Sample Size and Statistical Theory

Marketing ResearchAaker, Kumar, Leone and Day Twelfth EditionInstructor’s Presentation Slides1Chapter Fifteen2Sample Size and Statistical TheoryMarketing Research 12th Edition Determining the Sample SizeAd Hoc MethodsUsed when a person knows from experience what sample size to adoptUsed when budgetary constraints dictate the size of the sampleRule of Thumb Sample should be large enough, so that when divided into groups, each group will have a minimum sample size of 100 or moreIf analysis involves comparison between subgroups, sample size in each subgroup should be 20 to 50Use disproportionate sampling if one of groups of population is relatively smallBudget Constraints Researcher must decide whether sample size dictated by budget constraints allows a worthwhile study to be conductedComparative StudiesFind similar studies and use their sample sizes as a guide3Marketing Research 12th Edition Factors Determining Sample SizeNumber of groups and subgroups within the sampleValue of information in the studyAccuracy level required in resultsCost of sampleVariability of the population4Marketing Research 12th Edition Population Characteristics/ParametersPopulation MeanNormally unknownDetermine value as closely as possible by taking a sample from populationPopulation VarianceMeasure of population dispersionBased on degree to which a response differs from population average responseThe difference of each value from its mean is squared and averaged across all responses5Marketing Research 12th Edition Population Characteristics/Parameters6The population opinion on symphony starting time (7:30 P.M. on weekdays)Marketing Research 12th Edition Sample Characteristics/Statistics7Sample mean ( ) is used to estimate the unknown population meanExample: A sample of symphony season-ticket holdersMarketing Research 12th Edition Sample Characteristics/Statistics (Contd.)8Sample meanMarketing Research 12th Edition Sample ReliabilityX will vary from sample to sampleAs sample size (n) increases, variation in X will decrease9standard error of decreases as the sample size gets largerMarketing Research 12th Edition Sampling Distribution10The normal distribution ofIndicates probability of getting a particular sample meanMarketing Research 12th Edition Sampling Distribution (Contd.)11The effect of increasing sample size on the normal distribution ofMarketing Research 12th Edition Interval Estimation varies from sample to sample The difference between the sample mean ( ) and the population mean is the sampling errorInterval size depends on the confidence level the researcher wants for the interval to contain the true population meanIf the population standard deviation is not known, it is necessary to estimate it with the sample standard deviation12Marketing Research 12th Edition Interval Estimation (Contd.)13Size of Interval Estimate depends on:Confidence levelPopulation standard deviationSample sizeMarketing Research 12th Edition Sample Size QuestionSize of the sampling error that is desiredConfidence levelExpected variance14Marketing Research 12th Edition Determining the Population Standard DeviationOptions:Use a sample standard deviation obtained from a previous comparable survey or from a pilot surveyEstimate the sample standard deviation (s) subjectively15Marketing Research 12th Edition Proportions16Population variance,Marketing Research 12th Edition Sample Size Formulas17Marketing Research 12th Edition Coefficient of VariationResearcher may require the sample estimate be within plus or minus G percentage points of the population value Therefore, D = GmThe sample size formula may be written as: C is the Coefficient of variation18Marketing Research 12th Edition Stratified SamplingUseful when:The population standard deviation differs by strataThe interview cost differs by strata Optimal allocation of sampling budget to various strata: Neyman’s solution19whereMarketing Research 12th Edition Allocating Sample Size to Strata20whereMarketing Research 12th Edition 21End of Chapter FifteenMarketing Research 12th Edition