Repeated-Measures-ANOVA-in-SPSS

Repeated-MeasuresANOVAinSPSSCorrectdataformattingforarepeated-measuresANOVAinSPSSinvolveshavingasinglelineofdataforeachparticipant,withtherepeatedmeasuresenteredasseparatevariablesonthatsameline(inthisexample,theyarecalled“trial1,”“trial2,”“trial3,”and“trial4”).NotethatthisisdifferentfromthesetupforaHierarchicalLinearModel,whereyouwouldhaveaseparatelineofdataforeachobservationandrepeatthesubjectnumberoneachseparateline,withavariablenamed“trial”thatgoesfrom1to4foreachparticipant,andaseparatevariablecalled“score”thatjusthasthenumberinitthatcorrespondstothattrialforthatparticipant.Theprocedureisfoundunder“Analyze”/“GeneralLinearModel”/“RepeatedMeasures.”Usethefirstpop-updialogboxtodefineyourrepeated-measuresfactor–thisishowyoutellSPSSthatthefourdifferent“trial”variablesarereallyallasingleperson’sscoresovertimeononevariable.Giveyourvariableaname(like“trial”),andspecifyhowmanydifferentlevelsithas(i.e.,howmanytimestheobservationwasrepeated).Besuretothenhitthe“Add”buttonsothatthenewvariableappearsonalist.Youcancreatemultiplerepeated-measuresvariablesatthisstepifyouneedto.Thenclickon“Define.”Selectthecolumnsinyourdatasetthatrepresentthevariouslevelsoftherepeated-measuresvariable,andusethearrowbuttontomovethemintothe“blanks”intheright-handcolumn.Next,specifyyourmodel.Thewithin-subjectsfactorsrepresentscoresontheDVateachtrial.Therefore,theywillbetreatedasthedependent(criterion)variableforthisanalysis.Forpredictors,entergroupingvariables(e.g.,treatmentvs.control)as“between-subjectsfactors,”andotherinterval/ratio-levelpredictorsas“covariates.”Inthisexample,participants’anxietylevel(“Anxiety”)andtensionlevel(“Tension”)werebothmanipulatedexperimentally,sotheseareenteredasgroupingvariables(“between-subjectsfactors”).Therefore,thisisa2(twolevelsofanxiety)x2(twolevelsoftension)factorialrepeated-measuresANOVAdesign.Usethe“Options”buttontoopenthiswindow,andclickonthecheck-boxtoselect“HomogeneityTests.”Thiswillallowyoutotestthehomogeneityofvarianceassumptionfortherepeated-measuresdependentvariable.Thiswindowalsoshowsyouallthedifferentinteractionsthatwillbetestedaspartofyouranalysis.Ifyoudon’twantalloftheseresults,youcanselectjustspecificmaineffectsandinteractionsbyusingthe“Model”buttoninthemaindialogwindow.Click“Continue”togoon.Oneothertypeofoutputyoumightwantisagraphshowingtheaveragechangeinscoresonthedependentvariableforindividualsovertime,maybewiththeresultssortedbasedontheexperimentalgroupthepersonisin.The“Plots”buttononthemaindialogboxletsyoudothis.Inthisdialogbox,theDV(repeated-measuresvariable)goesonthe“horizontalaxis”ofthegraph.Ifyoujustwanttoseethatvariable’schangeovertime,justenterthatforthehorizontalaxisandleavetheotherfieldsblank.Ifyouwanttoseeseparatelinesonthegraphforpeopleindifferentgroups,putthegroupingvariableintothe“separatelines”box.Remembertohitthe“Add”buttontoaddyourgraphtothelistthatSPSSwillprovide.Nowreturntothemaindialogboxandhit“OK”toseetheoutput.SPSSusesamultivariateanalysistodetectrepeated-measureseffects.Thisapproachassumesthatthereissomechangefromeachtimeperiodtothenextontherepeatedmeasure.Ifyouexpectmoreofa“stepwise”patterninyourresults,itmaybeadvisabletotestonlythepre-postdifferenceintherepeatedmeasure.Alternately,youmaywanttoconsiderusingadifferentprocedurelikeANCOVAorHLM.Herearetheresultsofthemultivariatetest:MultivariateTestsb.985127.686a3.0006.000.000.015127.686a3.0006.000.00063.843127.686a3.0006.000.00063.843127.686a3.0006.000.000.7566.183a3.0006.000.029.2446.183a3.0006.000.0293.0916.183a3.0006.000.0293.0916.183a3.0006.000.029.6393.546a3.0006.000.088.3613.546a3.0006.000.0881.7733.546a3.0006.000.0881.7733.546a3.0006.000.088.6724.099a3.0006.000.067.3284.099a3.0006.000.0672.0504.099a3.0006.000.0672.0504.099a3.0006.000.067Pillai'sTraceWilks'LambdaHotelling'sTraceRoy'sLargestRootPillai'sTraceWilks'LambdaHotelling'sTraceRoy'sLargestRootPillai'sTraceWilks'LambdaHotelling'sTraceRoy'sLargestRootPillai'sTraceWilks'LambdaHotelling'sTraceRoy'sLargestRootEffecttrialtrial*anxietytrial*tensiontrial*anxiety*tensionValueFHypothesisdfErrordfSig.Exactstatistica.Design:Intercept+anxiety+tension+anxiety*tensionWithinSubjectsDesign:trialb.Thesignificantp-valuesshowaneffectoftime(trial)onthedependentvariable–awithin-subjectseffectreflectedbytherepeatedmeasures.Allfourmultivariatetestsalsoshowasignificantinteractionbetweentrialandanxietylevel,meaningthatthelevelofanxietyinducedintheparticipanthadasignificanteffectontheirperformanceovertime.Theeffectoftension,bycontrast,didnotreachconventionallevelsofstatisticalsignificance.Becausetensionhadanon-significanteffect,itprobablydoesn’tmakesensetolookattheresultsforthethree-wayinteractionbetweentension,anxiety,andtime.Nextisatestfortheassumptionofsphericity,whichisimportantinmultivariatetests.Mauchly'sTestofSphericitybMeasure:MEASURE_1.18711.2545.049.536.902.333WithinSubjectsEffecttrialMauchly'sWApprox.Chi-SquaredfSig.Greenhouse-GeisserHuynh-FeldtLower-boundEpsilonaTeststhenullhypothesisthattheerrorcovariancematrixoftheorthonormalizedtransformeddependentvariablesisproport