市场调查方法第十五章课件

2024/5/12市场调查方法第十五章LEARNINGOUTCOMESUnderstandwhatmultivariatestatisticalanalysisinvolvesandknowthetwotypesofmultivariateanalysisInterpretresultsfrommultipleregressionanalysis.Interpretresultsfrommultivariateanalysisofvariance(MANOVA)InterpretbasicexploratoryfactoranalysisresultsAfterstudyingthischapter,youshouldbeableto©2007Thomson/South-Western.Allrightsreserved.WhatIstheAppropriateTestofDifference?TestofDifferencesAninvestigationofahypothesisthattwo(ormore)groupsdifferwithrespecttomeasuresonavariable.Behavior,characteristics,beliefs,opinions,emotions,orattitudesBivariateTestsofDifferencesInvolveonlytwovariables:avariablethatactslikeadependentvariableandavariablethatactsasaclassificationvariable.Differencesinmeanscoresbetweengroupsorincomparinghowtwogroups’scoresaredistributedacrosspossibleresponsecategories.©2007Thomson/South-Western.Allrightsreserved.EXHIBIT15.1

ChoosingtheRightStatistic©2007Thomson/South-Western.Allrightsreserved.EXHIBIT15.1

ChoosingtheRightStatistic(cont’d)©2007Thomson/South-Western.Allrightsreserved.TypeofMeasurementDifferencesbetweentwoindependentgroupsDifferencesamongthreeormoreindependentgroupsOrdinalMann-WhitneyU-testWilcoxontestKruskal-WallistestCommonBivariateTestsNominalZ-test(twoproportions)Chi-squaretestChi-squaretestIntervalandratioIndependentgroups:t-testorZ-testOne-wayANOVA©2007Thomson/South-Western.Allrightsreserved.Cross-TabulationTables:Theχ2TestforGoodness-of-FitCross-Tabulation(Contingency)TableAjointfrequencydistributionofobservationsontwomorevariables.χ2DistributionProvidesameansfortestingthestatisticalsignificanceofacontingencytable.Involvescomparingobservedfrequencies(Oi)withexpectedfrequencies(Ei)ineachcellofthetable.Capturesthegoodness-(orcloseness-)of-fitoftheobserveddistributionwiththeexpecteddistribution.©2007Thomson/South-Western.Allrightsreserved.Example:PapaJohn’sRestaurantsUnivariateHypothesis:

PapaJohn’srestaurantsaremorelikelytobelocatedinastand-alonelocationorinashoppingcenter.BivariateHypothesis:Stand-alonelocationsaremorelikelytobeprofitablethanareshoppingcenterlocations.©2007Thomson/South-Western.Allrightsreserved.Chi-SquareTestχ²=chi-squarestatisticOi

=observedfrequencyintheithcellEi=expectedfrequencyontheithcellRi=totalobservedfrequencyintheithrowCj=totalobservedfrequencyinthejthcolumnn=samplesize©2007Thomson/South-Western.Allrightsreserved.DegreesofFreedom(d.f.)(R-1)(C-1)=(2-1)(2-1)=1d.f.=(R-1)(C-1)©2007Thomson/South-Western.Allrightsreserved.Thet-TestforComparingTwoMeansIndependentSamplest-TestAtestforhypothesesstatingthatthemeanscoresforsomeinterval-orratio-scaledvariablegroupedbasedonsomelessthanintervalclassificatoryvariable.©2007Thomson/South-Western.Allrightsreserved.Thet-TestforComparingTwoMeans(cont’d)Determiningwhenanindependentsamples

t-testisappropriate:Isthedependentvariableintervalorratio?Canthedependentvariablescoresbegroupedbaseduponsomecategoricalvariable?Doesthegroupingresultinscoresdrawnfromindependentsamples?Aretwogroupsinvolvedintheresearchquestion?©2007Thomson/South-Western.Allrightsreserved.Thet-TestforComparingTwoMeans(cont’d)PooledEstimateoftheStandardErrorAnestimateofthestandarderrorforat-testofindependentmeansthatassumesthevariancesofbothgroupsareequal.©2007Thomson/South-Western.Allrightsreserved.Thet-TestforComparingTwoMeans(cont’d)©2007Thomson/South-Western.Allrightsreserved.EXHIBIT15.2

