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Two-Way Independent ANOVA Using SPSS
Introduction Uptonowwehavelookedonlyatsituationsinwhichasingleindependentvariablewasmanipulated.Nowwemoveontomorecomplexdesignsinwhichmorethanoneindependentvariablehasbeenmanipulated.ThesedesignsarecalledFactorialDesigns.WhenyouhavetwoindependentvariablesthecorrespondingANOVAisknownasatwo-wayANOVA, andwhen both variables have beenmanipulated using different participants the test is called a two-wayindependentANOVA(somebooksusethewordunrelatedratherthanindependent).So,atwo-wayindependentANOVAisusedwhentwoindependentvariableshavebeenmanipulatedusingdifferentparticipantsinallconditions.
The ‘Beer-Goggles’ Effect Apsychologistwasinterestedintheeffectsofalcoholonmateselectionatnight-clubs.Herrationalewasthatafteralcoholhadbeenconsumed,subjectiveperceptionsofphysicalattractivenesswouldbecomemoreinaccurate(thewell-known‘beer-goggleseffect’).Shewasalso interested inwhetherthiseffectwasdifferent formenandwomen.Shepicked48students:24maleand24female.Shethentookgroupsof8participantstoanight-clubandgavethemnoalcohol(participantsreceivedplacebodrinksofalcohol-freelager),2pintsofstronglager,or4pintsofstronglager.Attheendoftheeveningshetookaphotographofthepersonthattheparticipantwaschattingup.Shethengotapoolofindependentraterstoassesstheattractivenessofthepersonineachphotograph(outof100).ThedataarepresentedinTable1.
Table1:Dataforthebeer-goggleseffect
Alcohol None 2Pints 4Pints
Gender Female Male Female Male Female Male
65 50 70 45 55 30
70 55 65 60 65 30
60 80 60 85 70 30
60 65 70 65 55 55
60 70 65 70 55 35
55 75 60 70 60 20
60 75 60 80 50 45
55 65 50 60 50 40
Wesawearlierinthemodulethatone-wayANOVAcouldbeconceptualizedasaregressionequation(agenerallinearmodel)—see Field (2013), Chapter 11 for more detail. We’ll now consider how we extend this linear model toincorporatetwoindependentvariables.TokeepthingsassimpleaspossibleIwantyoutoimaginethatwehaveonlytwolevelsofthealcoholvariableinourexample(noneand4pints).Assuch,wehavetwopredictorvariables,eachwithtwolevels.Allofthegenerallinearmodelswe’veconsideredtakethegeneralformof:
outcome' = model + error'
Forexample,whenweencounteredmultipleregressioninwesawthatthismodelwaswrittenas:
𝑌𝑌' = 𝑏𝑏/ + 𝑏𝑏0𝑋𝑋0' + 𝑏𝑏2𝑋𝑋2' + ⋯ + 𝑏𝑏4𝑋𝑋4' + 𝜀𝜀'
Also,whenwecameacrossone-wayANOVA,weadaptedthisregressionmodeltoconceptualizeourViagraexample,as:
©Prof.AndyField,2016 www.discoveringstatistics.com Page2
Libido' = 𝑏𝑏/ + 𝑏𝑏2high' + 𝑏𝑏0low' + 𝜀𝜀'
Inthismodel,theHighandLowvariablesweredummyvariables(i.e.,variablesthatcantakeonlyvaluesof0or1).Inourcurrentexample,wehavetwovariables:gender(maleorfemale)andalcohol(noneand4pints).Wecancodeeachofthesewithzerosandones,forexample,wecouldcodegenderasmale=0,female=1,andwecouldcodethealcoholvariableas0=none,1=4pints.Wecouldthendirectlycopythemodelwehadinone-wayANOVA:
Attractiveness' = 𝑏𝑏/ + 𝑏𝑏0Gender' + 𝑏𝑏2Alcohol' + 𝜀𝜀'
