling and Nonsampling Errors (cont’d) Random Sampling Error Random sampling error is the difference between thesample result and the result of a census conducted usingidentical procedures. Random sampling error occurs because of chancevariation in the scientific selection of sampling units. Because random sampling errors follow chance variations,they tend to cancel one another out when averaged. This means that properly selected samples are generallygood approximations of the population. Random sampling error is a function of sample size. As sample size increases, random sampling errordecreases It is possible to estimate the random sampling error thatmay be expected with various sample sizes.
- 28. Random Sampling andRandom Sampling andNonsampling Errors (cont’d)Nonsampling Errors (cont’d) Systematic Sampling Error Systematic (nonsampling) errors resultfrom nonsampling factors, primarily thenature of a study’s design and thecorrectness of execution. These errors are not due to chancefluctuations. Sample biases account for a large portionof errors in research.
- 29. Random Sampling andRandom Sampling andNonsampling Errors (cont’d)Nonsampling Errors (cont’d) Less than Perfectly RepresentativeSamples Random sampling errors and systematicerrors associated with the sampling processmay combine to yield a sample that is lessthan perfectly representative of thepopulation. Additional errors will occur if individualsrefuse to be interviewed or cannot becontacted. Such nonresponse error may also cause thesample to be less than perfectlyrepresentative.
- 30. EXHIBIT 16.EXHIBIT 16.44 Errors Associated with SamplingErrors Associated with Sampling
- 31. Probability versusProbability versusNonprobability SamplingNonprobability Sampling Several alternative ways to takeSeveral alternative ways to takea sample are available.a sample are available. The main alternative samplingThe main alternative samplingplans may be grouped into twoplans may be grouped into twocategories:categories: 1. probability techniques1. probability techniques 2. nonprobability techniques.2. nonprobability techniques.
- 32. Probability versus Nonprobability SamplingProbability versus Nonprobability Sampling(cont’d)(cont’d) Probability Sampling In probability sampling, every element inthe population has a known, nonzeroprobability of selection. The simple random sample, in which eachmember of the population has an equalprobability of being selected, is the best-known probability sample.
- 33. Probability versus NonprobabilityProbability versus NonprobabilitySampling (cont’d)Sampling (cont’d) Nonprobability sampling In nonprobability sampling, the probability of anyparticular member of the population being chosenis unknown. The selection of sampling units in nonprobabilitysampling is quite arbitrary, as researchers relyheavily on personal judgment. Technically, no appropriate statistical techniquesexist for measuring random sampling error from anonprobability sample. Therefore, projecting the data beyond the sample istechnically speaking, statistically inappropriate. Nevertheless, nonprobability samples arepragmatic and are used in business research.
- 34. 14-34Nonprobability SamplesNonprobability SamplesCostCostFeasibilityFeasibilityFeasibilityFeasibilityTimeTimeTimeTimeNo need toNo need togeneralizegeneralizeLimitedLimitedobjectivesobjectivesLimitedLimitedobjectivesobjectives
- 35. 14-35NonprobabilityNonprobabilitySampling MethodsSampling MethodsConvenienceConvenienceConvenienceConvenienceJudgmentJudgmentJudgmentJudgmentQuotaQuotaQuotaQuotaSnowballSnowballSnowballSnowball
- 36. Nonprobability SamplingNonprobability SamplingMethodsMethods Convenience Sampling Obtaining those people or units that are mostconveniently available. Mall interception survey is applying thismethod. Judgment (Purposive) Sampling An experienced individual selects the samplebased on personal judgment about someappropriate characteristic of the samplemember. E.g. Consumer Price Index (CPI)
- 37. Nonprobability Sampling (cont’d)Nonprobability Sampling (cont’d) Quota Sampling Ensures that various subgroups of a population will berepresented on pertinent characteristics to the exact extent thatthe investigator desires. E.g. SOT – 20, SBS - 30 Possible Sources Of Bias Respondents chosen because they were: Similar to interviewer Easily found Willing to be interviewed Middle-class Advantages of Quota Sampling Speed of data collection Lower costs Convenience
- 38. Nonprobability SamplingNonprobability Sampling(cont’d)(cont’d) Snowball Sampling A sampling procedure in which initialrespondents are selected by probabilitymethods and additional respondents areobtained from information provided by theinitial respondents. E.g. 1 respondent (selected throughprobability method) recommended another5 respondents; then the 5 additionalrespondents recommended another 25respondents.
