Repeated Measures ANOVA - Discovering Statistics
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© Prof. Andy Field, 2016 www.discoveringstatistics.com Page 1 Repeated Measures ANOVA Issues with Repeated Measures Designs Repeated measures is a term used when the same entities take part in all conditions of an experiment. So, for example, you might want to test the effects of alcohol on enjoyment of a party. In this type of experiment it is important to control for individual differences in tolerance to alcohol: some people can drink a lot of alcohol without really feeling the consequences, whereas others, like me, only have to sniff a pint of lager and they fall to the floor and pretend to be a fish. To control for these individual differences we can test the same people in all conditions of the experiment: so we would test each subject after they had consumed one pint, two pints, three pints and four pints of lager. After each drink the participant might be given a questionnaire assessing their enjoyment of the party. Therefore, every participant provides a score representing their enjoyment before the study (no alcohol consumed), after one pint, after two pints, and so on. This design is said to use repeated measures. What is Sphericity? We have seen that parametric tests based on the normal distribution assume that data points are independent. This is not the case in a repeated measures design because data for different conditions have come from the same entities. This means that data from different experimental conditions will be related; because of this we have to make an additional assumption to those of the independent ANOVAs you have so far studied. Put simply (and not entirely accurately), we assume that the relationship between pairs of experimental conditions is similar (i.e. the level of dependence between pairs of groups is roughly equal). This assumption is known as the assumption of sphericity. The more accurate but complex explanation is as follows. Table 1 shows data from an experiment with three conditions. Imagine we calculated the differences between pairs of scores in all combinations of the treatment levels. Having done this, we calculated the variance of these differences. Sphericity is met when these variances are roughly equal. In these data there is some deviation from sphericity because the variance of the differences between conditions A and B (15.7) is greater than the variance of the differences between A and C (10.3) and between B and C (10.7). However, these data have local circularity (or local sphericity) because two of the variances of differences are very similar. Table 1: Hypothetical data to illustrate the calculation of the variance of the differences between conditions Condition A Condition B Condition C A−B A−C B−C 10 12 8 −2 2 4 15 15 12 0 3 3 25 30 20 −5 5 10 35 30 28 5 7 2 30 27 20 3 10 7 Variance: 15.7 10.3 10.7 What is the Effect of Violating the Assumption of Sphericity? The effect of violating sphericity is a loss of power (i.e. an increased probability of a Type II error) and a test statistic (F- ratio) that simply cannot be compared to tabulated values of the F-distribution (for more details see Field, 2009; 2013). Assessing the Severity of Departures from Sphericity Departures from sphericity can be measured in three ways: 1. Greenhouse and Geisser (1959) 2. Huynh and Feldt (1976) 3. The Lower Bound estimate (the lowest possible theoretical value for the data) The Greenhouse-Geisser and Huynh-Feldt estimates can both range from the lower bound (the most severe departure from sphericity possible given the data) and 1 (no departure from sphjercitiy at all). For more detail on these estimates see Field (2013) or Girden (1992).
Transcript of Repeated Measures ANOVA - Discovering Statistics
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Repeated Measures ANOVA
Issues with Repeated Measures Designs Repeatedmeasuresisatermusedwhenthesameentitiestakepartinallconditionsofanexperiment.So,forexample,youmightwanttotesttheeffectsofalcoholonenjoymentofaparty.Inthistypeofexperimentitisimportanttocontrolfor individual differences in tolerance to alcohol: somepeople can drink a lot of alcoholwithout really feeling theconsequences,whereasothers,likeme,onlyhavetosniffapintoflagerandtheyfalltothefloorandpretendtobeafish.Tocontrolfortheseindividualdifferenceswecantestthesamepeopleinallconditionsoftheexperiment:sowewouldtesteachsubjectaftertheyhadconsumedonepint,twopints,threepintsandfourpintsoflager.Aftereachdrinktheparticipantmightbegivenaquestionnaireassessingtheirenjoymentoftheparty.Therefore,everyparticipantprovidesascorerepresentingtheirenjoymentbeforethestudy(noalcoholconsumed),afteronepint,aftertwopints,andsoon.Thisdesignissaidtouserepeatedmeasures.
