explainingη2单因素方差分析.

ByHuiBianOfficeforFacultyExcellence1One-wayANOVAwithSPSSTwo-wayFactorialANOVAwithSPSSHowtointerpretSPSSoutputsHowtoreportresults2Weuse2009YouthRiskBehaviorSurveillanceSystem(YRBSS,CDC)asanexample.YRBSSmonitorspriorityhealth-riskbehaviorsandtheprevalenceofobesityandasthmaamongyouthandyoungadults.ThetargetpopulationishighschoolstudentsMultiplehealthbehaviorsincludedrinking,smoking,exercise,eatinghabits,etc.3ANOVAmeansAnalysisofVarianceANOVA:comparemeansoftwoormorelevelsoftheindependentvariableOneindependentvariableOnedependentvariableThebasictestusesFdistributionComparingmeansisaspecialcaseofaregressionanalysis4Thepartitioningofthetotalsumofsquaresofdeviations5TotalsumofSquaresofdeviationsofDVIndependentvariable1Independentvariable2Independentvariable3ErrorResearchdesignBetween-subjectsdesign*:differentindividualsareassignedtodifferentgroups(levelofindependentvariable).Within-subjectsdesign:alltheparticipantsareexposedtoseveralconditions.*Thispresentationonlyfocusesonbetween-subjectdesign.6DataconsiderationsIndependentvariable(factorvariable)iscategorical.Dependentvariableshouldbequantitative(intervallevelofmeasurement).AssumptionsIndependent:eachgroupisanindependentrandomsamplefromanormalpopulation.Normality:analysisofvarianceisrobusttodeparturesfromnormality,althoughthedatashouldbesymmetric.Homogeneity:thegroupsshouldcomefrompopulationswithequalvariances.7Example:Researchdesign:between-subjectsdesignResearchquestion:Isthereadifferenceinsedentarybehavioracrossfourgradelevels?Oneindependentvariable:Gradewith4levels:9th,10th,11th,and12thgrade(Q3r).Onedependentvariable:sedentarybehavior(Q81:HowmanyhourswatchTV)HigherscoreofQ81=MorehoursonwatchingTV.8Runningaone-waybetween-subjectsANOVAwithSPSS.SelectAnalyzeGeneralLinearModelUnivariateMoveQ81MoveQ3rClickPostHoc9PostHocComparisonsThisanalysesassessmeandifferencesbetweenallcombinationsofpairsofgroups(6comparions)IftheFratiosfortheindependentvariableissignificantTodeterminewhichgroupsdifferfromwhichItisafollow-upanalysisCheckTukeycheckboxClickContinue10OptionsIntheDisplaybox:check•Descriptivestatistics•Estimateofeffectsize•HomogeneitytestClickContinueThenclickOK11SPSSoutput12SPSSoutputTheLeven’stestisaboutequalvariance.p=.48,meanshomogeneousvariancesacrossfourgroups.13SPSSoutputTherewasasignificantdifferenceacrossfourgradesinQ81,Q3raccountingfor1%ofthetotalvarianceinQ81.14SPSSoutput15ResultsTheone-wayANOVAtestshowedtherewasastatisticallysignificantdifferenceacrossgradelevelsinsedentarybehavior,F(3,15709)=26.86,p.01,partialη2=.01.ATukeyHSDtestindicatedthat9th(M=3.91,SD=1.76)and10th(M=3.83,SD=1.76)gradersspentmoretimeonwatchingTVonaverageschooldaythan11th(M=3.65,SD=1.71)and12th(M=3.61,SD=1.71)gradersdid(p.01).16Two-waybetween-subjectsANOVAAfactorialcombinationoftwoindependentvariablesTwomaineffects:comparingthemeansofthevariouslevelsofanindependentvariable.Eachindependentvariablehasitsownmaineffect.Oneinteractioneffect:reflectstheeffectassociatedwiththevariouscombinationsoftwoindependentvariables.17Example:Researchdesign:between-subjectsdesignResearchquestion:Isthereadifferentrelationshipbetweengradelevelsandsedentarybehavioracrossthegender?Twoindependentvariables:Gradewith4levels:9th,10th,11th,and12thgrade(Q3r);Gender(Q2)withtwolevels:femaleandmale.Onedependentvariable:sedentarybehavior(Q81)18SPSSoutputItissignificant,whichmeansviolationofhomogeneityofvariance.19SelectAnalyzeGeneralLinearModelUnivariateClickPlots20SPSSoutputTheinteractioneffectissignificant21SPSSoutputYoumightneedtoreportthistableforyourpaper22SPSSoutput23PosthoccomparisonSelectingFemale(useselectcases),thenrunningone-wayANOVA(TukeyasPosthoctest).SelectingMale(useselectcases),thenrunningone-wayANOVA(TukeyasPosthoctest).24PosthoctestforsignificantinteractioneffectMalesFemales25ResultsThesedentarybehaviorwasanalyzedbymeansofatwo-waybetween-subjectsANOVAtestwithfourlevelsofgradeandtwolevelsofgender.Alleffectswerestatisticallysignificant.Theinteractioneffect,F(3,15687)=2.73,p.05,partialη2=.001,wasanalyzedusingone-wayANOVAandTukeyHSDcomparisontest.26ResultsFormales,9thand10thgradersspentmoretimeonwatchingTVonaverageschooldaythan11thand12thgradersdid.Forfemales,thepatternwasdifferent.Therewasnodifferencefoundinsedentarybehaviorbetween10thand12thgraders.Thoseresults,collectively,producedthesignificantinteractioneffect.27Meyers,L.S.,Gamst,G.,&Guarino,A.J.(2006).Appliedmultivariateresearch:designandinterpretation.ThousandOaks,CA:SagePublications,Inc.2829