- 39. Probability SamplingProbability Sampling Simple Random Sampling Simple random sampling is a sampling procedurethat assures that each element in the populationwill have an equal chance of being included in thesample. Drawing names from a hat is a typical example ofsimple random sampling; each person has anequal chance of being selected. To use this method, we must have a list of allmembers in a population, then we draw lots. Systematic Sampling A starting point is selected by a random processand then every nth number on the list is selected. E.g. for the list of all members in a population,every 10thname will be selected.
- 40. 14-40Simple RandomSimple RandomAdvantagesAdvantages•Easy to implementEasy to implementwith random dialingwith random dialingDisadvantagesDisadvantages•Requires list ofRequires list ofpopulation elementspopulation elements•Time consumingTime consuming•Larger sampleLarger sampleneededneeded•Produces largerProduces largererrorserrors•High costHigh cost
- 41. 14-41SystematicSystematicAdvantagesAdvantages•Simple to designSimple to design•Easier than simpleEasier than simplerandomrandom•Easy to determineEasy to determinesampling distributionsampling distributionof mean or proportionof mean or proportionDisadvantagesDisadvantages•Periodicity withinPeriodicity withinpopulation may skewpopulation may skewsample and resultssample and results•Trends in list mayTrends in list maybias resultsbias results•Moderate costModerate cost
- 42. Proportional versus DisproportionalProportional versus DisproportionalSamplingSampling Stratified Sampling Simple random subsamples that are more or less equal onsome characteristic are drawn from within each stratum(subgroup) of the population. E.g. based on the same characteristics, we divide studentsinto 3 subgroups (e.g. students with straight-pass,students with re-sit units, students with repeat units), thenwe use simple random sampling method to draw asubsample. Proportional Stratified Sample The number of sampling units drawn from each stratumis in proportion to the population size of that stratum. Disproportional Stratified Sample The sample size for each stratum is allocated accordingto analytical considerations.
- 43. EXHIBIT 16.EXHIBIT 16.55 Disproportional Sampling: Hypothetical ExampleDisproportional Sampling: Hypothetical Example
- 44. 14-44StratifiedStratifiedAdvantagesAdvantages•Control of sample size inControl of sample size instratastrata•Increased statisticalIncreased statisticalefficiencyefficiency•Provides data toProvides data torepresent and analyzerepresent and analyzesubgroupssubgroups•Enables use of differentEnables use of differentmethods in stratamethods in strataDisadvantagesDisadvantages•Increased error ifIncreased error ifsubgroups are selected atsubgroups are selected atdifferent ratesdifferent rates•Especially expensive ifEspecially expensive ifstrata on population muststrata on population mustbe createdbe created•High costHigh cost
- 45. Cluster SamplingCluster Sampling The purpose of cluster sampling is to sampleeconomically while retaining the characteristics of aprobability sample. In a cluster sample, the primary sampling unit is nolonger the individual element in the population (e.g.,grocery stores) but a larger cluster of elementslocated in proximity to one another (e.g., cities). Cluster sampling is classified as a probabilitysampling technique because of either the randomselection of clusters or the random selection ofelements within each cluster. Cluster samples frequently are used when lists of thesample population are not available.
- 46. EXHIBIT 16.EXHIBIT 16.66 Examples of ClustersExamples of Clusters
- 47. 14-47ClusterClusterAdvantagesAdvantages•Provides an unbiasedProvides an unbiasedestimate of populationestimate of populationparameters if properlyparameters if properlydonedone•Economically moreEconomically moreefficient than simpleefficient than simplerandomrandom•Lowest cost per sampleLowest cost per sample•Easy to do without listEasy to do without listDisadvantagesDisadvantages•Often lower statisticalOften lower statisticalefficiency due toefficiency due tosubgroups beingsubgroups beinghomogeneous rather thanhomogeneous rather thanheterogeneousheterogeneous•Moderate costModerate cost
- 48. Multistage Area SamplingMultistage Area Sampling Multistage Area Sampling Involves using a combination of two ormore probability sampling techniques. Typically, geographic areas are randomlyselected in progressively smaller (lower-population) units. Researchers may take as many steps asnecessary to achieve a representative sample. Progressively smaller geographic areas arechosen until a single housing unit is selectedfor interviewing.
