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ChapterSixteen16-1
EvaluatingDifferencesandChangesTheissueofwhethercertainmeasurementsaredifferentfromoneanotheriscentraltomanyquestionsofcriticalinteresttomarketingmanagers.Seethetextforsomespecificexamplesofmanagers’questionsrelatingtoevaluatingthesedifferencesandchanges.16-2KeyTerms&Definitions
MathematicalDifferences:Bydefinition,ifnumbersarenotexactlythesame,theyaredifferent.Thisdoesnot,however,meanthatthedifferenceiseitherimportantorstatisticallysignificant.StatisticalSignificance:Adifferencethatislargeenoughthatitisnotlikelytohaveoccurredbecauseofchanceorsamplingerror.StatisticalSignificance16-3KeyTerms&Definitions
ImportantDifferencesforManagers:Onemustbeabletodistinguishbetweenmathematicaldifferencesandstatisticallysignificantdifferencesinusingthedataanalysisinmanagerialdecisionmaking.Hypothesis:Assumptionortheorythataresearcherormanagermakesaboutsomecharacteristicofthepopulationunderstudy.StatisticalSignificance16-4KeyTerms&Definitions
StepOne:Statingthehypothesis“NullHypothesis”–Thehypothesisofstatusquo,nodifference,noeffect.“AlternativeHypothesis”-anotheralternativeisproventobetrue.StepTwo:ChoosingtheappropriateteststatisticTestofmeans,testofproportions,ANOVA,etc.StepThree:DevelopingadecisionruleDeterminethesignificancelevel.Neededtodeterminewhethertorejectorfailtorejectthenullhypothesis.TheKeySteps:HypothesisTesting16-5KeyTerms&Definitions
StepFour:CalculatingthevalueoftheteststatisticUsetheappropriateformulatocalculatethevalueofthestatistic.StepFive:StatingtheconclusionStatedfromtheperspectiveoftheoriginalresearchquestion.TheKeySteps:HypothesisTesting16-6KeyTerms&Definitions
StatisticalTestsandTheirUses16-7KeyTerms&Definitions
StatisticalTestsandTheirUsesContinued16-8KeyTerms&Definitions
Rejectionofthenullhypothesiswhen,infact,itistrue.Acceptanceofthenullhypothesiswhen,infact,itisfalse.Testsareeitheroneortwo-tailed.Thisapproachdependsonthenatureofthesituationandwhattheresearcherisdemonstrating.One-Tailed:“Ifyoutakethemedicine,youwillgetbetter.”Two-Tailed:“Ifyoutakethemedicine,youwillgeteitherbetterorworse.”OneandTwoTailedTestsHypothesisTesting–ErrorTypes16-9KeyTerms&Definitions
TypeIandTypeIIErrors16-10KeyTerms&DefinitionsRejectionofthenullhypothesiswhen,infact,itistrue.Acceptanceofthenullhypothesiswhen,infact,itisfalse.TypeI:TypeII:
IndependentSamples:Samplesinwhichthemeasurementofavariableinonepopulationhasnoeffectonthemeasurementofthevariableintheother.RelatedSamples:Samplesinwhichthemeasurementofavariableinonepopulationmayinfluencethemeasurementofthevariableintheother.DegreesofFreedom:Numberofobservationsinastatisticalproblemthatarefreetovary.Isequaltothenumberofobservationsminusthenumberofassumptionsorconstraintsnecessarytocalculateastatistic.CommonlyUsedStatisticalHypothesisTests16-11KeyTerms&Definitions
GoodnessofFitChi-SquareTest:TestofthegoodnessoffitbetweentheOBSERVEDdistributionandtheEXPECTEDdistributionofavariable.1.Chi-SquareTestofaSingleSample2.Chi-SquareTestofTwoIndependentSamples:Marketingresearchersoftenneedtodeterminewhetherthereisanyassociationbetweentwoormorevariables.16-12KeyTerms&Definitions
ZTest:Hypothesistestusedforasinglemeanifthesampleislargeenoughanddrawnatrandom.Usuallyforsamplesofabout30andabove.tTest:HypothesistestusedforasinglemeanifthesampleistoosmalltousetheZtest.Usuallyforsamplesbelow30.Hypothesistestingthatteststhedifferencesbetweengroupsofdata.AboutOneMean:AboutTwoMeans:TypesofHypothesisTests16-13KeyTerms&Definitions
ZTest-Example16-14KeyTerms&Definitions
ZTest–ExampleContinued16-15KeyTerms&Definitions
ZTest–ExampleContinued16-16KeyTerms&Definitions
HypothesisAboutTwoMeans-Example16-17KeyTerms&Definitions
HypothesisAboutTwoMeansContinued16-18KeyTerms&Definitions
ProportioninOneSample:Testtodeterminewhetherthedifferencebetweenproportionsisgreaterthanwouldbeexpectedbecauseofsamplingerror.TwoProportionsinIndependentSamples:Testtodeterminetheproportionaldifferencesbetweentwoormoregroups.TypesofHypothesisTests16-19KeyTerms&Definitions
AnalysisofVariance(ANOVA)ANOVA:Testforthedifferencesamongthemeansoftwoormoreindependentsamples.Whenthegoalistotestthedifferencesamongthemeansoftwoormoreindependentsamples,analysisofvariance(ANOVA)isanappropriatestatisticaltool.Althoughitcanbeusedtotestdifferencesbetweentwomeans,ANOVAismorecommonlyusedforhypothesistestsregardingthedifferencesamongthemeansofseveral(C)independentgroups(whereC>or=3).ItisastatisticaltechniquethatpermitstheresearchertodeterminewhetherthevariabilityamongoracrosstheCsamplemeansisgreaterthanexpectedbecauseofsamplingerror.16-20KeyTerms&Definitions
FTestFTest:Testoftheprobabilitythataparticularcalculatedvaluecouldhavebeenduetochance.16-21KeyTerms&Definitions
pValuesandSignificanceTestingpValue:Exactprobabilityofgettingacomputedteststatisticthatisduetochance.Thesmallerthepvalue,thesmallertheprobabilitythattheobservedresultoccurredbychance.16-22KeyTerms&Definitions
16-23KeyTerms&DefinitionsStatisticalSignificanceHypothesisNullHypothesisDecisionRuleTypeIErrorTypeIIErrorIndependentSamplesRelatedSamplesDegreesofFreedomLinksandbuttonareactivewhenin“SlideShowMode”KeyTerms&DefinitionsChi-squareTestZTesttTestZTestExampleHypothesisAboutTwoMeansHypothesisTestofProportionsAnalysisofVariance(ANOVA)FTestpValue