市场调查方法(英文版)第十五章.pptx
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市场调查方法(英文版)第十五章.pptx
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Chapter15DifferencesBetweenGroupsandRelationshipsAmongVariables,2007Thomson/South-Western.Allrightsreserved.,LEARNINGOUTCOMES,UnderstandwhatmultivariatestatisticalanalysisinvolvesandknowthetwotypesofmultivariateanalysisInterpretresultsfrommultipleregressionanalysis.Interpretresultsfrommultivariateanalysisofvariance(MANOVA)Interpretbasicexploratoryfactoranalysisresults,Afterstudyingthischapter,youshouldbeableto,2,2007Thomson/South-Western.Allrightsreserved.,WhatIstheAppropriateTestofDifference?
TestofDifferencesAninvestigationofahypothesisthattwo(ormore)groupsdifferwithrespecttomeasuresonavariable.Behavior,characteristics,beliefs,opinions,emotions,orattitudesBivariateTestsofDifferencesInvolveonlytwovariables:
avariablethatactslikeadependentvariableandavariablethatactsasaclassificationvariable.Differencesinmeanscoresbetweengroupsorincomparinghowtwogroupsscoresaredistributedacrosspossibleresponsecategories.,3,2007Thomson/South-Western.Allrightsreserved.,EXHIBIT15.1ChoosingtheRightStatistic,4,2007Thomson/South-Western.Allrightsreserved.,EXHIBIT15.1ChoosingtheRightStatistic(contd),5,2007Thomson/South-Western.Allrightsreserved.,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,6,2007Thomson/South-Western.Allrightsreserved.,Cross-TabulationTables:
The2TestforGoodness-of-Fit,Cross-Tabulation(Contingency)TableAjointfrequencydistributionofobservationsontwomorevariables.2DistributionProvidesameansfortestingthestatisticalsignificanceofacontingencytable.Involvescomparingobservedfrequencies(Oi)withexpectedfrequencies(Ei)ineachcellofthetable.Capturesthegoodness-(orcloseness-)of-fitoftheobserveddistributionwiththeexpecteddistribution.,7,2007Thomson/South-Western.Allrightsreserved.,Example:
PapaJohnsRestaurants,UnivariateHypothesis:
PapaJohnsrestaurantsaremorelikelytobelocatedinastand-alonelocationorinashoppingcenter.,BivariateHypothesis:
Stand-alonelocationsaremorelikelytobeprofitablethanareshoppingcenterlocations.,8,2007Thomson/South-Western.Allrightsreserved.,Chi-SquareTest,=chi-squarestatisticOi=observedfrequencyintheithcellEi=expectedfrequencyontheithcell,Ri=totalobservedfrequencyintheithrowCj=totalobservedfrequencyinthejthcolumnn=samplesize,9,2007Thomson/South-Western.Allrightsreserved.,DegreesofFreedom(d.f.),(R-1)(C-1)=(2-1)(2-1)=1,d.f.=(R-1)(C-1),10,2007Thomson/South-Western.Allrightsreserved.,Thet-TestforComparingTwoMeans,IndependentSamplest-TestAtestforhypothesesstatingthatthemeanscoresforsomeinterval-orratio-scaledvariablegroupedbasedonsomelessthanintervalclassificatoryvariable.,11,2007Thomson/South-Western.Allrightsreserved.,Thet-TestforComparingTwoMeans(contd),Determiningwhenanindependentsamplest-testisappropriate:
Isthedependentvariableintervalorratio?
Canthedependentvariablescoresbegroupedbaseduponsomecategoricalvariable?
Doesthegroupingresultinscoresdrawnfromindependentsamples?
Aretwogroupsinvolvedintheresearchquestion?
12,2007Thomson/South-Western.Allrightsreserved.,Thet-TestforComparingTwoMeans(contd),PooledEstimateoftheStandardErrorAnestimateofthestandarderrorforat-testofindependentmeansthatassumesthevariancesofbothgroupsareequal.,13,2007Thomson/South-Western.Allrightsreserved.,Thet-TestforComparingTwoMeans(contd),14,2007Thomson/South-Western.Allrightsreserved.,EXHIBIT15.2IndependentSamplest-TestResults,15,2007Thomson/South-Western.Allrightsreserved.,WhatIsANOVA?
