two-way independent anova - discovering statistics · the options for factorial anova are fairly...

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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:


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:


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.


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.


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


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.


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.


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).


® Therewasanonsignificantmaineffectofgenderontheattractivenessofselectedmates,F(1,42)=2.03,p=.161.


Figure7:Graphtoshowtheeffectofgenderonmateselection

Figure7showsthattheaverageattractivenessofthepartnersofmaleandfemaleparticipantswasfairlysimilar(themeansaredifferentbyonly4%).Therefore,thisnonsignificanteffectreflectsthefactthatthemeanattractivenesswassimilar.Wecanconcludefromthisthat,ceterisparibus,menandwomenchoseequallyattractivepartners.

Finally,Output3tellsusabouttheinteractionbetweentheeffectofgenderandtheeffectofalcohol.TheFvalueishighlysignificant(becausethep-valueislessthan.05).


® 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.


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,


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


® SavethedataontoadiskinafilecalledZhang(2013).sav.

® Plottwoerrorbargraphsofthemeantestscore(outof100)acrossthedifferentlevelsofparticipantsex,andthetypenameusedonthetestbooklet.

® Conductatwo-wayindependentANOVAtoseewhetherthetestscorewaspredictedbytheparticipant’ssex,thenameusedonthetestbookletortheirinteraction.

Whataretheindependentvariablesandhowmanylevelsdotheyhave?

YourAnswer:

Whatisthedependentvariable?

YourAnswer:


Describetheassumptionofhomogeneityofvariance.Hasthisassumptionbeenmet?(QuoterelevantstatisticsinAPAformat).

YourAnswer:

ReportthemaineffectofparticipantsexinAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?

YourAnswer:

Reportthemaineffectof‘nameusedonthetestbooklet’inAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?

YourAnswer:

Reporttheinteractioneffectbetweenparticipantsexand‘nameusedonthetestbooklet’inAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?


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).


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


® 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).


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.

http://creativecommons.org/licenses/by-nc-nd/4.0/

two-way independent anova - discovering statistics · the options for factorial anova are fairly...

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