市场调查方法(英文版)第十五章

2007Thomson/South-Western.Allrightsreserved.,Chapter15DifferencesBetweenGroupsandRelationshipsAmongVariables,2007Thomson/South-Western.Allrightsreserved.,152,LEARNINGOUTCOMES,UnderstandwhatmultivariatestatisticalanalysisinvolvesandknowthetwotypesofmultivariateanalysisInterpretresultsfrommultipleregressionanalysis.Interpretresultsfrommultivariateanalysisofvariance(MANOVA)Interpretbasicexploratoryfactoranalysisresults,Afterstudyingthischapter,youshouldbeableto,2007Thomson/South-Western.Allrightsreserved.,153,WhatIstheAppropriateTestofDifference?,TestofDifferencesAninvestigationofahypothesisthattwo(ormore)groupsdifferwithrespecttomeasuresonavariable.Behavior,characteristics,beliefs,opinions,emotions,orattitudesBivariateTestsofDifferencesInvolveonlytwovariables:avariablethatactslikeadependentvariableandavariablethatactsasaclassificationvariable.Differencesinmeanscoresbetweengroupsorincomparinghowtwogroupsscoresaredistributedacrosspossibleresponsecategories.,2007Thomson/South-Western.Allrightsreserved.,154,EXHIBIT15.1ChoosingtheRightStatistic,2007Thomson/South-Western.Allrightsreserved.,155,EXHIBIT15.1ChoosingtheRightStatistic(contd),2007Thomson/South-Western.Allrightsreserved.,156,TypeofMeasurement,Differencesbetweentwoindependentgroups,Differencesamongthreeormoreindependentgroups,Ordinal,Mann-WhitneyU-testWilcoxontest,Kruskal-Wallistest,CommonBivariateTests,Nominal,Z-test(twoproportions)Chi-squaretest,Chi-squaretest,Intervalandratio,Independentgroups:t-testorZ-test,One-wayANOVA,2007Thomson/South-Western.Allrightsreserved.,157,Cross-TabulationTables:The2TestforGoodness-of-Fit,Cross-Tabulation(Contingency)TableAjointfrequencydistributionofobservationsontwomorevariables.2DistributionProvidesameansfortestingthestatisticalsignificanceofacontingencytable.Involvescomparingobservedfrequencies(Oi)withexpectedfrequencies(Ei)ineachcellofthetable.Capturesthegoodness-(orcloseness-)of-fitoftheobserveddistributionwiththeexpecteddistribution.,2007Thomson/South-Western.Allrightsreserved.,158,Example:PapaJohnsRestaurants,UnivariateHypothesis:PapaJohnsrestaurantsaremorelikelytobelocatedinastand-alonelocationorinashoppingcenter.,BivariateHypothesis:Stand-alonelocationsaremorelikelytobeprofitablethanareshoppingcenterlocations.,2007Thomson/South-Western.Allrightsreserved.,159,Chi-SquareTest,=chi-squarestatisticOi=observedfrequencyintheithcellEi=expectedfrequencyontheithcell,Ri=totalobservedfrequencyintheithrowCj=totalobservedfrequencyinthejthcolumnn=samplesize,2007Thomson/South-Western.Allrightsreserved.,1510,DegreesofFreedom(d.f.),(R-1)(C-1)=(2-1)(2-1)=1,d.f.=(R-1)(C-1),2007Thomson/South-Western.Allrightsreserved.,1511,Thet-TestforComparingTwoMeans,IndependentSamplest-TestAtestforhypothesesstatingthatthemeanscoresforsomeinterval-orratio-scaledvariablegroupedbasedonsomelessthanintervalclassificatoryvariable.,2007Thomson/South-Western.Allrightsreserved.,1512,Thet-TestforComparingTwoMeans(contd),Determiningwhenanindependentsamplest-testisappropriate:Isthedependentvariableintervalorratio?Canthedependentvariablescoresbegroupedbaseduponsomecategoricalvariable?Doesthegroupingresultinscoresdrawnfromindependentsamples?Aretwogroupsinvolvedintheresearchquestion?,2007Thomson/South-Western.Allrightsreserved.,1513,Thet-TestforComparingTwoMeans(contd),PooledEstimateoftheStandardErrorAnestimateofthestandarderrorforat-testofindependentmeansthatassumesthevariancesofbothgroupsareequal.,2007Thomson/South-Western.Allrightsreserved.,1514,Thet-TestforComparingTwoMeans(contd),2007Thomson/South-Western.Allrightsreserved.,1515,EXHIBIT15.2IndependentSamplest-TestResults,2007Thomson