市场调查方法(英文版)第十五章.ppt

2007Thomson South Western Allrightsreserved Chapter15DifferencesBetweenGroupsandRelationshipsAmongVariables 2007Thomson South Western Allrightsreserved 15 2 LEARNINGOUTCOMES UnderstandwhatmultivariatestatisticalanalysisinvolvesandknowthetwotypesofmultivariateanalysisInterpretresultsfrommultipleregressionanalysis Interpretresultsfrommultivariateanalysisofvariance MANOVA Interpretbasicexploratoryfactoranalysisresults Afterstudyingthischapter youshouldbeableto 2007Thomson South Western Allrightsreserved 15 3 WhatIstheAppropriateTestofDifference TestofDifferencesAninvestigationofahypothesisthattwo ormore groupsdifferwithrespecttomeasuresonavariable Behavior characteristics beliefs opinions emotions orattitudesBivariateTestsofDifferencesInvolveonlytwovariables avariablethatactslikeadependentvariableandavariablethatactsasaclassificationvariable Differencesinmeanscoresbetweengroupsorincomparinghowtwogroups scoresaredistributedacrosspossibleresponsecategories 2007Thomson South Western Allrightsreserved 15 4 EXHIBIT15 1ChoosingtheRightStatistic 2007Thomson South Western Allrightsreserved 15 5 EXHIBIT15 1ChoosingtheRightStatistic cont d 2007Thomson South Western Allrightsreserved 15 6 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 15 7 Cross TabulationTables The 2TestforGoodness of Fit Cross Tabulation Contingency TableAjointfrequencydistributionofobservationsontwomorevariables 2DistributionProvidesameansfortestingthestatisticalsignificanceofacontingencytable Involvescomparingobservedfrequencies Oi withexpectedfrequencies Ei ineachcellofthetable Capturesthegoodness orcloseness of fitoftheobserveddistributionwiththeexpecteddistribution 2007Thomson South Western Allrightsreserved 15 8 Example PapaJohn sRestaurants UnivariateHypothesis PapaJohn srestaurantsaremorelikelytobelocatedinastand alonelocationorinashoppingcenter BivariateHypothesis Stand alonelocationsaremorelikelytobeprofitablethanareshoppingcenterlocations 2007Thomson South Western Allrightsreserved 15 9 Chi SquareTest chi squarestatisticOi observedfrequencyintheithcellEi expectedfrequencyontheithcell Ri totalobservedfrequencyintheithrowCj totalobservedfrequencyinthejthcolumnn samplesize 2007Thomson South Western Allrightsreserved 15 10 DegreesofFreedom d f R 1 C 1 2 1 2 1 1 d f R 1 C 1 2007Thomson South Western Allrightsreserved 15 11 Thet TestforComparingTwoMeans IndependentSamplest TestAtestforhypothesesstatingthatthemeanscoresforsomeinterval orratio scaledvariablegroupedbasedonsomelessthanintervalclassificatoryvariable 2007Thomson South Western Allrightsreserved 15 12 Thet TestforComparingTwoMeans cont d Determiningwhenanindependentsamplest testisappropriate Isthedependentvariableintervalorratio Canthedependentvariablescoresbegroupedbaseduponsomecategoricalvariable Doesthegroupingresultinscoresdrawnfromindependentsamples Aretwogroupsinvolvedintheresearchquestion 2007Thomson South Western Allrightsreserved 15 13 Thet TestforComparingTwoMeans cont d PooledEstimateoftheStandardErrorAnestimateofthestandarderrorforat testofindependentmeansthatassumesthevariancesofbothgroupsareequal 2007Thomson South Western Allrightsreserved 15 14 Thet TestforComparingTwoMeans cont d 2007Thomson South Western Allrightsreserved 15 15 EXHIBIT15 2IndependentSamplest TestResults 2007Thomson South Western Allrightsreserved 15 16 WhatIsANOVA AnalysisofVariance ANOVA Ananalysisinvolvingtheinvestigationoftheeffectsofonetreatmentvariableonaninterval scaleddependentvariableAhypothesis