However,thismodeldoesnotconsidertheinteractionbetweengenderandalcohol.Ifwewanttoincludethistermtoo,thenthemodelsimplyextendstobecome(firstexpressedgenerallyandthenintermsofthisspecificexample):
Attractiveness' = 𝑏𝑏/ + 𝑏𝑏0A' + 𝑏𝑏2B' + 𝑏𝑏=AB' + 𝜀𝜀'Attractiveness' = 𝑏𝑏/ + 𝑏𝑏0Gender' + 𝑏𝑏2Alcohol' + 𝑏𝑏=Interaction' + 𝜀𝜀'
Thequestionis:howdowecodetheinteractionterm?Theinteractiontermrepresentsthecombinedeffectofalcoholandgender;togetanyinteractiontermyousimplymultiplythevariablesinvolved.Thisiswhyyouseeinteractiontermswrittenasgender´alcohol,becauseinregressiontermstheinteractionvariableliterallyisthetwovariablesmultipliedbyeachother.FormoredetailabouthowallofthecodingworksreadField(2013),Chapters10and12.ForthepurposeofthisexerciseallIreallywantyoutounderstandisthat(1)we’restillfittingalinearmodel;(2)SPSSwillcodeyourpredictors (independent variables) using the dummy coding thatwe have discussed before; and (3)we include aninteractionterm,whichiscodedbymultiplyingthedummycodesforanyofthepredictorsinvolvedintheinteraction.
Two-Way Independent ANOVA Using SPSS Inputting Data
® LevelsofbetweengroupvariablesgoinasinglecolumnoftheSPSSdataeditor.
Applyingtheruleabovetothedatawehaveherewearegoingtoneedtocreate2differentcodingvariables(seeField,2013,Chapter3)inthedataeditor.Thesecolumnswillrepresentgenderandalcoholconsumption.So,createavariablecalledGenderinthedataeditorandactivatethelabelsdialogbox.Youshoulddefinevaluelabelstorepresentthetwogenders.Wehavehadalotofexperiencewithcodingvalues,soyoushouldbefairlyhappyaboutassigningnumericalcodestodifferentgroups.IrecommendusingthecodeMale=0,andFemale=1.Onceyouhavedonethis,youcanenteracodeofzerooroneinthiscolumnindicatingtowhichgrouptheparticipantbelonged.CreateasecondvariablecalledAlcoholandassigngroupcodesbyusingthelabelsdialogbox.Isuggestthatyoucodethisvariablewiththreevalues:Placebo(noAlcohol)=1,2Pints=2,and4pints=3.Youcannowenter1,2or3intothiscolumntorepresenttheamountofalcoholconsumedbytheparticipant.Rememberthatifyouturnthevaluelabelsoptionon( )youwillseetextinthedataeditorratherthanthenumericalcodes.Now,thewaythiscodingworksisasfollows:
Gender Alcohol Participantwas..
0 1 Malewhoconsumednoalcohol
0 2 Malewhoconsumed2pints
0 3 Malewhoconsumed4pints
1 1 Femalewhoconsumednoalcohol
1 2 Femalewhoconsumed2pints
1 3 Femalewhoconsumed4pints
Onceyouhavecreatedthetwocodingvariables,youcancreateathirdvariable inwhichtoplacethevaluesofthedependentvariable.Callthisvariableattractandusethelabelsoptiontogiveitthefullernameof‘AttractivenessofDate’. In thisexample, therearetwo independentvariablesanddifferentparticipantswereused ineachcondition:
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hence,wecanusethegeneralfactorialANOVAprocedureinSPSS.Thisprocedureisdesignedforanalysingbetween-groupfactorialdesigns.
® EnterthedataintoSPSS.
® SavethedataontoadiskinafilecalledBeerGoggles.sav.
® Plotanerrorbargraphofthemeanattractivenessofmatesacrossthedifferentlevelsofalcohol.
® Plotanerrorbargraphofthemeanattractivenessofmatesselectedbymalesandfemales.
