當(dāng)代市場調(diào)研 （原第12版）課件英文第13章　差異和關(guān)系的統(tǒng)計檢驗

MarketingResearchTwelfthEditionCarlD.McDanielandRogerGatesChapter#13StatisticalTestingofDifferencesandRelationshipsLearningObjectivesLearnhowtoevaluatedifferencesandchanges.Understandtheconceptofhypothesisdevelopmentandhowtotesthypotheses.Befamiliarwithseveralofthemorecommonstatisticaltestsofgoodnessoffit,hypothesesaboutonemean,hypothesesabouttwomeans,andhypothesesaboutproportions.Learnthehypothesesaboutonemean,twomeansandproportions.Learnaboutanalysisofvariance.UnderstandthePvaluesandsignificancetesting.Copyright?2021JohnWiley&Sons,Inc.13-2IntroductionStatisticaltestsaddresstheissueofwhetherthedifferenceortherelationshipweareobservingisgreaterthanorlessthanwouldbeexpectedduetochanceThechancewearetalkingaboutrelatestosamplingerrorTheissueofwhethercertainmeasurementsaredifferentfromoneanotheriscentraltomanyquestionsofcriticalinteresttomarketingmanagersStatisticalhypothesistestingisimportantbecauseithelpsresearchersgetclosertotheanswerstoquestionsaboutthesedifferences13-3Copyright?2021JohnWiley&Sons,Inc.StatisticalSignificanceThebasicmotiveformakingstatisticalinferencesistogeneralizefromsampleresultstopopulationcharacteristicsMathematicaldifferences:ifnumbersarenotexactlythesame,theyaredifferentThisdoesnot,however,meanthatthedifferenceiseitherimportantorstatisticallysignificantStatisticalsignificance:ifadifferenceislargeenoughtobeunlikelytohaveoccurredbecauseofchanceorsamplingerror,thenthedifferenceisstatisticallysignificantManageriallyimportantdifferences:isthestatisticallysignificantdifferencelargeenoughtobeimportanttomanagement13-4Copyright?2021JohnWiley&Sons,Inc.RemindersRandomsamplesareassumedIfthedatayouareworkingwithdonotcomefromrandomsamples,thenthesignificancetestsarenotappropriateBigDatadoesnotmean“good”dataBigDatahasverylargesamplesizessoverysmalldifferenceswillbestatisticallysignificantbecausesamplesizealwaysfiguresintothecalculationofsignificanceDon’toverrelyonsignificancetestingPlacingtotalrelianceonsignificancetestingisnotagoodidea13-5Copyright?2021JohnWiley&Sons,Inc.HypothesisTestingAhypothesisisanassumptionortheorythataresearcherormanagermakesaboutsomecharacteristicofthepopulationbeinginvestigatedTheresearcherdetermineswhetherahypothesisconcerningsomecharacteristicofthepopulationislikelytobetrue,giventheevidenceAstatisticalhypothesistestallowsustocalculatetheprobabilityofobservingaparticularresultifthestatedhypothesisisactuallytrueTherearetwobasicexplanationsforanobserveddifferencebetweenahypothesizedvalueandaparticularresearchresult:ThehypothesisistrueandtheobserveddifferenceislikelyduetosamplingerrorThehypothesisisfalseandthetruevalueissomeothervalue13-6Copyright?2021JohnWiley&Sons,Inc.StepsinHypothesisTestingStepone:statingthehypothesisSteptwo:choosingtheappropriatestatisticaltestStepthree:developingadecisionruleStepfour:calculatingthevalueoftheteststatisticStepfive:statingtheconclusion13-7Copyright?2021JohnWiley&Sons,Inc.StepOne:StatingtheHypothesis

13-8Copyright?2021JohnWiley&Sons,Inc.StepTwo:ChoosingtheAppropriateStatisticalTestAreaofApplicationSubgroupsorSamplesLevelScalingTestSpecialRequirementsHypothesesaboutfrequencydistributionOneNominalχ2Randomsample