IndependentSamplest-TestResults©2007Thomson/South-Western.Allrightsreserved.WhatIsANOVA?AnalysisofVariance(ANOVA)Ananalysisinvolvingtheinvestigationoftheeffectsofonetreatmentvariableonaninterval-scaleddependentvariableAhypothesis-testingtechniquetodeterminewhetherstatisticallysignificantdifferencesinmeansoccurbetweentwoormoregroups.Amethodofcomparingvariancestomakeinferencesaboutthemeans.ANOVAtestswhether“grouping”observationsexplainsvarianceinthedependentvariable.©2007Thomson/South-Western.Allrightsreserved.SimpleIllustrationofANOVAHowmuchcoffeerespondentsreportdrinkingeachdaybasedonwhichshifttheywork(GYstandsforGraveyardshift).Day 1Day 3Day 4Day 0Day 2GY 7GY 2GY 1GY 6Night 6Night 8Night 3Night 7Night 6©2007Thomson/South-Western.Allrightsreserved.EXHIBIT15.3

IllustrationofANOVALogic©2007Thomson/South-Western.Allrightsreserved.PartitioningVarianceinANOVATotalVariabilityGrandmeanThemeanofavariableoverallobservations.SSTThetotalobservedvariationacrossallgroupsandindividualobservationsSST=Totalof(observedvalue-grandmean)2©2007Thomson/South-Western.Allrightsreserved.PartitioningVarianceinANOVABetween-groupsVarianceThesumofdifferencesbetweenthegroupmeanandthegrandmeansummedoverallgroupsforagivensetofobservations.SSBSystematicvariationofscoresbetweengroupsduetomanipulationofanexperimentalvariableorgroupclassificationsofameasuredindependentvariableorbetween-groupvariance.SSB=Totalofngroup(GroupMean−GrandMean)2©2007Thomson/South-Western.Allrightsreserved.PartitioningVarianceinANOVAWithin-groupErrororVarianceThesumofthedifferencesbetweenobservedvaluesandthegroupmeanforagivensetofobservations;alsoknownastotalerrorvariance.SSEVariationofscoresduetorandomerrororwithin-groupvarianceduetoindividualdifferencesfromthegroupmean.Thisistheerrorofprediction.SSE=Totalof(ObservedMean−GroupMean)2©2007Thomson/South-Western.Allrightsreserved.TheF-TestF-TestIsusedtodeterminewhetherthereismorevariabilityinthescoresofonesamplethaninthescoresofanothersample.Variancecomponentsareusedtocomputef-ratiosSSE,SSB,SST©2007Thomson/South-Western.Allrightsreserved.EXHIBIT15.4

InterpretingANOVA©2007Thomson/South-Western.Allrightsreserved.CorrelationCoefficientAnalysisCorrelationcoefficientAstatisticalmeasureofthecovariation,orassociation,betweentwoat-leastintervalvariables.CovarianceExtenttowhichtwovariablesareassociatedsystematicallywitheachother.©2007Thomson/South-Western.Allrightsreserved.SimpleCorrelationCoefficientCorrelationcoefficient(r)Rangesfrom+1to-1Perfectpositivelinearrelationship=+1Perfectnegative(inverse)linearrelationship=-1Nocorrelation=0Correlationcoefficientfortwovariables(X,Y)©2007Thomson/South-Western.Allrightsreserved.Correlation,Covariance,andCausationWhentwovariablescovary,theydisplayconcomitantvariation.Thissystematiccovariationdoesnotinandofitselfestablishcausality.Rooster’scrowandtherisingofthesunRoosterdoesnotcausethesuntorise.©2007Thomson/South-Western.Allrightsreserved.CoefficientofDeterminationCoefficientofDetermination(R2)Ameasureobtainedbysquaringthecorrelationcoefficient;theproportionofthetotalvarianceofavariableaccountedforbyanothervalueofanothervariable.MeasuresthatpartofthetotalvarianceofYthatisaccountedforbyknowingthevalueofX.©2007Thomson/South-Western.Allrightsreserved.RegressionAnalysisSimple(Bivariate)LinearRegressionAmeasureoflinearassociationthatinvestigatesstraight-linerelationshipsbetweenacontinuousdependentvariableandanindependentvariablethatisusuallycontinuous,butcanbeacategoricaldummyvariable.TheRegressionEquation(Y=α+βX)Y=thecontinuousdependentvariableX=theindependentvariableα=theYintercept(regressionlineinterceptsYaxis)β=theslopeofthecoefficient(riseoverrun)©2007Thomson/South-Western.Allrightsreserved.TheRegressionEquationParameterEstimateChoicesβisindicativeofthestrengthanddirectionoftherelationshipbetweentheindependentanddependentvariable.α(Yintercept)isafixedpointthatisconsideredaconstant(howmuchYcanexistwithoutX)StandardizedRegressionCoefficient(β)Estimatedcoefficientofthestrengthofrelationshipbetweentheindependentanddependentvariables.Expressedonastandardizedscalewherehigherabsolutevaluesindicatestrongerrelationships(rangeisfrom-1to1).©2007Thomson/South-Western.Allrightsreserved.EXHIBIT15.5