- 49. EXHIBIT 16.EXHIBIT 16.88 Geographic Hierarchy Inside Urbanized AreasGeographic Hierarchy Inside Urbanized Areas
- 50. 14-50Stratified and Cluster SamplingStratified and Cluster SamplingStratifiedStratified•Population divided intoPopulation divided intofew subgroupsfew subgroups•Homogeneity withinHomogeneity withinsubgroupssubgroups•Heterogeneity betweenHeterogeneity betweensubgroupssubgroups•Choice of elementsChoice of elementsfrom within eachfrom within eachsubgroupsubgroupClusterCluster•Population divided intoPopulation divided intomany subgroupsmany subgroups•Heterogeneity withinHeterogeneity withinsubgroupssubgroups•Homogeneity betweenHomogeneity betweensubgroupssubgroups•Random choice ofRandom choice ofsubgroupssubgroups
- 51. 14-51Area SamplingArea Sampling
- 52. 14-52Double SamplingDouble SamplingAdvantagesAdvantages•May reduce costs ifMay reduce costs iffirst stage results infirst stage results inenough data to stratifyenough data to stratifyor cluster theor cluster thepopulationpopulationDisadvantagesDisadvantages•Increased costs ifIncreased costs ifdiscriminately useddiscriminately used
- 53. What Is the AppropriateWhat Is the AppropriateSample Design? (cont’d)Sample Design? (cont’d) Resources The cost associated with the differentsampling techniques varies tremendously. If the researcher’s financial and humanresources are restricted, certain options willhave to be eliminated. Managers concerned with the cost of theresearch versus the value of the informationoften will opt for cost savings from a certainnonprobability sample design rather thanmake the decision to conduct no research atall.
- 54. What Is the Appropriate SampleWhat Is the Appropriate SampleDesign? (cont’d)Design? (cont’d) Time Researchers who need to meet a deadline orcomplete a project quickly will be more likely toselect simple, less time-consuming sampledesigns. Advance Knowledge of the Population In many cases, a list of population elementswill not be available to the researcher. A lack of adequate listslack of adequate lists may automatically ruleout systematic sampling, stratified sampling,or other sampling designs, or it may dictatethat a preliminary study, such as a shorttelephone survey using random digit dialing,be conducted to generate information to builda sampling frame for the primary study.
- 55. What Is the AppropriateWhat Is the AppropriateSample Design? (cont’d)Sample Design? (cont’d) National versus Local Project Geographic proximity of populationelements will influence sample design. When population elements are unequallydistributed geographically, a clustersample may become much more attractive.
- 56. © 2010 South-Western/CengageLearning. All rights reserved. May notbe scanned, copied or duplicated, orposted to a publically accessiblewebsite, in whole or in part.16–56EXHIBIT 16.EXHIBIT 16.99 Comparison of Sampling Techniques: Nonprobability SamplesComparison of Sampling Techniques: Nonprobability Samples
- 57. © 2010 South-Western/CengageLearning. All rights reserved. May notbe scanned, copied or duplicated, orposted to a publically accessiblewebsite, in whole or in part.16–57EXHIBIT 16.EXHIBIT 16.1010 Comparison of Sampling Techniques: Probability SamplesComparison of Sampling Techniques: Probability Samples
- 58. Determination of sample sizeDetermination of sample size Descriptive and Inferential StatisticsThere are two applications ofstatistics:(1) to describe characteristics ofthe population or sample(descriptive statistics) and(2) to generalize from the sample tothe population (inferentialstatistics).
- 59. Sample Statistics and PopulationSample Statistics and PopulationParametersParameters The primary purpose of inferential statistics is to make ajudgment about the population, or the collection of allelements about which one seeks information. The sample is a subset or relatively small fraction of thetotal number of elements in the population. Sample statistics are variables in the sample ormeasures computed from the sample data. Population parameters are variables or measuredcharacteristics of the population. We will generally use Greek lowercase letters to denotepopulation parameters (e.g., μ or σ) and English lettersto denote sample statistics (e.g., X or S).