What is Sphericity? Wehaveseenthatparametrictestsbasedonthenormaldistributionassumethatdatapointsareindependent.Thisisnotthecaseinarepeatedmeasuresdesignbecausedatafordifferentconditionshavecomefromthesameentities.Thismeans that data from different experimental conditionswill be related; because of thiswe have tomake anadditional assumption to those of the independent ANOVAs you have so far studied. Put simply (and not entirelyaccurately), we assume that the relationship between pairs of experimental conditions is similar (i.e. the level ofdependencebetweenpairsofgroupsisroughlyequal).Thisassumptionisknownastheassumptionofsphericity.Themoreaccuratebutcomplexexplanationisasfollows.Table1showsdatafromanexperimentwiththreeconditions.Imaginewecalculatedthedifferencesbetweenpairsofscoresinallcombinationsofthetreatmentlevels.Havingdonethis,wecalculatedthevarianceofthesedifferences.Sphericityismetwhenthesevariancesareroughlyequal.InthesedatathereissomedeviationfromsphericitybecausethevarianceofthedifferencesbetweenconditionsAandB(15.7)isgreaterthanthevarianceofthedifferencesbetweenAandC(10.3)andbetweenBandC(10.7).However,thesedatahavelocalcircularity(orlocalsphericity)becausetwoofthevariancesofdifferencesareverysimilar.
Table1:Hypotheticaldatatoillustratethecalculationofthevarianceofthedifferencesbetweenconditions
ConditionA ConditionB ConditionC A−B A−C B−C10 12 8 −2 2 415 15 12 0 3 325 30 20 −5 5 1035 30 28 5 7 230 27 20 3 10 7 Variance: 15.7 10.3 10.7
What is the Effect of Violating the Assumption of Sphericity? Theeffectofviolatingsphericityisalossofpower(i.e.anincreasedprobabilityofaTypeIIerror)andateststatistic(F-ratio)thatsimplycannotbecomparedtotabulatedvaluesoftheF-distribution(formoredetailsseeField,2009;2013).
Assessing the Severity of Departures from Sphericity Departuresfromsphericitycanbemeasuredinthreeways:
1. GreenhouseandGeisser(1959)
2. HuynhandFeldt(1976)
3. TheLowerBoundestimate(thelowestpossibletheoreticalvalueforthedata)
TheGreenhouse-GeisserandHuynh-Feldtestimatescanbothrangefromthelowerbound(themostseveredeparturefromsphericitypossiblegiventhedata)and1(nodeparturefromsphjercitiyatall).FormoredetailontheseestimatesseeField(2013)orGirden(1992).
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SPSSalsoproducesatestknownasMauchly’stest,whichteststhehypothesisthatthevariancesofthedifferencesbetweenconditionsareequal.
® If Mauchly’s test statistic is significant (i.e. has a probability value less than .05) weconcludethattherearesignificantdifferencesbetweenthevarianceofdifferences:theconditionofsphericityhasnotbeenmet.
® If,Mauchly’steststatisticisnonsignificant(i.e.p>.05)thenitisreasonabletoconcludethatthevariancesofdifferencesarenotsignificantlydifferent(i.e.theyareroughlyequal).
® IfMauchly’stestissignificantthenwecannottrusttheF-ratiosproducedbySPSS.
® Rememberthat,aswithanysignificancetest,thepowerofMauchley’stestdependsonthesamplesize.Therefore,itmustbeinterpretedwithinthecontextofthesamplesizebecause:
o In small samples large deviations from sphericity might be deemed non-significant.
o Inlargesamples,smalldeviationsfromsphericitymightbedeemedsignificant.
Correcting for Violations of Sphericity Fortunately, if data violate the sphericity assumption we simply adjust the defrees of freedom for the effect bymultiplyingitbyoneoftheaforementionedsphericityestimates.Thiswillmakethedegreesoffreedomsmaller;byreducing the degrees of freedom we make the F-ratio more conservative (i.e. it has to be bigger to be deemedsignificant).SPSSappliestheseadjustmentsautomatically.
WhichcorrectionshouldIuse?
® LookattheGreenhouse-Geisserestimateofsphericity(ε)intheSPSShandout.
® Whenε > .75thenusetheHuynh-Feldtcorrection.
® Whenε < .75thenusetheGreenhouse-Geissercorrection.
One-Way Repeated Measures ANOVA using SPSS “I’macelebrity,getmeoutofhere”isaTVshowinwhichcelebrities(well,Imean,they’renotreallyarethey…I’mstrugglingtoknowwhoanyoneisintheseriesthesedays)inapitifulattempttosalvagetheircareers(orjusthavecareersinthefirstplace)goandliveinthejungleandsubjectthemselvestoritual humiliation and/or creepy crawlies in places where creepy crawliesshouldn’tgo.It’scruel,voyeuristic,gratuitous,carcrashTV,andI loveit.Aparticular favourite bit is the Bushtucker trials in which the celebritieswillinglyeatthingslikestickinsects,Witchettygrubs,fisheyes,andkangarootesticles/penises,nomnomnoms….
I’veoftenwondered(perhapsalittletoomuch)whichofthebushtuckerfoodsismostrevolting.SoIgot8celebrities,andmadethemeatfourdifferentanimals(theaforementionedstickinsect,kangarootesticle,fisheyeandWitchettygrub)incounterbalancedorder.OneachoccasionImeasuredthetimeittookthecelebritytoretch,inseconds.ThedataareinTable2.