The Main Dialog Box Toaccessthemaindialogboxusethefilepath .TheresultingdialogboxisshowninFigure1.First,selectthedependentvariableAttractivenessfromthevariableslistontheleft-handsideofthedialogboxanddragittothespacelabelledDependentVariableorclickon .InthespacelabelledFixedFactor(s)weneedtoplaceanyindependentvariablesrelevanttotheanalysis.SelectAlcoholandGenderinthevariableslist(thesevariablescanbeselectedsimultaneouslybyholdingdownCtrlwhileclickingonthevariables)anddragthemtotheFixedFactor(s)box(orclickon ).Therearevariousoptionsavailabletous,weonlyneedworryabouttheonescoveredinthishandout(anyoneinterestedinfurtheroptionsshouldreadmy2013textbook,chapter13).
Figure1:MaindialogboxforunivariateANOVA
Simple and horrible looking graphs of Interactions Clickon toaccessthedialogboxinFigure2.Theplotsdialogboxallowsyoutoselectlinegraphsofyourdataandthesegraphsareveryusefulforinterpretinginteractioneffects(however,reallyweshouldplotgraphsofthemeansbeforethedataareanalysed).Wehaveonlytwoindependentvariables,andthemostusefulplotisonethatshowstheinteractionbetweenthesevariables(theplotthatdisplayslevelsofoneindependentvariableagainsttheother).Inthiscase,the interactiongraphwillhelpusto interpretthecombinedeffectofgenderandalcoholconsumption.SelectAlcoholfromthevariableslistontheleft-handsideofthedialogboxanddragittothespacelabelledHorizontalAxis(or clickon ). In the space labelledSeparate Lines place the remaining independent variable,Gender. It doesn’tmatterwhichwayroundthevariablesareplotted;youshoulduseyourdiscretionastowhichwayproducesthemostsensiblegraph.Whenyouhavemovedthetwoindependentvariablestotheappropriatebox,clickon andthisplotwillbeaddedtothelistatthebottomofthebox.Youcanplotawholevarietyofgraphs,andifyouhadathirdindependentvariable,youhavetheoptionofplottingdifferentgraphsforeachlevelofthatthirdvariablebyspecifyingavariableundertheheadingSeparatePlots.Whenyouhavefinishedspecifyinggraphs,clickon toreturntothemaindialogbox.
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Figure2:Specifyingplots
Post Hoc Tests Theposthoctestsdialogboxisobtainedbyclickingon inthemaindialogbox(Figure3).ThevariableGenderhasonlytwolevelsandsowedon’tneedtoselectposthoctestsforthatvariable(becauseanysignificanteffectscanreflectonlythedifferencebetweenmalesandfemales).However,therewerethreelevelsoftheAlcoholvariable(noalcohol,2pintsand4pints);hencewecanconductposthoctests(althoughrememberthatnormallyyouwouldconductcontrastsorposthoctests,notboth).First,youshouldselectthevariableAlcoholfromtheboxlabelledFactorsandtransferittotheboxlabelledPostHocTestsfor.Myrecommendationsforwhichposthocprocedurestouseareinlastweekshandout(andIdon’twanttorepeatmyself).SufficetosayyoushouldselecttheonesinFigure3!Clickon toreturntothemaindialogbox.
Figure3:Dialogboxforposthoctests
Options Clickon toactivatethedialogboxinFigure4.TheoptionsforfactorialANOVAarefairlystraightforward.Firstyoucanaskforsomedescriptivestatistics,whichwilldisplayatableofthemeansandstandarddeviations.Thisisausefuloptiontoselectbecauseitassistsininterpretingthefinalresults.Youcanselectthehomogeneityofvariancetests(seeyourhandoutonbias).Oncetheseoptionshavebeenselectedclickon toreturntothemaindialogbox.
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Figure4:Dialogboxforoptions
Bootstrapping Aswith any ANOVA, themain dialog box contains the button,which enables you to select bootstrappedconfidenceintervalsfortheestimatedmarginalmeans,descriptivesandposthoctests,butnotthemainFtest.Themainuseoftheseisifyouplantolookattheposthoctests,whichweare,soselecttheoptionsinFigure5.Oncetheseoptionshavebeenselectedclickon toreturntothemaindialogbox,thenclickon runtheanalysis.