- 60. Making Data UsableMaking Data Usable To make data usable, this informationmust be organized and summarized. Methods for doing this include:frequency distributionsproportionsmeasures of central tendencyand dispersion
- 61. Making Data Usable (cont’d)Making Data Usable (cont’d) Frequency Distributions Constructing a frequency table or frequencydistribution is one of the most common means ofsummarizing a set of data. The frequency of a value is the number of timesa particular value of a variable occurs. Exhibit 17.1 represents a frequency distributionof respondents’ answers to a question askinghow much customers had deposited in thesavings and loan. It is also quite simple to construct a distributionof relative frequency, or a percentagedistribution, which is developed by dividing thefrequency of each
- 62. EXHIBIT 17.EXHIBIT 17.11 Frequency Distribution of DepositsFrequency Distribution of Deposits
- 63. EXHIBIT 17.EXHIBIT 17.22 Percentage Distribution of DepositsPercentage Distribution of Deposits
- 64. EXHIBIT 17.EXHIBIT 17.33 Probability Distribution of DepositsProbability Distribution of Deposits
- 65. Population MeanMaking Data Usable (cont’d)Making Data Usable (cont’d) Proportion The percentage of elements that meetsome criterion Measures of Central Tendency Mean: the arithmetic average. Median: the midpoint; the value belowwhich half the values in a distribution fall. Mode: the value that occurs most often.Sample Mean
- 66. EXHIBIT 17.EXHIBIT 17.44 Number of Sales Calls per Day by SalespersonNumber of Sales Calls per Day by Salesperson
- 67. EXHIBIT 17.EXHIBIT 17.55 Sales Levels for Two Products with Identical Average SalesSales Levels for Two Products with Identical Average Sales
- 68. Measures of DispersionMeasures of DispersionThe RangeThe distance between thesmallest and the largestvalues of a frequencydistribution.
- 69. EXHIBIT 17.EXHIBIT 17.66 Low Dispersion versus High DispersionLow Dispersion versus High Dispersion
- 70. Measures of Dispersion (cont’d)Measures of Dispersion (cont’d) Why Use the Standard Deviation? Variance A measure of variability or dispersion. Its square root is the standard deviation. Standard deviation A quantitative index of a distribution’s spread, orvariability; the square root of the variance for adistribution. The average of the amount of variance for adistribution. Used to calculate the likelihood (probability) of anevent occurring.
- 71. Calculating DeviationCalculating DeviationStandard Deviation =
- 72. EXHIBIT 17.EXHIBIT 17.77 Calculating a Standard Deviation: Number of Sales Calls per Day for EightCalculating a Standard Deviation: Number of Sales Calls per Day for EightSalespeopleSalespeople
- 73. The Normal DistributionThe Normal Distribution Normal Distribution A symmetrical, bell-shaped distribution(normal curve) that describes the expectedprobability distribution of many chanceoccurrences. 99% of its values are within ± 3 standarddeviations from its mean. Example: IQ scores Standardized Normal Distribution A purely theoretical probability distributionthat reflects a specific normal curve for thestandardized value, z.
- 74. EXHIBIT 17.EXHIBIT 17.88 Normal Distribution: Distribution of Intelligence Quotient (IQ) ScoresNormal Distribution: Distribution of Intelligence Quotient (IQ) Scores
- 75. The Normal Distribution (cont’d)The Normal Distribution (cont’d) Characteristics of a Standardized NormalDistribution1. It is symmetrical about its mean; the tails onboth sides are equal.2. The mean identifies the normal curve’s highestpoint (the mode) and the vertical line aboutwhich this normal curve is symmetrical.3. The normal curve has an infinite number ofcases (it is a continuous distribution), and thearea under the curve has a probability densityequal to 1.0.4. The standardized normal distribution has amean of 0 and a standard deviation of 1.
- 76. EXHIBIT 17.EXHIBIT 17.99 Standardized Normal DistributionStandardized Normal Distribution
- 77. The Normal Distribution (cont’d)The Normal Distribution (cont’d) Standardized Values, Z Used to compare an individual value to thepopulation mean in units of the standarddeviation The standardized normal distribution can beused to translate/transform any normal variable,X, into the standardized value, Z. Researchers can evaluate the probability of theoccurrence of many events without anydifficulty.
- 78. EXHIBIT 17.EXHIBIT 17.1010 Standardized Normal Table: Area under Half of the Normal CurveStandardized Normal Table: Area under Half of the Normal Curveaa
- 79. EXHIBIT 17.EXHIBIT 17.1111 StandardizedStandardizedValues can beValues can beComputed fromComputed fromFlat or PeakedFlat or PeakedDistributionsDistributionsResulting in aResulting in aStandardizedStandardizedNormal CurveNormal Curve
- 80. EXHIBIT 17.12EXHIBIT 17.12 Standardized Distribution CurveStandardized Distribution Curve
- 81. 17–81Population Distribution, SamplePopulation Distribution, SampleDistribution, and SamplingDistribution, and SamplingDistributionDistribution Population Distribution A frequency distribution of the elements of apopulation. Sample Distribution A frequency distribution of a sample. Sampling Distribution A theoretical probability distribution of samplemeans for all possible samples of a certain sizedrawn from a particular population. Standard Error of the Mean The standard deviation of the samplingdistribution.