Entering the Data Theindependentvariablewastheanimalthatwasbeingeaten(stick,insect,kangarootesticle,fisheyeandwitchettygrub)andthedependentvariablewasthetimeittooktoretch,inseconds.
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® LevelsofrepeatedmeasuresvariablesgoindifferentcolumnsoftheSPSSdataeditor.
Therefore,separatecolumnsshouldrepresenteachlevelofarepeatedmeasuresvariable.Assuch,thereisnoneedforacodingvariable(aswithbetween-groupdesigns).Thedatacan,therefore,beenteredastheyareinTable2.
• Savethesedatainafilecalledbushtucker.sav
Table2:DatafortheBushtuckerexample
Celebrity StickInsect KangarooTesticle FishEye WitchettyGrub
1 8 7 1 6
2 9 5 2 5
3 6 2 3 8
4 5 3 1 9
5 8 4 5 8
6 7 5 6 7
7 10 2 7 2
8 12 6 8 1
Drawanerrorbarchartofthesedata.TheresultinggraphisinFigure1.
Figure1:Graphofthemeantimetoretchaftereatingeachoftheanimals(errorbarsshowthe95%confidenceinterval)
ToconductanANOVAusingarepeatedmeasuresdesign,activatethedefinefactorsdialogboxbyselecting.IntheDefineFactorsdialogbox(Figure2),youareaskedtosupplyaname
forthewithin-subject(repeated-measures)variable.Inthiscasetherepeatedmeasuresvariablewasthetypeofanimaleateninthebushtuckertrial,soreplacethewordfactor1withthewordAnimal.Thenameyougivetotherepeatedmeasuresvariablecannothavespacesinit.Whenyouhavegiventherepeatedmeasuresfactoraname,youhavetotellthecomputerhowmanylevelsthereweretothatvariable(i.e.howmanyexperimentalconditionstherewere).Inthiscase,therewere4differentanimalseatenbyeachperson,sowehavetoenterthenumber4intotheboxlabelledNumberofLevels.Clickon toaddthisvariabletothelistofrepeatedmeasuresvariables.Thisvariablewillnow
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appearinthewhiteboxatthebottomofthedialogboxandappearsasAnimal(4).Ifyourdesignhasseveralrepeatedmeasuresvariablesthenyoucanaddmorefactorstothelist(seeTwoWayANOVAexamplebelow).Whenyouhaveenteredalloftherepeatedmeasuresfactorsthatweremeasuredclickon togototheMainDialogBox.
Figure2:DefineFactorsdialogboxforrepeatedmeasuresANOVA
Figure3:MaindialogboxforrepeatedmeasuresANOVA
Themaindialogbox(Figure3)hasaspacelabelledwithinsubjectsvariablelistthatcontainsalistof4questionmarksproceeded by a number. These questionmarks are for the variables representing the 4 levels of the independentvariable.Thevariablescorrespondingtotheselevelsshouldbeselectedandplacedintheappropriatespace.Wehaveonly4variablesinthedataeditor,soitispossibletoselectallfourvariablesatonce(byclickingonthevariableatthetop,holdingthemousebuttondownanddraggingdownovertheothervariables).Theselectedvariablescanthenbetransferredbydraggingthemorclickingon .
Whenallfourvariableshavebeentransferred,youcanselectvariousoptionsfortheanalysis.Thereareseveraloptionsthatcanbeaccessedwiththebuttonsatthebottomofthemaindialogbox.Theseoptionsaresimilartotheoneswehavealreadyencountered.
Post Hoc Tests ThereisnoproperfacilityforproducingposthoctestsforrepeatedmeasuresvariablesinSPSS(youwillfindthatifyouaccesstheposthoctestdialogboxitwillnotlistanyrepeated-measuredfactors).However,youcangetabasicsetofposthoctestsclicking inthemaindialogbox.Tospecifyposthoctests,selecttherepeatedmeasuresvariable
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(inthiscaseAnimal)fromtheboxlabelledEstimatedMarginalMeans:Factor(s)andFactorInteractionsandtransferittotheboxlabelledDisplayMeansforbyclickingon (Figure4).Onceavariablehasbeentransferred,theboxlabelledComparemaineffects( )becomesactiveandyoushouldselectthisoption.Ifthisoptionisselected,theboxlabelledConfidenceintervaladjustmentbecomesactiveandyoucanclickon toseeachoiceofthreeadjustmentlevels.ThedefaultistohavenoadjustmentandsimplyperformaTukeyLSDposthoctest(thisisnot recommended). The secondoption is a Bonferroni correction (whichwe’ve encounteredbefore), and the finaloptionisaSidakcorrection,whichshouldbeselectedifyouareconcernedaboutthelossofpowerassociatedwithBonferronicorrectedvalues.Whenyouhaveselectedtheoptionsof interest,clickon to return to themaindialogbox,andthenclickon toruntheanalysis.