Figure5:Bootstrapdialogbox
Output from Factorial ANOVA Output for the Preliminary Analysis Output1showsatableofdescriptivestatisticsproducedbecauseweaskedfordescriptivesintheoptionsdialogbox(seeFigure4)(ifyoudon’taskforbootstrappingthistablewillbeabitmorestraightforward);itdisplaysthemeans,standard deviations, confidence intervals and number of participants in all conditions of the experiment. So, for
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example,wecanseethatintheplacebocondition,Malestypicallychattedupafemalethatwasratedatabout67%ontheattractivenessscaleandthebootstrappedconfidenceintervalforthemeanrangesfrom59.54to73.33.Femalesontheotherhandselectedamatethatwasratedas61%onthatscaleandthebootstrappedconfidenceintervalforthemeanrangesfrom57.50to64.50.Notethattheconfidenceintervalsforthetwogroupsoverlap,implyingthattheymightbefromthesamepopulation.Thesemeanswillbeusefulininterpretingthedirectionofanyeffectsthatemergeintheanalysis.
Output1
Effect Sizes (Cohen’s d) WecouldusethemeansinOutput1tocomputeeffectsizes.Forexample,wemightlookattheeffectofgenderwithineachalcoholcondition.Remember fromearlier in themodulethatCohen’sd is thedifferencebetweentwomeansdividedbysomeestimateofthestandarddeviationofthosemeans:
𝑑𝑑 =𝑋𝑋0 − 𝑋𝑋2
𝑠𝑠
Thescanbethestandarddeviationofthecontrolgroup,orapooledestimate(seethehandoutonOne-wayANOVA,or Field, 2013, chapter 2). Ifwe’re looking at gender there isn't a logical control group sowe shoulduse apooledestimate.Haveagoatcalculatingtheseeffectsizes.TheresultsareinTable2.
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Table2:Cohen’sdfortheeffectofgenderwithineachalcoholgroup
Comparison Sp dpooled
NoPints(Malevs.Female) 8.10 0.77
2Pints(Malevs.Female) 9.99 0.44
4Pints(Malevs.Female) 9.15 -2.39
Levene’s Test Output2showstheresultsofLevene’stest(seehandoutsonbiasandone-wayindependentANOVA).Youshouldrecallthatanon-significantresult(asfoundhere) is indicativeofthehomogeneityofvarianceassumptionbeingmet.Youshouldalsobearinmindthevariousdiscussionswe’vehadaboutbeingcautiousinusingtestssuchasLevene’s.
Output2
The Main ANOVA Table Output3isthemostimportantpartoftheoutputbecauseittellsuswhetheranyoftheindependentvariableshavehadaneffect.Theimportantthingstolookatinthetablearethesignificancevaluesoftheindependentvariables.Thefirstthingtonoticeisthatthereisasignificanteffectofalcohol(becausethesignificancevalueislessthan.05).TheFratio is highly significant indicating that theamountof alcohol consumed significantly effectedwho theparticipantwouldtrytochatup.Thiseffectmeansthatoverall,whenweignorewhethertheparticipantwasmaleorfemale,theamountofalcoholinfluencedtheirmateselection.Thebestwaytoseewhatthismeansistolookatthebarchartthatyou(should)haveplottedoftheaveragemarkforeachlevelofalcohol(ignoringgendercompletely)—thisshowsthemeansinOutput1.
Output3
Thiseffectshouldbereportedas:
® Therewasasignificantmaineffectoftheamountofalcoholconsumedatthenight-club,ontheattractivenessofthematethatwasselected,F(2,42)=20.07,p<.001.