AnalysisofVariance(ANOVA)Ananalysisinvolvingtheinvestigationoftheeffectsofonetreatmentvariableonaninterval-scaleddependentvariableAhypothesis-testingtechniquetodeterminewhetherstatisticallysignificantdifferencesinmeansoccurbetweentwoormoregroups.Amethodofcomparingvariancestomakeinferencesaboutthemeans.ANOVAtestswhether“grouping”observationsexplainsvarianceinthedependentvariable.,16,2007Thomson/South-Western.Allrightsreserved.,SimpleIllustrationofANOVA,Howmuchcoffeerespondentsreportdrinkingeachdaybasedonwhichshifttheywork(GYstandsforGraveyardshift).,Day1Day3Day4Day0Day2GY7GY2GY1GY6Night6Night8Night3Night7Night6,17,2007Thomson/South-Western.Allrightsreserved.,EXHIBIT15.3IllustrationofANOVALogic,18,2007Thomson/South-Western.Allrightsreserved.,PartitioningVarianceinANOVA,TotalVariabilityGrandmeanThemeanofavariableoverallobservations.SSTThetotalobservedvariationacrossallgroupsandindividualobservationsSST=Totalof(observedvalue-grandmean)2,19,2007Thomson/South-Western.Allrightsreserved.,PartitioningVarianceinANOVA,Between-groupsVarianceThesumofdifferencesbetweenthegroupmeanandthegrandmeansummedoverallgroupsforagivensetofobservations.SSBSystematicvariationofscoresbetweengroupsduetomanipulationofanexperimentalvariableorgroupclassificationsofameasuredindependentvariableorbetween-groupvariance.SSB=Totalofngroup(GroupMeanGrandMean)2,20,2007Thomson/South-Western.Allrightsreserved.,PartitioningVarianceinANOVA,Within-groupErrororVarianceThesumofthedifferencesbetweenobservedvaluesandthegroupmeanforagivensetofobservations;alsoknownastotalerrorvariance.SSEVariationofscoresduetorandomerrororwithin-groupvarianceduetoindividualdifferencesfromthegroupmean.Thisistheerrorofprediction.SSE=Totalof(ObservedMeanGroupMean)2,21,2007Thomson/South-Western.Allrightsreserved.,TheF-Test,F-TestIsusedtodeterminewhetherthereismorevariabilityinthescoresofonesamplethaninthescoresofanothersample.Variancecomponentsareusedtocomputef-ratiosSSE,SSB,SST,22,2007Thomson/South-Western.Allrightsreserved.,EXHIBIT15.4InterpretingANOVA,23,2007Thomson/South-Western.Allrightsreserved.,CorrelationCoefficientAnalysis,CorrelationcoefficientAstatisticalmeasureofthecovariation,orassociation,betweentwoat-leastintervalvariables.CovarianceExtenttowhichtwovariablesareassociatedsystematicallywitheachother.,24,2007Thomson/South-Western.Allrightsreserved.,SimpleCorrelationCoefficient,Correlationcoefficient(r)Rangesfrom+1to-1Perfectpositivelinearrelationship=+1Perfectnegative(inverse)linearrelationship=-1Nocorrelation=0Correlationcoefficientfortwovariables(X,Y),25,2007Thomson/South-Western.Allrightsreserved.,Correlation,Covariance,andCausation,Whentwovariablescovary,theydisplayconcomitantvariation.Thissystematiccovariationdoesnotinandofitselfestablishcausality.RoosterscrowandtherisingofthesunRoosterdoesnotcausethesuntorise.,26,2007Thomson/South-Western.Allrightsreserved.,CoefficientofDetermination,CoefficientofDetermination(R2)Ameasureobtainedbysquaringthecorrelationcoefficient;theproportionofthetotalvarianceofavariableaccountedforbyanothervalueofanothervariable.MeasuresthatpartofthetotalvarianceofYthatisaccountedforbyknowingthevalueofX.,27,2007Thomson/South-Western.Allrightsreserved.,RegressionAnalysis,Simple(Bivariate)LinearRegressionAmeasureoflinearassociationthatinvestigatesstraight-linerelationshipsbetweenacontinuousdependentvariableandanindependentvariablethatisusuallycontinuous,butcanbeacategoricaldummyvariable.TheRegressionEquation(Y=+X)Y=thecontinuousdependentvariableX=theindependentvariable=theYintercept(regressionlineinterceptsYaxis)=theslopeofthecoefficient(riseoverrun),28,2007Thomson/South-Western.Allrightsreserved.,TheRegressionEquation,ParameterEstimateChoicesisindicativeofthestrengthanddirectionoftherelationshipbetweentheindependentanddependentvariable.(Yintercept)isafixedpointthatisconsideredaconstant(howmuchYcanexistwithoutX)StandardizedRegressionCoefficient()Estimatedcoefficientofthestrengthofrelationshipbetweentheindependentanddependentvariables.Expressedonastandardizedscalewherehigherabsolutevaluesindicatestrongerrelationships(rangeisfrom-1to1).,29,2007Thomson/South-Western.Allrightsreserved.,EXHIBIT15.5TheAdvantageofStandardizedRegressionWeights,30,2007Thomson/South-Western.Allrightsreserved.,TheRegressionEquation(contd),ParameterEstimateChoices(contd)Rawregressionestimates(b1)Rawregressionweightshavetheadvantageofretainingthescalemetricwhichisalsotheirkeydisadvantage.Ifthepurposeoftheregressionanalysisisforecasting,thenrawparameterestimatesmustbeused.Thisisanotherwayofsayingwhentheresearcherisinterestedonlyinprediction.Standardizedregressionestimates
(1)Standardizedregressionestimateshavetheadvantageofaconstantscale.Standardizedregressionestimatesshouldbeusedwhentheresearcheristestingexplanatoryhypotheses.,31,2007Thomson/South-Western.Allrightsreserved.,MultipleRegressionAnalysis,MultipleRegressionAnalysisAnanalysisofassociationinwhichtheeffectsoftwoormoreindependentvariablesonasingle,interval-scaleddependentvariableareinvestigatedsimultaneously.,DummyvariableThewayadichotomous(twogroup)independentvariableisrepresentedinregressionanalysisbyassigninga0toonegroupanda1totheother.,32,2007Thomson/South-Western.Allrightsreserved.,MultipleRegressionAnalysis(contd),ASimpleExampleAssumethatatoymanufacturerwishestoexplainstoresales(dependentvariable)usingasampleofstoresfromCanadaandEurope.Severalhy
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