Figure4:Optionsdialogbox
Output for Repeated Measures ANOVA Descriptive statistics and other Diagnostics
Output1
Output1showstwotables.Thefirstliststhevariablesthatrepresenteachleveloftheindependentvariable,whichisusefultocheckthatthevariableswereenteredinthecorrectorder.Thesecondtableprovidesbasicdescriptivestatisticsforthefourlevelsoftheindependentvariable.Fromthistablewecanseethat,onaverage,thequickestretchingwasafterthekangarootesticleandfisheyeball(implyingtheyaremoredisgusting).
Assessing Sphericity EarlieryouweretoldthatSPSSproducesatestthatlooksatwhetherthedatahaveviolatedtheassumptionofsphericity.Thenextpartoftheoutputcontainsinformationaboutthistest.
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® Mauchly’stestshouldbenonsignificantifwearetoassumethattheconditionofsphericityhasbeenmet.
® Sometimeswhenyoulookatthesignificance,allyouseeisadot.Thereisnosignificancevalue.Thereasonthatthishappensisthatyouneedatleastthreeconditionsforsphericitytobean issue. Therefore, if youhavea repeated-measures variable thathasonly twolevelsthensphericity ismet,theestimatescomputedbySPSSare1(perfectsphericity)andtheresultingsignificancetestcannotbecomputed(hencewhythetablehasavalueof0forthechi-squaretestanddegreesoffreedomandablankspaceforthesignificance).ItwouldbealoteasierifSPSSjustdidn’tproducethetable,butthenIguesswe’dallbeconfusedaboutwhythetablehadn’tappeared;maybeitshouldjustprintinbigletters‘Hooray!Hooray!Sphericityhasgoneaway!’Wecandream.
Output2showsMauchly’stestforthesedata,andtheimportantcolumnistheonecontainingthesignificancevale.Thesignificancevalueis.047,whichislessthan.05,sowemustacceptthehypothesisthatthevariancesofthedifferencesbetweenlevelsweresignificantlydifferent.Inotherwordstheassumptionofsphericityhasbeenviolated.WecouldreportMauchly’stestforthesedataas:
® Mauchly’stestindicatedthattheassumptionofsphericityhadbeenviolated,χ2(5)=11.41,p=.047.
Output2
The Main ANOVA Output3showstheresultsoftheANOVAforthewithin-subjectsvariable.Thetableyouseewilllookslightlydifferent(itwilllooklikeOutput4infact),butforthetimebeingI’vesimplifieditabit.Bearwithmefornow.ThistablecanbereadmuchthesameasforOne-wayindependentANOVA(seeyourhandout).ThesignificanceofFis.026,whichissignificantbecauseitislessthanthecriterionvalueof.05.Wecan,therefore,concludethattherewasasignificantdifferenceinthetimetakentoretchaftereatingdifferentanimals.However,thismaintestdoesnottelluswhichanimalsresultedinthequickestretchingtimes.
Although this result seems very plausible,we saw earlier that the assumption ofsphericity had been violated. I also mentioned that a violation of the sphericityassumptionmakes theF-test inaccurate. So,whatdowedo?Well, Imentionedearlieron thatwe can correct thedegreesoffreedominsuchawaythatitisaccuratewhensphericityisviolated.ThisiswhatSPSSdoes.Output4(whichistheoutputyouwillseeinyourownSPSSanalysis)showsthemainANOVA.Asyoucanseeinthisoutput,thevalueofF does not change, only the degrees of freedom. But the effect of changing the degrees of freedom is that thesignificanceofthevalueofFchanges:theeffectofthetypeofanimalislesssignificantaftercorrectingforsphericity.
Output3
Tests of Within-Subjects Effects
Measure: MEASURE_1Sphericity Assumed
83.125 3 27.708 3.794 .026153.375 21 7.304
SourceAnimalError(Animal)
Type III Sumof Squares df Mean Square F Sig.
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Output4
Thenextissueiswhichofthethreecorrectionstouse.EarlierIgaveyousometipsandtheywerethatwhenε > .75then use the Huynh-Feldt correction, andwhen ε < .75, or nothing is known about sphericity at all, then use theGreenhouse-Geissercorrection;εistheestimateofsphericityfromOutput2andthesevaluesare.533and.666(thecorrectionofthebeast….);becausethesevaluesarelessthan.75weshouldusetheGreenhouse-Geissercorrectedvalues.Usingthiscorrection,Fisnotsignificantbecauseitspvalueis.063,whichismorethanthenormalcriterionof.05.