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Figure6showsthatwhenyouignoregendertheoverallattractivenessoftheselectedmateisverysimilarwhennoalcoholhasbeendrunk,andwhen2pintsweredrunk(themeansofthesegroupsareapproximatelyequal).Hence,thissignificantmaineffect is likelytoreflectthedropintheattractivenessoftheselectedmateswhen4pintshasbeendrunk.Thisfindingseemstoindicatethatapersoniswillingtoacceptalessattractivemateafter4pints.
Figure6:Graphshowingthemaineffectofalcohol.
Output3alsoreportsthemaineffectofgender.ThistimetheFratioisnotsignificant(p=.161,whichislargerthan.05).Thiseffectmeansthatoverall,whenweignorehowmuchalcoholhadbeendrunk,thegenderoftheparticipantdidnotinfluencetheattractivenessofthepartnerthattheparticipantselected.Inotherwords,otherthingsbeingequal,malesandfemalesselectedequallyattractivemates.Themeaningofthismaineffectcanbeseenintheerrorbarchartyouwereaskedtoplotatthebeginningofthishandout:itshowstheaverageattractivenessofmatesformenandwomen(ignoringhowmuchalcoholhadbeenconsumed).
Thiseffectshouldbereportedas:
® Therewasanonsignificantmaineffectofgenderontheattractivenessofselectedmates,F(1,42)=2.03,p=.161.
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Figure7:Graphtoshowtheeffectofgenderonmateselection
Figure7showsthattheaverageattractivenessofthepartnersofmaleandfemaleparticipantswasfairlysimilar(themeansaredifferentbyonly4%).Therefore,thisnonsignificanteffectreflectsthefactthatthemeanattractivenesswassimilar.Wecanconcludefromthisthat,ceterisparibus,menandwomenchoseequallyattractivepartners.
Finally,Output3tellsusabouttheinteractionbetweentheeffectofgenderandtheeffectofalcohol.TheFvalueishighlysignificant(becausethep-valueislessthan.05).
Thiseffectshouldbereportedas:
® Therewas a significant interaction between the amount of alcohol consumed and thegenderofthepersonselectingamate,ontheattractivenessofthepartnerselected,F(2,42)=11.91,p<.001.
Figure8:Graphoftheinteractioneffect
Whatthisactuallymeansthough,isthattheeffectofalcoholonmateselectionwasdifferentformaleparticipantsthanitwasforfemales.TheSPSSoutputincludesaplotthatweaskedfor(seeFigure2)whichtellsussomethingaboutthenature of this interaction effect. The graph that SPSS produces looks horrible and scales the y-axis such that theinteractioneffectismaximised.This,aswehaveseeninpreviousweeksisbadpractice.Figure8showsabettergraphthatIeditedtolookniceJ.
Figure8showsthatforwomen,alcoholhasverylittleeffect:theattractivenessoftheirselectedpartnersisquitestableacrossthethreeconditions(asshownbythenear-horizontalline).However,forthemen,theattractivenessoftheirpartners isstablewhenonlyasmallamounthasbeendrunk,butrapidlydeclineswhenmore isdrunk.Asignificantinteractioneffectisusuallyshownbynon-parallellinesonagraphlikethisone.Inthisparticulargraphthelinesactuallycross,which indicates a fairly large interaction between independent variables. The interaction effect tells us thatalcoholhaslittleeffectonmateselectionuntil4pintshavebeendrunkandthattheeffectofalcoholisprevalentonlyinmaleparticipants(so,basically,womenmaintainhighstandardsintheirmateselectionregardlessofalcohol,whereasmenhaveafewbeersandgoforanythingonlegs!).
Oneinterestingpointthatthesedatademonstrateisthatweconcludedearlierthatalcoholsignificantlyaffectedhowattractiveamatewasselected(thealcoholmaineffect);however,theinteractioneffecttellsusthatthisistrueonlyinmales(femalesareunaffected).Thisshowshowmisleadingmaineffectscanbe:itisusuallytheinteractionsbetweenvariablesthataremostinterestinginafactorialdesign.
