explaining η2 单因素方差分析

ByHuiBianOfficeforFacultyExcellence*One-wayANOVAwithSPSSTwo-wayFactorialANOVAwithSPSSHowtointerpretSPSSoutputsHowtoreportresults*Weuse2009YouthRiskBehaviorSurveillanceSystem(YRBSS,CDC)asanexample.YRBSSmonitorspriorityhealth-riskbehaviorsandtheprevalenceofobesityandasthmaamongyouthandyoungadults.ThetargetpopulationishighschoolstudentsMultiplehealthbehaviorsincludedrinking,smoking,exercise,eatinghabits,etc.*ANOVAmeansAnalysisofVarianceANOVA:comparemeansoftwoormorelevelsoftheindependentvariableOneindependentvariableOnedependentvariableThebasictestusesFdistributionComparingmeansisaspecialcaseofaregressionanalysis*Thepartitioningofthetotalsumofsquaresofdeviations*TotalsumofSquaresofdeviationsofDVIndependentvariable1Independentvariable2Independentvariable3ErrorResearchdesignBetween-subjectsdesign*:differentindividualsareassignedtodifferentgroups(levelofindependentvariable).Within-subjectsdesign:alltheparticipantsareexposedtoseveralconditions.*Thispresentationonlyfocusesonbetween-subjectdesign.*DataconsiderationsIndependentvariable(factorvariable)iscategorical.Dependentvariableshouldbequantitative(intervallevelofmeasurement).AssumptionsIndependent:eachgroupisanindependentrandomsamplefromanormalpopulation.Normality:analysisofvarianceisrobusttodeparturesfromnormality,althoughthedatashouldbesymmetric.Homogeneity:thegroupsshouldcomefrompopulationswithequalvariances.*Example:Researchdesign:between-subjectsdesignResearchquestion:Isthereadifferenceinsedentarybehavioracrossfourgradelevels?Oneindependentvariable:Gradewith4levels:9th,10th,11th,and12thgrade(Q3r).Onedependentvariable:sedentarybehavior(Q81:HowmanyhourswatchTV)HigherscoreofQ81=MorehoursonwatchingTV.*Runningaone-waybetween-subjectsANOVAwithSPSS.SelectAnalyzeGeneralLinearModelUnivariateMoveQ81MoveQ3rClickPostHoc*PostHocComparisonsThisanalysesassessmeandifferencesbetweenallcombinationsofpairsofgroups(6comparions)IftheFratiosfortheindependentvariableissignificantTodeterminewhichgroupsdifferfromwhichItisafollow-upanalysisCheckTukeycheckboxClickContinue*OptionsIntheDisplaybox:checkDescriptivestatisticsEstimateofeffectsizeHomogeneitytestClickContinueThenclickOK*SPSSoutput*SPSSoutputTheLeven’stestisaboutequalvariance.p=.48,meanshomogeneousvariancesacrossfourgroups.*SPSSoutputTherewasasignificantdifferenceacrossfourgradesinQ81,Q3raccountingfor1%ofthetotalvarianceinQ81.*SPSSoutput*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).*Two-waybetween-subjectsANOVAAfactorialcombinationoftwoindependentvariablesTwomaineffects:comparingthemeansofthevariouslevelsofanindependentvariable.Eachindependentvariablehasitsownmaineffect.Oneinteractioneffect:reflectstheeffectassociatedwiththevariouscombinationsoftwoindependentvariables.*Example:Researchdesign:between-subjectsdesignResearchquestion:Isthereadifferentrelationshipbetweengradelevelsandsedentarybehavioracrossthegender?Twoindependentvariables:Gradewith4levels:9th,10th,11th,and12thgrade(Q3r);Gender(Q2)withtwolevels:femaleandmale.Onedependentvariable:sedentarybehavior(Q81)*SPSSoutputItissignificant,whichmeansviolationofhomogeneityofvariance.*SelectAnalyzeGeneralLinearModelUnivariateClickPlots*SPSSoutputTheinteractioneffectissignificant*SPSSoutputYoumightneedtoreportthistableforyourpaper*SPSSoutput*PosthoccomparisonSelectingFemale(useselectcases),thenrunningone-wayANOVA(TukeyasPosthoctest).SelectingMale(useselectcases),thenrunningone-wayANOVA(TukeyasPosthoctest).*PosthoctestforsignificantinteractioneffectMalesFemales*ResultsThesedentarybehaviorwasanalyzedbymeansofatwo-waybetween-subjectsANOVAtestwithfourlevelsofgradeandtwolevelsofgender.Alleffectswerestatisticallysignificant.Theinteractioneffect,F(3,15687)=2.73,p<.05,partialη2=.001,wasanalyzedusingone-wayANOVAandTukeyHSDcomparisontest.*ResultsFormales,9thand10thgradersspentmoretimeonwatchingTVonaverageschooldaythan11thand12thgradersdid.Forfemales,thepatternwasdifferent.Therewasnodifferencefoundinsedentarybehaviorbetween10thand12thgraders.Thoseresults,collectively,producedthesignificantinteractioneffect.*Meyers,L.S.,Gamst,G.,&Guarino,A.J.(2006).Appliedmultivariateresearch:designandinterpretation.ThousandOaks,CA:SagePublications,Inc.**