® Inthisexampletheresultsarequiteweirdbecauseuncorrectedtheyaresignificant,andapplying the Huynh-Feldt correction they are also significant. However, with theGreenhouse-Geissercorrectionappliedtheyarenot.
® Thishighlightshowarbitrarythewhole.05criterionforsignificanceis.Clearly,theseFsrepresentthesamesizedeffect,butusingonecriteriontheyare ‘significant’andusinganothertheyarenot.
Post Hoc Tests Giventhemaineffectwasnotsignificant,weshouldnotfollowthiseffectupwithposthoctests,butinsteadconcludethatthetypeofanimaldidnothaveasignificanteffectonhowquicklycontestantsretched(perhapsweshouldhaveusedbeansontoastasabaselineagainstwhichtocompare…).
However,justtoillustratehowyouwouldinterprettheSPSSoutputIhavereproduceditinOutput5:thedifferencebetweengroupmeansisdisplayed,thestandarderror,thesignificancevalueandaconfidenceintervalforthedifferencebetweenmeans.Bylookingatthesignificancevalueswecanseethattheonlysignificantdifferencesbetweengroupmeansisbetweenthestickinsectandthekangarootesticle,andthestickinsectandthefisheye.Nootherdifferencesaresignificant.
Output5
Tests of Within-Subjects Effects
Measure: MEASURE_1
83.125 3 27.708 3.794 .02683.125 1.599 52.001 3.794 .06383.125 1.997 41.619 3.794 .04883.125 1.000 83.125 3.794 .092
153.375 21 7.304153.375 11.190 13.707153.375 13.981 10.970153.375 7.000 21.911
Sphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-bound
SourceAnimal
Error(Animal)
Type III Sumof Squares df Mean Square F Sig.
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Reporting One-Way Repeated Measures ANOVA WecanreportrepeatedmeasuresANOVAinthesamewayasanindependentANOVA(seeyourhandout).Theonlyadditional thingwe should concern ourselveswith is reporting the corrected degrees of freedom if sphericitywasviolated.Personally,I’malsokeenonreportingtheresultsofsphericitytestsaswell.Therefore,wecouldreportthemainfindingas:
® Mauchly’stestindicatedthattheassumptionofsphericityhadbeenviolated,χ2(5)=11.41,p=.047,thereforedegreesof freedomwerecorrectedusingGreenhouse-Geisserestimatesof sphericity (ε= .53).The resultsshowthattherewasnosignificanteffectofwhichanimalwaseatenonthetimetakentoretch,F(1.60,11.19)=3.79,p=.06.Theseresultssuggestedthatnoanimalwassignificantlymoredisgustingtoeatthantheothers.
Two-Way Repeated Measures ANOVA Using SPSS Aswehaveseenbefore,thenameofanyANOVAcanbebrokendowntotellusthetypeofdesignthatwasused.The‘two-way’partofthenamesimplymeansthattwoindependentvariableshavebeenmanipulatedintheexperiment.The‘repeatedmeasures’partofthenametellsusthatthesameparticipantshavebeenusedinallconditions.Therefore,thisanalysisisappropriatewhenyouhavetworepeated-measuresindependentvariables:eachparticipantdoesalloftheconditionsintheexperiment,andprovidesascoreforeachpermutationofthetwovariables.
A Speed-Dating Example Itseemsthatlotsofmagazinesgoonallthetimeabouthowmenandwomenwantdifferentthingsfromrelationships(orperhapsit’sjustmywife’scopiesofMarieClare’s,whichobviouslyIdon’tread,honestly).Thebigquestiontowhichweallwanttoknowtheanswerisarelooksorpersonalitymoreimportant.Imagineyouwantedtoputthistothetest.Youdevisedacunningplanwherebyyou’dsetupaspeed-datingnight.Littledidthepeoplewhocamealongknowthatyou’dgotsomeofyourfriendstoactasthedates.Specificallyyoufound9mentoactasthedate.Ineachofthesegroupsthreepeoplewereextremelyattractivepeoplebutdifferedintheirpersonality:onehadtonnesofcharisma,one had some charisma, and the third personwas as dull as this handout. Another three peoplewere of averageattractiveness,andagaindifferedintheirpersonality:onewashighlycharismatic,onehadsomecharismaandthethirdwasadullard.Thefinalthreewere,notwishingtobeunkindinanyway,butt-uglyandagainonewascharismatic,onehadsomecharismaandthefinalpoorsoulwasmind-numbinglytedious.Theparticipantswereheterosexualwomenwhocametothespeeddatingnight,andoverthecourseoftheeveningtheyspeed-datedall9men.Aftertheir5minutedate,theyratedhowmuchthey’dliketohaveaproperdatewiththepersonasapercentage(100%=‘I’dpaylargesumsofmoneyforyourphonenumber’,0%=‘I’dpayalargesumofmoneyforaplanetickettogetmeasfarawayaspossiblefromyou’).Assuch,eachwomanrated9differentpeoplewhovariedintheirattractivenessandpersonality.So,therearetworepeatedmeasuresvariables:looks(withthreelevelsbecausethepersoncouldbeattractive,averageorugly)andpersonality(againwiththreelevelsbecausethepersoncouldhavelotsofcharisma,havesomecharisma,orbeadullard).