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Post Hoc Analysis TheBonferroniposthoctests(Output4)breakdownthemaineffectofalcoholandcanbeinterpretedasifaone-wayANOVAhadbeenconductedontheAlcoholvariable(i.e.,thereportedeffectsforalcoholarecollapsedwithregardtogender).Thetestsshow(bothbythesignificanceandwhetherthebootstrapconfidenceintervalscrosszero)thatwhenparticipantshaddrunknoalcoholor2pintsofalcohol, they selectedequallyattractivemates,p =1.00 (this is themaximumthatpcanbewhichreflectsthefactthatthemeansarealmostidentical).However,after4pintshadbeenconsumed,participantsselectedsignificantlylessattractivematesthanafterboth2pints(p<.001)andnoalcohol(p<.001).Itisinterestingtonotethatthemeanattractivenessofpartnersafternoalcoholand2pintsweresosimilarthattheprobabilityoftheobtaineddifferencebetweenthosemeansis1(i.e.completelyprobable!).TheR-E-G-W-Qtest(Output5)confirmsthatthemeansoftheplaceboand2pintconditionswereequalwhereasthemeanofthe4-pintgroupwasdifferent.Itshouldbenotedthattheseposthoctestsignoretheinteractiveeffectofgenderandalcohol.
Output4
Output5
Theseposthoctestsshouldbereportedas:
® Confidence intervals are based on 1000 bootstrap samples. Bonferroni post hoc testsshowedthattheattractivenessofpartnerswassimilarafternoalcoholand2pints,Mdiff=-0.94,95%CI[-6.72,5.23],p=1;however,itwaslowerafter4pintscomparedtonone,
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Mdiff=17.19,95%CI[9.77,25.61],p<.001andsignificantlylowerafter4pintscomparedto2,Mdiff=18.13,95%CI[10.40,25.73],p<.001.
Guided Example Backinyourweek1handoutonrevisingSPSSwecameacrossanexamplebasedonZhang,Schmader,andHall(2013).Theupshotofthestudywasthatwomenwhocompletedamathstestusingadifferentnameperformedbetterthanthosewhocompletedthetestusingtheirownname.(Therewerenosucheffectsformen.)Zhangetal.concludedthatperformingunderadifferentnamefreedwomenfromfearsofself-evaluation,allowingthemtoperformbetter.Table3containsasmallsubsetofthedatafromZhangetal.’sstudy.
Table3:AsubsampleofZhangetal.’s(2013)data
Male Female
FemaleFakeName
MaleFakeName
OwnName
FemaleFakeName
MaleFakeName
OwnName
33 69 75 53 31 70
22 60 33 47 63 57
46 82 83 87 34 33
53 78 42 41 40 83
14 38 10 62 22 86
27 63 44 67 17 65
64 46 27 57 60 64
62 27 47 37
75 61 57 80
50 29
® EnterthedataintoSPSS.
® SavethedataontoadiskinafilecalledZhang(2013).sav.
® Plottwoerrorbargraphsofthemeantestscore(outof100)acrossthedifferentlevelsofparticipantsex,andthetypenameusedonthetestbooklet.
® Conductatwo-wayindependentANOVAtoseewhetherthetestscorewaspredictedbytheparticipant’ssex,thenameusedonthetestbookletortheirinteraction.
Whataretheindependentvariablesandhowmanylevelsdotheyhave?
YourAnswer:
Whatisthedependentvariable?
YourAnswer:
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Describetheassumptionofhomogeneityofvariance.Hasthisassumptionbeenmet?(QuoterelevantstatisticsinAPAformat).
YourAnswer:
ReportthemaineffectofparticipantsexinAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?
YourAnswer:
Reportthemaineffectof‘nameusedonthetestbooklet’inAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?
YourAnswer:
Reporttheinteractioneffectbetweenparticipantsexand‘nameusedonthetestbooklet’inAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?
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YourAnswer:
DotheresultssupportZhangetal.’s(2013)findings?Explainyouranswer.