- 82. Three Important DistributionsThree Important Distributions
- 83. EXHIBIT 17.EXHIBIT 17.1313FundamentalFundamentalTypes ofTypes ofDistributionsDistributions
- 84. Central-limit TheoremCentral-limit Theorem Central-limit Theorem The theory that, as sample size increases,the distribution of sample means of size n,randomly selected, approaches a normaldistribution.
- 85. © 2010 South-Western/CengageLearning. All rights reserved. May notbe scanned, copied or duplicated, orposted to a publically accessiblewebsite, in whole or in part.17–85EXHIBIT 17.14EXHIBIT 17.14The MeanThe MeanDistribution ofDistribution ofAnyAnyDistributionDistributionApproachesApproachesNormal asNormal as nnIncreasesIncreases
- 86. EXHIBIT 17.15EXHIBIT 17.15 Population Distribution: Hypothetical Product DefectPopulation Distribution: Hypothetical Product Defect
- 87. EXHIBIT 17.16EXHIBIT 17.16 Calculation of Population MeanCalculation of Population Mean
- 88. EXHIBIT 17.17EXHIBIT 17.17 ArithmeticArithmeticMeans ofMeans ofSamples andSamples andFrequencyFrequencyDistributionDistributionof Sampleof SampleMeansMeans
- 89. Estimation of Parameters and ConfidenceEstimation of Parameters and ConfidenceIntervals (for inference statistics)Intervals (for inference statistics) Point Estimates An estimate of the population mean in the formof a single value, usually the sample mean. Gives no information about the possible magnitudeof random sampling error. Confidence Interval Estimate A specified range of numbers within which apopulation mean is expected to lie. An estimate of the population mean based onthe knowledge that it will be equal to the samplemean plus or minus a small sampling error. i.e. μ = X + a small sampling error.
- 90. The information can be used toestimate market demand. E.g. with 95 percent confidence, theaverage number of unit used per week isbetween 2.3 and 2.9.
- 91. Confidence IntervalsConfidence Intervals Confidence Level A percentage or decimal value that tellshow confident a researcher can be aboutbeing correct. It states the long-run percentage ofconfidence intervals that will include thetrue population mean. The crux of the problem for a researcher isto determine how much random samplingerror to tolerate. Traditionally, researchers have used the95% confidence level (a 5% tolerance forerror).
- 92. Calculating a ConfidenceCalculating a ConfidenceIntervalIntervalEstimation of the sampling errorApproximate location (value) of the populationmean
- 93. Calculating a Confidence IntervalCalculating a Confidence Interval(cont’d)(cont’d)
- 94. Sample SizeSample Size Random Error and Sample Size Random sampling error varies with samplesof different sizes. Increases in sample size reduce samplingerror at a decreasing rate. Diminishing returns - random sampling error isinversely proportional to the square root of n.
- 95. EXHIBIT 17.18EXHIBIT 17.18 Relationship between Sample Size and ErrorRelationship between Sample Size and Error
- 96. EXHIBIT 17.19EXHIBIT 17.19 Statistical Information Needed to Determine Sample Size forStatistical Information Needed to Determine Sample Size forQuestions Involving MeansQuestions Involving Means
- 97. Factors of Concern in ChoosingFactors of Concern in ChoosingSample SizeSample Size Variance (or Heterogeneity) A heterogeneous population has morevariance (a larger standard deviation) whichwill require a larger sample. A homogeneous population has lessvariance (a smaller standard deviation) whichpermits a smaller sample. Magnitude of Error (Confidence Interval) How precise must the estimate be? Confidence Level How much error will be tolerated? Forbusiness research, 95 percent confidence95 percent confidencelevel is used.
- 98. Estimating Sample Size forEstimating Sample Size forQuestions Involving MeansQuestions Involving Means Sequential Sampling Conducting a pilot study to estimate thepopulation parameters so that another, largersample of the appropriate sample size may bedrawn. Estimating sample size:
- 99. Sample Size ExampleSample Size Example Suppose a survey researcher, studying expenditureson lipstick, wishes to have a 95 percent confidencelevel (Z) and a range of error (E) of less than $2.00.The estimate of the standard deviation is $29.00.What is the calculated sample size?