Data Entry ToenterthesedataintoSPSSweusethesameprocedureastheone-wayrepeatedmeasuresANOVAthatwecameacrossinthepreviousexample.
® LevelsofrepeatedmeasuresvariablesgoindifferentcolumnsoftheSPSSdataeditor.
Ifapersonparticipatesinallexperimentalconditions(inthiscaseshedatesallofthemenwhodifferinattractivenessandallofthemenwhodifferintheircharisma)theneachexperimentalconditionmustberepresentedbyacolumninthedataeditor.Inthisexperimenttherearenineexperimentalconditionsandsothedataneedtobeenteredinninecolumns.Therefore,createthefollowingninevariablesinthedataeditorwiththenamesasgiven.Foreachone,youshouldalsoenterafullvariablenameforclarityintheoutput.
att_high Attractive + HighCharisma
av_high AverageLooks + HighCharisma
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ug_high Ugly + HighCharisma
att_some Attractive + SomeCharisma
av_some AverageLooks + SomeCharisma
ug_some Ugly + SomeCharisma
att_none Attractive + Dullard
av_none AverageLooks + Dullard
ug_none Ugly + Dullard
Figure5:DefinefactorsdialogboxforfactorialrepeatedmeasuresANOVA
ThedataareinthefileFemaleLooksOrPersonality.savfromthecoursewebsite.Firstwehavetodefineourrepeatedmeasuresvariables,soaccessthedefinefactorsdialogboxselect .As with one-way repeatedmeasures ANOVA (see the previous example) we need to give names to our repeatedmeasuresvariablesand specifyhowmany levels theyhave. In this case thereare twowithin-subject factors: looks(attractive,averageorugly)andcharisma(highcharisma,somecharismaanddullard).Inthedefinefactorsdialogboxreplacethewordfactor1withtheword looks.Whenyouhavegiventhisrepeatedmeasuresfactoraname,tellthecomputerthatthisvariablehas3levelsbytypingthenumber3intotheboxlabelledNumberofLevels(Figure5).Clickon toaddthisvariabletothelistofrepeatedmeasuresvariables.Thisvariablewillnowappearinthewhiteboxatthebottomofthedialogboxandappearsaslooks(3).
Nowrepeatthisprocessforthesecondindependentvariable.EnterthewordcharismaintothespacelabelledWithin-SubjectFactorNameandthen,becausetherewerethree levelsof thisvariable,enter thenumber3 intothespacelabelledNumberofLevels.Clickon toincludethisvariableinthelistoffactors;itwillappearascharisma(3).ThefinisheddialogboxisshowninFigure5.Whenyouhaveenteredbothofthewithin-subjectfactorsclickon togotothemaindialogbox.
ThemaindialogboxisshowninFigure6.AtthetopoftheWithin-SubjectsVariablesbox,SPSSstatesthattherearetwofactors:looksandcharisma.Intheboxbelowthereisaseriesofquestionmarksfollowedbybracketednumbers.Thenumbers in brackets represent the levels of the factors (independent variables). In this example, there are twoindependentvariablesandsotherearetwonumbersinthebrackets.Thefirstnumberreferstolevelsofthefirstfactorlistedabovethebox(inthiscaselooks).Thesecondnumberinthebracketreferstolevelsofthesecondfactorlistedabovethebox(inthiscasecharisma).Wehavetoreplacethequestionmarkswithvariablesfromthelistontheleft-handsideofthedialogbox.Withbetween-groupdesigns,inwhichcodingvariablesareused,thelevelsofaparticularfactorarespecifiedbythecodesassignedtotheminthedataeditor.However,inrepeatedmeasuresdesigns,nosuchcodingscheme isusedandsowedeterminewhichconditiontoassigntoa levelat thisstage.Thevariablescanbeenteredasfollows:
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att_high _?_(1,1)
att_some _?_(1,2)
att_none _?_(1,3)
av_high _?_(2,1)
av_some _?_(2,2)
av_none _?_(2,3)
ug_high _?_(3,1)
ug_some _?_(3,2)
ug_none _?_(3,3)
Figure6:Mainrepeatedmeasuresdialogbox
ThecompleteddialogboxshouldlookexactlylikeFigure6.I’vealreadydiscussedtheoptionsforthebuttonsatthebottomofthisdialogbox,soI’lltalkonlyabouttheonesofparticularinterestforthisexample.