TwoormoreNominalχ2Randomsample,independentsamplesHypothesesaboutmeansOne(largesample)Metric(intervalorratio)ZtestforonemeanRandomsample,

n

≥30

One(smallsample)Two(largesample)Metric(intervalorratio)Metric(intervalorratio)ttestforonemeanZ

testforonemeanRandomsample,

n

<30

Randomsample,n≥30

ThreeormoreMetric(intervalorratio)One-wayANOVARandomsample13-9Copyright?2021JohnWiley&Sons,Inc.StepTwo:ChoosingtheAppropriateStatisticalTestContinuedAreaofApplicationSubgroupsorSamplesLevelScalingTestSpecialRequirementsHypothesesaboutproportionsOne(largesample)Metric(intervalorratio)ZtestforoneproportionRandomsample,

n

≥30

Two(largesample)Metric(intervalorratio)ZtestfortwoproportionsRandomsample,

n

≥3013-10Copyright?2021JohnWiley&Sons,Inc.StepThree:DevelopingaDecisionRuleAdecisionrule,orstandard,isneededtodeterminewhethertorejectorfailtorejectthenullhypothesisStatisticiansstatesuchdecisionrulesintermsofsignificancelevelsThesignificancelevel(α)iscriticalintheprocessofchoosingbetweenthenullandalternativehypothesesRejectionofthenullhypothesisisequivalenttosupportingthealternativehypothesis13-11Copyright?2021JohnWiley&Sons,Inc.StepFour:CalculatingtheValueoftheTestStatisticUsetheappropriateformulatocalculatethevalueofthestatisticforthetestchosenComparethevaluejustcalculatedtothecriticalvalueofthestatisticbasedonthedecisionrulechosenBasedonthecomparison,determinetoeitherrejectorfailtorejectthenullhypothesisH013-12Copyright?2021JohnWiley&Sons,Inc.StepFive:StatingtheConclusionTheconclusionsummarizestheresultsofthetestItshouldbestatedfromtheperspectiveoftheoriginalresearchquestion13-13Copyright?2021JohnWiley&Sons,Inc.TypesofErrorsinHypothesisTestingFailtoRejectH0RejectH0H0istrueH0isfalse(HAistrue)13-14Copyright?2021JohnWiley&Sons,Inc.TypesofErrorsinHypothesisTestingContinued

13-15Copyright?2021JohnWiley&Sons,Inc.AcceptingH0versusFailingtoReject(FTR)H0Whenahypothesisistested,thenullhypothesisispresumedtobetrueuntilitisdemonstratedaslikelytobefalseInanyhypothesistestingsituation,theonlyotherhypothesisthatcanbeacceptedisthealternativehypothesisEitherthereissufficientevidencetosupportHa(rejectH0)orthereisnot(failtorejectH0)13-16Copyright?2021JohnWiley&Sons,Inc.One-TailedversusTwo-TailedTestTestsareeitherone-tailedortwo-tailedThedecisionastowhichtousedependsonwhattheresearcheristryingtodemonstrate13-17Copyright?2021JohnWiley&Sons,Inc.ExampleofPerformingaStatisticalTest

13-18Copyright?2021JohnWiley&Sons,Inc.ShadedAreaIsSignificanceLevelα13-19Copyright?2021JohnWiley&Sons,Inc.ExampleofPerformingaStatisticalTestContinued

13-20Copyright?2021JohnWiley&Sons,Inc.CommonlyUsedStatisticalHypothesisTestsIndependentversusrelatedsamplesGoodnessoffitChi-squaretestHypothesesaboutonemeanHypothesesabouttwomeansHypothesesaboutproportionsOnesampleTwoproportionsinindependentsamplesAnalysisofvariance13-21Copyright?2021JohnWiley&Sons,Inc.IndependentversusRelatedSamplesSometimes,oneneedstotestthehypothesisthatthevalueofavariableinonepopulationisequaltothevalueofthatsamevariableinanotherpopulationIndependentsamplesarethoseinwhichmeasurementofthevariableofinterestinonesamplehasnoeffectonmeasurementofthevariableintheothersampleRelatedsamplesarethoseinwhichmeasurementofthevariableofinterestinonesamplemayinfluencemeasurementofthevariableinanothersample13-22Copyright?2021JohnWiley&Sons,Inc.DegreesofFreedomThenumberofdegreesoffreedom(d.f.)isthenumberofobservationsinastatisticalproblemthatarenotrestrictedorarefreetovaryThenumberofdegreesoffreedomisequaltothenumberofobservationsminusthenumberofassumptionsorconstraintsnecessarytocalculateastatistic13-23Copyright?2021JohnWiley&Sons,Inc.Chi-SquareTestThechi-square(χ2)testenablestheresearchanalysttodeterminewhetheranobservedpatternoffrequenciescorrespondsto,orfits,an“expected”patternExample:SupposethemarketingmanagerofaretailelectronicschainneedstotesttheeffectivenessofthreespecialdealsEachdealwillbeofferedforamonthThemanagerwantstomeasuretheeffectofeachdealonthenumberofcustomersvisitingateststoreduringthetimethedealisonSalesareApril11,700,May12,100,andJune11,780foratotalof35,58013-24Copyright?2021JohnWiley&Sons,Inc.Chi-SquareTestExample