/South-Western.Allrightsreserved.,1516,WhatIsANOVA?,AnalysisofVariance(ANOVA)Ananalysisinvolvingtheinvestigationoftheeffectsofonetreatmentvariableonaninterval-scaleddependentvariableAhypothesis-testingtechniquetodeterminewhetherstatisticallysignificantdifferencesinmeansoccurbetweentwoormoregroups.Amethodofcomparingvariancestomakeinferencesaboutthemeans.ANOVAtestswhether“grouping”observationsexplainsvarianceinthedependentvariable.,2007Thomson/South-Western.Allrightsreserved.,1517,SimpleIllustrationofANOVA,Howmuchcoffeerespondentsreportdrinkingeachdaybasedonwhichshifttheywork(GYstandsforGraveyardshift).,Day1Day3Day4Day0Day2GY7GY2GY1GY6Night6Night8Night3Night7Night6,2007Thomson/South-Western.Allrightsreserved.,1518,EXHIBIT15.3IllustrationofANOVALogic,2007Thomson/South-Western.Allrightsreserved.,1519,PartitioningVarianceinANOVA,TotalVariabilityGrandmeanThemeanofavariableoverallobservations.SSTThetotalobservedvariationacrossallgroupsandindividualobservationsSST=Totalof(observedvalue-grandmean)2,2007Thomson/South-Western.Allrightsreserved.,1520,PartitioningVarianceinANOVA,Between-groupsVarianceThesumofdifferencesbetweenthegroupmeanandthegrandmeansummedoverallgroupsforagivensetofobservations.SSBSystematicvariationofscoresbetweengroupsduetomanipulationofanexperimentalvariableorgroupclassificationsofameasuredindependentvariableorbetween-groupvariance.SSB=Totalofngroup(GroupMeanGrandMean)2,2007Thomson/South-Western.Allrightsreserved.,1521,PartitioningVarianceinANOVA,Within-groupErrororVarianceThesumofthedifferencesbetweenobservedvaluesandthegroupmeanforagivensetofobservations;alsoknownastotalerrorvariance.SSEVariationofscoresduetorandomerrororwithin-groupvarianceduetoindividualdifferencesfromthegroupmean.Thisistheerrorofprediction.SSE=Totalof(ObservedMeanGroupMean)2,2007Thomson/South-Western.Allrightsreserved.,1522,TheF-Test,F-TestIsusedtodeterminewhetherthereismorevariabilityinthescoresofonesamplethaninthescoresofanothersample.Variancecomponentsareusedtocomputef-ratiosSSE,SSB,SST,2007Thomson/South-Western.Allrightsreserved.,1523,EXHIBIT15.4InterpretingANOVA,2007Thomson/South-Western.Allrightsreserved.,1524,CorrelationCoefficientAnalysis,CorrelationcoefficientAstatisticalmeasureofthecovariation,orassociation,betweentwoat-leastintervalvariables.CovarianceExtenttowhichtwovariablesareassociatedsystematicallywitheachother.,2007Thomson/South-Western.Allrightsreserved.,1525,SimpleCorrelationCoefficient,Correlationcoefficient(r)Rangesfrom+1to-1Perfectpositivelinearrelationship=+1Perfectnegative(inverse)linearrelationship=-1Nocorrelation=0Correlationcoefficientfortwovariables(X,Y),2007Thomson/South-Western.Allrightsreserved.,1526,Correlation,Covariance,andCausation,Whentwovariablescovary,theydisplayconcomitantvariation.Thissystematiccovariationdoesnotinandofitselfestablishcausality.RoosterscrowandtherisingofthesunRoosterdoesnotcausethesuntorise.,2007Thomson/South-Western.Allrightsreserved.,1527,CoefficientofDetermination,CoefficientofDetermination(R2)Ameasureobtainedbysquaringthecorrelationcoefficient;theproportionofthetotalvarianceofavariableaccountedforbyanothervalueofanothervariable.MeasuresthatpartofthetotalvarianceofYthatisaccountedforbyknowingthevalueofX.,2007Thomson/South-Western.Allrightsreserved.,1528,RegressionAnalysis,Simple(Bivariate)LinearRegressionAmeasureoflinearassociationthatinvestigatesstraight-linerelationshipsbetweenacontinuousdependentvariableandanindependentvariablethatisusuallycontinuous,butcanbeacategoricaldummyvariable.TheRegressionEquation(Y=+X)Y=thecontinuousdependentvariableX=theindependentvariable=theYintercept(regressionlineinterceptsYaxis)=theslopeofthecoefficient(riseoverrun),2007Thomson/South-Western.Allrightsreserved.,1529,TheRegressionEquation,ParameterEstimateChoicesisindicativeofthestrengthanddirectionoftherelationshipbetweentheindependentanddependentvariable.