- 100. Sample Size ExampleSample Size Example Suppose, in the same example as the one before,the range of error (E) is acceptable at $4.00. Samplesize is reduced.
- 101. Calculating Sample Size at theCalculating Sample Size at the99 Percent Confidence Level99 Percent Confidence Level
- 102. Determining Sample Size for ProportionsDetermining Sample Size for Proportions
- 103. Determining Sample Size for ProportionsDetermining Sample Size for Proportions(cont’d)(cont’d)
- 104. 753=001225.922.=001225)24)(.8416.3(=)035( .)4)(.6(.)961.(n4.q6.p22===Calculating Example SampleCalculating Example SampleSize at the 95 PercentSize at the 95 PercentConfidence LevelConfidence Level
- 105. EXHIBIT 17.20EXHIBIT 17.20 Selected Tables for Determining Sample Size When the Characteristic ofSelected Tables for Determining Sample Size When the Characteristic ofInterest Is a ProportionInterest Is a Proportion
- 106. EXHIBIT 17.21EXHIBIT 17.21 Allowance for Random Sampling Error (Plus and Minus PercentageAllowance for Random Sampling Error (Plus and Minus PercentagePoints) at 95 Percent Confidence LevelPoints) at 95 Percent Confidence Level
- 107. The Nature of FieldworkThe Nature of Fieldwork Fieldworker An individual who is responsible forgathering data in the field. Typical fieldwork activities: Administering a questionnaire door to door Telephone interview calling from a centrallocation Counting pedestrians in a shopping mall Supervising the collection of data
- 108. Making Initial ContactMaking Initial Contact Personal Interviews Making opening remarks that will convince therespondent that his or her cooperation is important. Telephone Interviews Giving the interviewer’s name personalizes the call. Providing the name of the research agency is usedto imply that the caller is trustworthy. Providing an accurate estimate of the time helpsgain cooperation. Internet Surveys Respondent may receive an e-mail requestingassistance.
- 109. Gaining ParticipationGaining Participation Foot-in-the-Door Compliance Technique Compliance with large or difficult task isinduced by first obtaining the respondent’scompliance with a smaller request. Door-in-the-Face Compliance Technique A two-step process for securing a highresponse rate. Step 1: An initial request, so large that nearlyeveryone refuses it, is made. Step 2: A second request is made for a smallerfavour; respondents are expected to comply withthis more reasonable request.
- 110. Asking the QuestionsAsking the Questions Major Rules for Asking Questions:1. Ask questions exactly as they are worded inthe questionnaire.2. Read each question very carefully andclearly.3. Ask the questions in the specified order.4. Ask every question specified in thequestionnaire.5. Repeat questions that are misunderstood ormisinterpreted.
- 111. Probing When No Response IsProbing When No Response IsGivenGiven Probing Verbal attempts made by a field-worker whenthe respondent must be motivated tocommunicate his or her answers more fully. Probing Tactics that Enlarge and Clarify: Repeating the question Using a silent probe Repeating the respondent’s reply Asking a neutral question
- 112. EXHIBIT 18.EXHIBIT 18.11 Commonly Used Probes and Their AbbreviationsCommonly Used Probes and Their Abbreviations
- 113. Recording the ResponsesRecording the Responses Rules for recording responses to fixed-alternativequestions vary with the specific questionnaire. Rules for recording open-ended answers include: Record responses during the interview. Use the respondent’s own words. Do not summarize or paraphrase the respondent’s answer. Include everything that pertains to the question objectives. Include all of your probes. How answers are recorded can affect researchers’interpretation of the respondent’s answers.
- 114. 18–114EXHIBIT 18.EXHIBIT 18.22 A Completed Portion of a Response Form with NotesA Completed Portion of a Response Form with Notes
- 115. Terminating the InterviewTerminating the Interview How to close the interview is important: Fieldworkers should wait to close theinterview until they have secured all pertinentinformation including spontaneous commentsof the respondent. Fieldworkers should answer any respondentquestions concerning the nature and purposeof the study to the best of his or her ability. Avoiding hasty departures is a matter ofcourtesy. It is important to thank the respondent for hisor her time and cooperation as reinterviewingmay be required.