Other Options Theadditionofanextravariablemakesitnecessarytochooseadifferentgraphtotheoneintheprevioushandout.Clickon toaccessthedialogboxinFigure7.PlacelooksintheslotlabelledHorizontalAxis:andcharismainslot labelled Separate Line. When both variables have been specified, don’t forget to click on to add thiscombinationtothelistofplots.ByaskingSPSStoplotthelooks´charismainteraction,weshouldgettheinteractiongraph for looks and charisma. You could also think about plotting graphs for the twomain effects (e.g. looks andcharisma).Asfarasotheroptionsareconcerned,youshouldselectthesameonesthatwerechosenforthepreviousexample.Itisworthselectingestimatedmarginalmeansforalleffects(becausethesevalueswillhelpyoutounderstandanysignificanteffects).
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Figure7:Plotsdialogboxforatwo-wayrepeatedmeasuresANOVA
Descriptives and Main Analysis Output6showstheinitialoutputfromthisANOVA.Thefirsttablemerelyliststhevariablesthathavebeenincludedfromthedataeditorandthelevelofeachindependentvariablethattheyrepresent.Thistableismoreimportantthanitmightseem,becauseitenablesyoutoverifythatthevariablesintheSPSSdataeditorrepresentthecorrectlevelsoftheindependentvariables.Thesecondtableisatableofdescriptivesandprovidesthemeanandstandarddeviationforeachofthenineconditions.ThenamesinthistablearethenamesIgavethevariablesinthedataeditor(therefore,ifyoudidn’tgivethesevariablesfullnames,thistablewilllookslightlydifferent).Thevaluesinthistablewillhelpuslatertointerpretthemaineffectsoftheanalysis.
Output6
Output7showstheresultsofMauchly’ssphericitytestforeachofthethreeeffectsinthemodel(twomaineffectsandone interaction).Thesignificancevaluesofthesetests indicatethatforthemaineffectsofLooksandCharisma theassumptionofsphericityismet(becausep>.05)soweneednotcorrecttheF-ratiosfortheseeffects.However,theLooks×CharismainteractionhasviolatedthisassumptionandsotheF-valueforthiseffectshouldbecorrected.
Output7
Within-Subjects Factors
Measure: MEASURE_1
att_highatt_someatt_noneav_highav_someav_noneug_highug_someug_none
Charisma123123123
Looks1
2
3
DependentVariable
Descriptive Statistics
89.60 6.637 1087.10 6.806 1051.80 3.458 1088.40 8.329 1068.90 5.953 1047.00 3.742 1086.70 5.438 1051.20 5.453 1046.10 3.071 10
Attractive and Highly CharismaticAttractive and Some CharismaAttractive and a DullardAverage and Highly CharismaticAverage and Some CharismaAverage and a DullardUgly and Highly CharismaticUgly and Some CharismaUgly and a Dullard
Mean Std. Deviation N
Mauchly's Test of Sphericityb
Measure: MEASURE_1
.904 .810 2 .667 .912 1.000 .500
.851 1.292 2 .524 .870 1.000 .500
.046 22.761 9 .008 .579 .791 .250
Within Subjects EffectLooksCharismaLooks * Charisma
Mauchly's WApprox.
Chi-Square df Sig.Greenhouse-Geisser Huynh-Feldt Lower-bound
Epsilona
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables isproportional to an identity matrix.
May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed inthe Tests of Within-Subjects Effects table.
a.
Design: Intercept Within Subjects Design: Looks+Charisma+Looks*Charisma
b.
©Prof.AndyField,2016 www.discoveringstatistics.com Page12
Output8showstheresultsoftheANOVA(withcorrectedFvalues).Theoutputissplitintosectionsthatrefertoeachoftheeffectsinthemodelandtheerrortermsassociatedwiththeseeffects.Theinterestingpartisthesignificancevaluesof theF-ratios. If these values are less than .05 thenwe can say that aneffect is significant. Lookingat thesignificancevaluesinthetableitisclearthatthereisasignificantmaineffectofhowattractivethedatewas(Looks),asignificantmaineffectofhowcharismaticthedatewas(Charisma),andasignificant interactionbetweenthesetwovariables.Iwillexamineeachoftheseeffectsinturn.
Output8
The Main Effect of Looks WecameacrossthemaineffectoflooksinOutput8.
® Wecanreportthat‘therewasasignificantmaineffectoflooks,F(2,18)=66.44,p<.001.’
® Thiseffect tellsus that ifwe ignoreallothervariables, ratingsweredifferent forattractive,averageandunattractivedates.