YourAnswer:
Task 1 People’smusicaltastestendtochangeastheygetolder:myparents,forexample,afteryearsoflisteningtorelativelycoolmusicwhenIwasakid,subsequentlyhittheirmid-fortiesanddevelopedaworryingobsessionwithcountryandwesternmusic.ThispossibilityworriesmeimmenselybecausethefutureseemsincrediblybleakifitisspentlisteningtoGarthBrooksandthinking‘ohboy,didIunderestimateGarth’simmensetalentwhenIwasinmy20s’.So,IthoughtI’ddosomeresearch;Itooktwogroups(age):youngpeople(whichIarbitrarilydecidedwasunder40yearsofage)andolderpeople(above40yearsofage).Ispliteachofthesegroupsof45intothreesmallergroupsof15andassignedthemtolistentoFugazi,ABBAorBarfGrooks(music).Igoteachpersontorateit(liking)onascalerangingfrom−100(Ihatethisfoulmusic)through0(Iamcompletelyindifferent)to+100(IlovethismusicsomuchI’mgoingtoexplode).
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Table4:Fugazidata
Music Fugazi Abba BarfGrooks
Age Young Old Young Old Young Old
96 -75 65 24 -54 69
69 -98 86 30 -56 92
61 -97 37 80 -97 76
39 -75 59 75 -40 76
94 -45 49 72 -65 81
71 -73 59 60 -88 51
62 -75 42 42 -77 27
62 -75 88 90 -52 91
38 -87 92 55 -54 97
69 -49 41 60 -118 83
40 -83 64 87 -41 56
45 -77 73 56 -84 66
86 -75 66 54 -66 122
93 -98 73 74 -77 62
68 -97 68 40 -103 65
® EnterthedataintoSPSS.
® SavethedataontoadiskinafilecalledFugazi.sav.
® Plottwoerrorbargraphsofthemeanlikingacrossthedifferentlevelsofageandtypeofmusicrespectively.
® Conductatwo-wayindependentANOVAtoseewhetherlikingratingswereaffectedbyage,styleofmusicortheirinteraction.
® Answerscanbefoundonthecompanionwebsiteofmybook.
Task 2 Thereare reportsof increases in injuries related toplayingNintendoWii (http://ow.ly/ceWPj). These injurieswereattributedmainlytomuscleandtendonstrains.Aresearcherhypothesizedthatastretchingwarm-upbeforeplayingWiiwouldhelplowerinjuries,andthatathleteswouldbelesssusceptibletoinjuriesbecausetheirregularactivitymakesthemmoreflexible.Shetook60athletesand60nonathletes(athlete),halfofthemplayedWiiandhalfwatchedothersplayingasacontrol(wii),andwithinthesegroupshalfdida5-minutestretchroutinebeforeplaying/watchingwhereastheotherhalfdidnot(stretch).Theoutcomewasapainscoreoutof10(where0isnopain,and10isseverepain)afterplayingfor4hours(injury).ThedataareinthefileWii.savconductathree-wayANOVAtotestwhetherathletesarelesspronetoinjury,andwhetherthepreventionprogramworked.
Answers are available on the companion website for my book(https://studysites.uk.sagepub.com/field4e/study/smartalex.htm).
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Multiple Choice Tests
Complete themultiple choice questions forChapter 13 on the companionwebsite to Field(2013):https://studysites.uk.sagepub.com/field4e/study/mcqs.htm.Ifyougetanywrong,re-readthishandout(orField,2013,Chapter13)anddothemagainuntilyougetthemallcorrect.
References Field,A.P.(2013).DiscoveringstatisticsusingIBMSPSSStatistics:Andsexanddrugsandrock'n'roll(4thed.).London:
Sage.
Terms of Use Thishandoutcontainsmaterialfrom:
Field,A.P.(2013).DiscoveringstatisticsusingSPSS:andsexanddrugsandrock‘n’roll(4thEdition).London:Sage.
ThismaterialiscopyrightAndyField(2000-2016).
This document is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 InternationalLicense,basicallyyoucanuseitforteachingandnon-profitactivitiesbutnotmeddlewithitwithoutpermissionfromtheauthor.
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