testingtechniquetodeterminewhetherstatisticallysignificantdifferencesinmeansoccurbetweentwoormoregroups Amethodofcomparingvariancestomakeinferencesaboutthemeans ANOVAtestswhether grouping observationsexplainsvarianceinthedependentvariable 2007Thomson South Western Allrightsreserved 15 17 SimpleIllustrationofANOVA Howmuchcoffeerespondentsreportdrinkingeachdaybasedonwhichshifttheywork GYstandsforGraveyardshift Day1Day3Day4Day0Day2GY7GY2GY1GY6Night6Night8Night3Night7Night6 2007Thomson South Western Allrightsreserved 15 18 EXHIBIT15 3IllustrationofANOVALogic 2007Thomson South Western Allrightsreserved 15 19 PartitioningVarianceinANOVA TotalVariabilityGrandmeanThemeanofavariableoverallobservations SSTThetotalobservedvariationacrossallgroupsandindividualobservationsSST Totalof observedvalue grandmean 2 2007Thomson South Western Allrightsreserved 15 20 PartitioningVarianceinANOVA Between groupsVarianceThesumofdifferencesbetweenthegroupmeanandthegrandmeansummedoverallgroupsforagivensetofobservations SSBSystematicvariationofscoresbetweengroupsduetomanipulationofanexperimentalvariableorgroupclassificationsofameasuredindependentvariableorbetween groupvariance SSB Totalofngroup GroupMean GrandMean 2 2007Thomson South Western Allrightsreserved 15 21 PartitioningVarianceinANOVA Within groupErrororVarianceThesumofthedifferencesbetweenobservedvaluesandthegroupmeanforagivensetofobservations alsoknownastotalerrorvariance SSEVariationofscoresduetorandomerrororwithin groupvarianceduetoindividualdifferencesfromthegroupmean Thisistheerrorofprediction SSE Totalof ObservedMean GroupMean 2 2007Thomson South Western Allrightsreserved 15 22 TheF Test F TestIsusedtodeterminewhetherthereismorevariabilityinthescoresofonesamplethaninthescoresofanothersample Variancecomponentsareusedtocomputef ratiosSSE SSB SST 2007Thomson South Western Allrightsreserved 15 23 EXHIBIT15 4InterpretingANOVA 2007Thomson South Western Allrightsreserved 15 24 CorrelationCoefficientAnalysis CorrelationcoefficientAstatisticalmeasureofthecovariation orassociation betweentwoat leastintervalvariables CovarianceExtenttowhichtwovariablesareassociatedsystematicallywitheachother 2007Thomson South Western Allrightsreserved 15 25 SimpleCorrelationCoefficient Correlationcoefficient r Rangesfrom 1to 1Perfectpositivelinearrelationship 1Perfectnegative inverse linearrelationship 1Nocorrelation 0Correlationcoefficientfortwovariables X Y 2007Thomson South Western Allrightsreserved 15 26 Correlation Covariance andCausation Whentwovariablescovary theydisplayconcomitantvariation Thissystematiccovariationdoesnotinandofitselfestablishcausality Rooster scrowandtherisingofthesunRoosterdoesnotcausethesuntorise 2007Thomson South Western Allrightsreserved 15 27 CoefficientofDetermination CoefficientofDetermination R2 Ameasureobtainedbysquaringthecorrelationcoefficient theproportionofthetotalvarianceofavariableaccountedforbyanothervalueofanothervariable MeasuresthatpartofthetotalvarianceofYthatisaccountedforbyknowingthevalueofX 2007Thomson South Western Allrightsreserved 15 28 RegressionAnalysis Simple Bivariate LinearRegressionAmeasureoflinearassociationthatinvestigatesstraight linerelationshipsbetweenacontinuousdependentvariableandanindependentvariablethatisusuallycontinuous butcanbeacategoricaldummyvariable TheRegressionEquation Y X Y thecontinuousdependentvariableX theindependentvariable theYintercept regressionlineinterceptsYaxis theslopeofthecoefficient riseoverrun 2007Thomson South Western Allrightsreserved 15 29 