- 116. Principles of Good InterviewingPrinciples of Good Interviewing The Basics:1. Have integrity, and be honest.2. Have patience and tact.3. Pay attention to accuracy and detail.4. Exhibit a real interest in the inquiry at hand,but keep your own opinions to yourself.5. Be a good listener.6. Keep the inquiry and respondents’ responsesconfidential.7. Respect others’ rights.
- 117. Principles of GoodPrinciples of GoodInterviewing (cont’d)Interviewing (cont’d) Required Practices1. Complete the number of interviews according to thesampling plan assigned to you.2. Follow the directions provided.3. Make every effort to keep schedules.4. Keep control of each interview you do.5. Complete the questionnaires meticulously.6. Check over each questionnaire you have completed.7. Compare your sample execution and assigned quota withthe total number of questionnaires you have completed.8. Clear up any questions with the research agency.
- 118. Further ReadingFurther Reading COOPER, D.R. AND SCHINDLER, P.S. (2011)BUSINESS RESEARCH METHODS, 11THEDN,MCGRAW HILL ZIKMUND, W.G., BABIN, B.J., CARR, J.C. ANDGRIFFIN, M. (2010) BUSINESS RESEARCHMETHODS, 8THEDN, SOUTH-WESTERN SAUNDERS, M., LEWIS, P. AND THORNHILL, A.(2012) RESEARCH METHODS FOR BUSINESSSTUDENTS, 6THEDN, PRENTICE HALL. SAUNDERS, M. AND LEWIS, P. (2012) DOINGRESEARCH IN BUSINESS & MANAGEMENT, FTPRENTICE HALL.
- 119. DETERMINING SAMPLE SIZEDETERMINING SAMPLE SIZEAPPENDIXAPPENDIX
- 120. 14-120Random SamplesRandom Samples
- 121. 14-121Increasing PrecisionIncreasing Precision
- 122. 14-122Confidence Levels & theConfidence Levels & theNormal CurveNormal Curve
- 123. 14-123Standard ErrorsStandard ErrorsStandard Error(Z score)% of Area ApproximateDegree ofConfidence1.00 68.27 68%1.65 90.10 90%1.96 95.00 95%3.00 99.73 99%
- 124. 14-124Central Limit TheoremCentral Limit Theorem
- 125. 14-125Estimates of Dining VisitsEstimates of Dining VisitsConfidence Zscore% ofAreaInterval Range(visits permonth)68% 1.00 68.27 9.48-10.5290% 1.65 90.10 9.14-10.8695% 1.96 95.00 8.98-11.0299% 3.00 99.73 8.44-11.56
- 126. 14-126Calculating Sample Size forCalculating Sample Size forQuestions involving MeansQuestions involving MeansPrecisionPrecisionConfidence levelConfidence levelSize of interval estimateSize of interval estimatePopulation DispersionPopulation DispersionNeed for FPANeed for FPA
- 127. 14-127Metro U Sample Size for MeansMetro U Sample Size for MeansSteps InformationInformationDesired confidence level 95% (z = 1.96)95% (z = 1.96)Size of the interval estimate ±± .5 meals per month.5 meals per monthExpected range inpopulation0 to 30 meals0 to 30 mealsSample mean 1010Standard deviation 4.14.1Need for finite populationadjustmentNoNoStandard error of the mean .5/1.96 = .255.5/1.96 = .255Sample size (4.1)(4.1)22/ (.255)/ (.255)22= 259= 259
- 128. 14-128Proxies of theProxies of thePopulation DispersionPopulation Dispersion Previous research on thePrevious research on thetopictopic Pilot test or pretestPilot test or pretest Rule-of-thumb calculationRule-of-thumb calculation 1/6 of the range1/6 of the range
- 129. 14-129Metro U Sample Size forMetro U Sample Size forProportionsProportionsSteps InformationInformationDesired confidence level 95% (z = 1.96)95% (z = 1.96)Size of the interval estimate ±± .10 (10%).10 (10%)Expected range in population 0 to 100%0 to 100%Sample proportion with givenattribute30%30%Sample dispersion Pq = .30(1-.30) = .21Pq = .30(1-.30) = .21Finite population adjustment NoNoStandard error of theproportion.10/1.96 = .051.10/1.96 = .051Sample size .21/ (.051).21/ (.051)22= 81= 81
- 130. 14-130Random SamplesRandom Samples
- 131. 14-131Confidence LevelsConfidence Levels
- 132. 14-132Metro U. Dining Club StudyMetro U. Dining Club Study

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