13-25Copyright?2021JohnWiley&Sons,Inc.Chi-SquareTestExampleContinued

13-26Copyright?2021JohnWiley&Sons,Inc.Chi-SquareTestofTwoIndependentSamplesMarketingresearchersoftenneedtodeterminewhetherthereisanyassociationbetweentwoormorevariablesThechi-squaretestfortwoindependentsamplesistheappropriatetestinsuchsituationsThecalculationsarethesameasthechi-squaretestforasinglesampleonly:TheexpectedfrequenciesarecalculateddifferentlyThedegreesoffreedomaredifferent13-27Copyright?2021JohnWiley&Sons,Inc.HypothesesaboutOneMean(tTest)Forhypothesesaboutonemean,withsmallsamples(n<30),thettestwithn?1degreesoffreedomistheappropriatetestformakingstatisticalinferencesItcanalsobeusedforlargersamplesHowever,itapproachesandbecomesindistinguishablefromthenormaldistributionforsamplesof30ormoreobservationsAlthoughtheZtestisgenerallyusedforlargesamples,nearlyallstatisticalpackagesusethettestforallsamplesizes13-28Copyright?2021JohnWiley&Sons,Inc.tTestExample

13-29Copyright?2021JohnWiley&Sons,Inc.tTestExampleContinued

13-30Copyright?2021JohnWiley&Sons,Inc.HypothesesaboutTwoMeansExampleThemanagementofaconveniencestorechainisinterestedindifferencesbetweenthestorevisitratesofmenandwomenBelievingthatmenvisitconveniencestoresmoreoftenthanwomen,managementcollecteddataonconveniencestorevisitsfrom1,000randomlyselectedconsumersThetwomeansaremen11.49andwomen8.51Thetwosamplestandarddeviationsaremen8.18andwomen5.23Thesamplesizewas45menand71women13-31Copyright?2021JohnWiley&Sons,Inc.HypothesesaboutTwoMeansExampleContinued

13-32Copyright?2021JohnWiley&Sons,Inc.HypothesesaboutTwoMeansExampleContinued

13-33Copyright?2021JohnWiley&Sons,Inc.HypothesesaboutProportionsInmanysituations,researchersareconcernedwithphenomenathatareexpressedintermsofpercentagesAlsoknownasproportionsForexample,marketersmightbeinterestedintestingfortheproportionofrespondentswhopreferbrandAversusthosewhopreferbrandBAhypothesistestofproportionsisatesttodeterminewhetherthedifferencebetweenproportionsisgreaterthanwouldbeexpectedbecauseofsamplingerrorInaonesampletest,asingleproportionistestedagainstavalueWithindependentsamples,two(ormore)proportionsaretestedagainsteachother13-34Copyright?2021JohnWiley&Sons,Inc.ProportioninOneSampleExample

13-35Copyright?2021JohnWiley&Sons,Inc.ProportioninOneSampleExampleContinued

13-36Copyright?2021JohnWiley&Sons,Inc.TwoProportionsinIndependentSamplesExample

13-37Copyright?2021JohnWiley&Sons,Inc.TwoProportionsinIndependentSamplesExampleContinued

13-38Copyright?2021JohnWiley&Sons,Inc.TwoProportionsinIndependentSamplesExampleContinued

13-39Copyright?2021JohnWiley&Sons,Inc.AnalysisofVariance(ANOVA)Whenthegoalistotestthedifferencesamongthemeansoftwoormoreindependentsamples,analysisofvariance(ANOVA)isanappropriatestatisticaltoolANOVAismorecommonlyusedforhypothesistestsregardingthedifferencesamongthemeansofseveral(C)indepe