TheAdvantageofStandardizedRegressionWeights©2007Thomson/South-Western.Allrightsreserved.TheRegressionEquation(cont’d)ParameterEstimateChoices(cont’d)Rawregressionestimates(b1)Rawregressionweightshavetheadvantageofretainingthescalemetric—whichisalsotheirkeydisadvantage.Ifthepurposeoftheregressionanalysisisforecasting,thenrawparameterestimatesmustbeused.Thisisanotherwayofsayingwhentheresearcherisinterestedonlyinprediction.Standardizedregressionestimates(β1)Standardizedregressionestimateshavetheadvantageofaconstantscale.Standardizedregressionestimatesshouldbeusedwhentheresearcheristestingexplanatoryhypotheses.©2007Thomson/South-Western.Allrightsreserved.MultipleRegressionAnalysisMultipleRegressionAnalysisAnanalysisofassociationinwhichtheeffectsoftwoormoreindependentvariablesonasingle,interval-scaleddependentvariableareinvestigatedsimultaneously.DummyvariableThewayadichotomous(twogroup)independentvariableisrepresentedinregressionanalysisbyassigninga0toonegroupanda1totheother.©2007Thomson/South-Western.Allrightsreserved.MultipleRegressionAnalysis(cont’d)ASimpleExampleAssumethatatoymanufacturerwishestoexplainstoresales(dependentvariable)usingasampleofstoresfromCanadaandEurope.Severalhypothesesareoffered:H1: Competitor’ssalesarerelatednegativelytosales.H2: Salesarehigherincommunitieswithasalesofficethan

whennosalesofficeispresent.H3: Grammarschoolenrollmentinacommunityisrelated

positivelytosales.©2007Thomson/South-Western.Allrightsreserved.MultipleRegressionAnalysis(cont’d)StatisticalResultsoftheMultipleRegressionRegressionEquation:Coefficientofmultipledetermination(R2):0.845F-value=14.6;p<.05©2007Thomson/South-Western.Allrightsreserved.MultipleRegressionAnalysis(cont’d)RegressionCoefficientsinMultipleRegressionPartialcorrelationThecorrelationbetweentwovariablesaftertakingintoaccountthefactthattheyarecorrelatedwithothervariablestoo.R2inMultipleRegressionThecoefficientofmultipledeterminationinmultipleregressionindicatesthepercentageofvariationinYexplainedbyallindependentvariables.©2007Thomson/South-Western.Allrightsreserved.MultipleRegressionAnalysis(cont’d)CoefficientsofPartialRegressionbnIndependentvariablescorrelatedwithoneanotherThepercentageofvarianceinthedependentvariablethatisexplainedbyasingleindependentvariable,holdingotherindependentvariablesconstantR2Thepercentageofvarianceinthedependentvariablethatisexplainedbythevariationintheindependentvariables.©2007Thomson/South-Western.Allrightsreserved.MultipleRegressionAnalysis(cont’d)StatisticalSignificanceinMultipleRegressionF-testTestsstatisticalsignificancebycomparingthevariationexplainedbytheregressionequationtothe