TheRegressionEquation ParameterEstimateChoices isindicativeofthestrengthanddirectionoftherelationshipbetweentheindependentanddependentvariable Yintercept isafixedpointthatisconsideredaconstant howmuchYcanexistwithoutX StandardizedRegressionCoefficient Estimatedcoefficientofthestrengthofrelationshipbetweentheindependentanddependentvariables Expressedonastandardizedscalewherehigherabsolutevaluesindicatestrongerrelationships rangeisfrom 1to1 2007Thomson South Western Allrightsreserved 15 30 EXHIBIT15 5TheAdvantageofStandardizedRegressionWeights 2007Thomson South Western Allrightsreserved 15 31 TheRegressionEquation cont d ParameterEstimateChoices cont d Rawregressionestimates b1 Rawregressionweightshavetheadvantageofretainingthescalemetric whichisalsotheirkeydisadvantage Ifthepurposeoftheregressionanalysisisforecasting thenrawparameterestimatesmustbeused Thisisanotherwayofsayingwhentheresearcherisinterestedonlyinprediction Standardizedregressionestimates 1 Standardizedregressionestimateshavetheadvantageofaconstantscale Standardizedregressionestimatesshouldbeusedwhentheresearcheristestingexplanatoryhypotheses 2007Thomson South Western Allrightsreserved 15 32 MultipleRegressionAnalysis MultipleRegressionAnalysisAnanalysisofassociationinwhichtheeffectsoftwoormoreindependentvariablesonasingle interval scaleddependentvariableareinvestigatedsimultaneously DummyvariableThewayadichotomous twogroup independentvariableisrepresentedinregressionanalysisbyassigninga0toonegroupanda1totheother 2007Thomson South Western Allrightsreserved 15 33 MultipleRegressionAnalysis cont d ASimpleExampleAssumethatatoymanufacturerwishestoexplainstoresales dependentvariable usingasampleofstoresfromCanadaandEurope Severalhypothesesareoffered H1 Competitor ssalesarerelatednegativelytosales H2 Salesarehigherincommunitieswithasalesofficethanwhennosalesofficeispresent H3 Grammarschoolenrollmentinacommunityisrelatedpositivelytosales 2007Thomson South Western Allrightsreserved 15 34 MultipleRegressionAnalysis cont d StatisticalResultsoftheMultipleRegressionRegressionEquation Coefficientofmultipledetermination R2 0 845F value 14 6 p 05 2007Thomson South Western Allrightsreserved 15 35 MultipleRegressionAnalysis cont d RegressionCoefficientsinMultipleRegressionPartialcorrelationThecorrelationbetweentwovariablesaftertakingintoaccountthefactthattheyarecorrelatedwithothervariablestoo R2inMultipleRegressionThecoefficientofmultipledeterminationinmultipleregressionindicatesthepercentageofvariationinYexplainedbyallindependentvariables 2007Thomson South Western Allrightsreserved 15 36 MultipleRegressionAnalysis cont d CoefficientsofPartialRegressionbnIndependentvariablescorrelatedwithoneanotherThepercentageofvarianceinthedependentvariablethatisexplainedbyasingleindependentvariable holdingotherindependentvariablesconstantR2Thepercentageofvarianceinthedependentvariablethatisexplainedbythevariationintheindependentvariables 2007Thomson South Western Allrightsreserved 15 37 MultipleRegressionAnalysis cont d StatisticalSignificanceinMultipleRegressionF testTestsstatisticalsignificancebycomparingthevariationexplainedbytheregressionequationtotheresidualerrorvariation Allowsfortestingoftherelativemagnitudesofthesumofsquaresduetotheregression SSR andtheerrorsumofsquares SSE 2007Thomson South Western Allrightsreserved 15 38 MultipleRegressionAnalysis cont d DegreesofFreedom d f k numberofindependentvariablesn numberofobservationsorrespondentsCalculatingDegreesofFreedom d f d f forthenumerator kd f fo