(Yintercept)isafixedpointthatisconsideredaconstant(howmuchYcanexistwithoutX)StandardizedRegressionCoefficient()Estimatedcoefficientofthestrengthofrelationshipbetweentheindependentanddependentvariables.Expressedonastandardizedscalewherehigherabsolutevaluesindicatestrongerrelationships(rangeisfrom-1to1).,2007Thomson/South-Western.Allrightsreserved.,1530,EXHIBIT15.5TheAdvantageofStandardizedRegressionWeights,2007Thomson/South-Western.Allrightsreserved.,1531,TheRegressionEquation(contd),ParameterEstimateChoices(contd)Rawregressionestimates(b1)Rawregressionweightshavetheadvantageofretainingthescalemetricwhichisalsotheirkeydisadvantage.Ifthepurposeoftheregressionanalysisisforecasting,thenrawparameterestimatesmustbeused.Thisisanotherwayofsayingwhentheresearcherisinterestedonlyinprediction.Standardizedregressionestimates(1)Standardizedregressionestimateshavetheadvantageofaconstantscale.Standardizedregressionestimatesshouldbeusedwhentheresearcheristestingexplanatoryhypotheses.,2007Thomson/South-Western.Allrightsreserved.,1532,MultipleRegressionAnalysis,MultipleRegressionAnalysisAnanalysisofassociationinwhichtheeffectsoftwoormoreindependentvariablesonasingle,interval-scaleddependentvariableareinvestigatedsimultaneously.,DummyvariableThewayadichotomous(twogroup)independentvariableisrepresentedinregressionanalysisbyassigninga0toonegroupanda1totheother.,2007Thomson/South-Western.Allrightsreserved.,1533,MultipleRegressionAnalysis(contd),ASimpleExampleAssumethatatoymanufacturerwishestoexplainstoresales(dependentvariable)usingasampleofstoresfromCanadaandEurope.Severalhypothesesareoffered:H1:Competitorssalesarerelatednegativelytosales.H2:Salesarehigherincommunitieswithasalesofficethanwhennosalesofficeispresent.H3:Grammarschoolenrollmentinacommunityisrelatedpositivelytosales.,2007Thomson/South-Western.Allrightsreserved.,1534,MultipleRegressionAnalysis(contd),StatisticalResultsoftheMultipleRegressionRegressionEquation:,Coefficientofmultipledetermination(R2):0.845F-value=14.6;p.05,2007Thomson/South-Western.Allrightsreserved.,1535,MultipleRegressionAnalysis(contd),RegressionCoefficientsinMultipleRegressionPartialcorrelationThecorrelationbetweentwovariablesaftertakingintoaccountthefactthattheyarecorrelatedwithothervariablestoo.R2inMultipleRegressionThecoefficientofmultipledeterminationinmultipleregressionindicatesthepercentageofvariationinYexplainedbyallindependentvariables.,2007Thomson/South-Western.Allrightsreserved.,1536,MultipleRegressionAnalysis(contd),CoefficientsofPartialRegressionbnIndependentvariablescorrelatedwithoneanotherThepercentageofvarianceinthedependentvariablethatisexplainedbyasingleindependentvariable,holdingotherindependentvariablesconstantR2Thepercentageofvarianceinthedependentvariablethatisexplainedbythevariationintheindependentvariables.,2007Thomson/South-Western.Allrightsreserved.,1537,MultipleRegressionAnalysis(contd),StatisticalSignificanceinMultipleRegressionF-testTestsstatisticalsignificancebycomparingthevariationexplainedbytheregressionequationtotheresidualerrorvariation.Allowsfortestingoftherelativemagnitudesofthesumofsquaresduetotheregression(SSR)andtheerrorsumofsquares(SSE).,2007Thomson/South-Western.Allrightsreserved.,1538,MultipleRegressionAnalysis(contd),DegreesofFreedom(d.f.)k=numberofindependentvariablesn=numberofobservationsorrespondentsCalculatingDegreesofFreedom(d.f.)d.f.forthenumerator=kd.f.f