IfyourequestedthatSPSSdisplaymeansforthelookseffect(I’llassumeyoudidfromnowon)youwillfindthetableina section headed EstimatedMarginalMeans. Output 9 is a table of means for themain effect of looks with theassociatedstandarderrors.Thelevelsoflooksarelabelledsimply1,2and3,andit’sdowntoyoutorememberhowyouenteredthevariables(oryoucanlookatthesummarytablethatSPSSproducesatthebeginningoftheoutput—seeOutput6).IfyoufollowedwhatIdidthenlevel1isattractive,level2isaverageandlevel3isugly.Tomakethingseasier,thisinformationisplottedinFigure8:asattractivenessfalls,themeanratingfallstoo.Thismaineffectseemstoreflectthatthewomenweremorelikelytoexpressagreaterinterestingoingoutwithattractivementhanaverageoruglymen.However,wereallyneedto lookatsomecontraststofindoutexactlywhat’sgoingon(seeField,2013 ifyou’reinterested).
Tests of Within-Subjects Effects
Measure: MEASURE_1
3308.867 2 1654.433 66.437 .0003308.867 1.824 1813.723 66.437 .0003308.867 2.000 1654.433 66.437 .0003308.867 1.000 3308.867 66.437 .000448.244 18 24.902448.244 16.419 27.300448.244 18.000 24.902448.244 9.000 49.805
23932.867 2 11966.433 274.888 .00023932.867 1.740 13751.549 274.888 .00023932.867 2.000 11966.433 274.888 .00023932.867 1.000 23932.867 274.888 .000
783.578 18 43.532783.578 15.663 50.026783.578 18.000 43.532783.578 9.000 87.064
3365.867 4 841.467 34.912 .0003365.867 2.315 1453.670 34.912 .0003365.867 3.165 1063.585 34.912 .0003365.867 1.000 3365.867 34.912 .000867.689 36 24.102867.689 20.839 41.638867.689 28.482 30.465867.689 9.000 96.410
Sphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-bound
SourceLooks
Error(Looks)
Charisma
Error(Charisma)
Looks * Charisma
Error(Looks*Charisma)
Type III Sumof Squares df Mean Square F Sig.
©Prof.AndyField,2016 www.discoveringstatistics.com Page13
Output9 Figure8:Themaineffectoflooks
The Effect of Charisma ThemaineffectofcharismawasinOutput8.
® Wecanreportthattherewasasignificantmaineffectofcharisma,F(2,18)=274.89,p<.001.
® This effect tells us that if we ignore all other variables, ratings were different for highlycharismatic,abitcharismaticanddullardpeople.
ThetablelabelledCHARISMAinthesectionheadedEstimatedMarginalMeanstellsuswhatthiseffectmeans(Output10.).Again,thelevelsofcharismaarelabelledsimply1,2and3.IfyoufollowedwhatIdidthenlevel1ishighcharisma,level2issomecharismaandlevel3isnocharisma.ThisinformationisplottedinFigure9:Ascharismadeclines,themeanratingfallstoo.Sothismaineffectseemstoreflectthatthewomenweremorelikelytoexpressagreaterinterestingoingoutwithcharismaticmenthanaveragemenordullards.Again,wewouldhavetolookatcontrastsorposthocteststobreakthiseffectdownfurther.
Output10 Figure9:Themaineffectofcharisma
Estimates
Measure: MEASURE_1
76.167 1.013 73.876 78.45768.100 1.218 65.344 70.85661.333 1.018 59.030 63.637
Looks123
Mean Std. Error Lower Bound Upper Bound95% Confidence Interval
Estimates
Measure: MEASURE_1
88.233 1.598 84.619 91.84869.067 1.293 66.142 71.99148.300 .751 46.601 49.999
Charisma123
Mean Std. Error Lower Bound Upper Bound95% Confidence Interval
©Prof.AndyField,2016 www.discoveringstatistics.com Page14
The Interaction between Looks and Charisma Output8indicatedthattheattractivenessofthedateinteractedinsomewaywithhowcharismaticthedatewas.
® Wecanreportthat‘therewasasignificantinteractionbetweentheattractivenessofthedateandthecharismaofthedate,F(2.32,20.84)=34.91,p<.001’.
® Thiseffecttellsusthattheprofileofratingsacrossdatesofdifferent levelsofcharismawasdifferentforattractive,averageanduglydates.
Theestimatedmarginalmeans(oraplotoflooks´charismausingthedialogboxinFigure4)tellusthemeaningofthisinteraction(seeFigure10andOutput11).
Output11 Figure10:Thelooks´charismainteraction
Thegraphshowstheaverageratingsofdatesofdifferentlevelsofattractivenesswhenthedatealsohadhighlevelsofcharisma(circles),somecharisma(squares)andnocharisma(triangles).Lookfirstatthehighlightcharismaticdates.Essentially,theratingsforthesedatesdonotchangeoverlevelsofattractiveness.Inotherwords,women’sratingsofdatesforhighlycharismaticmenwasunaffectedbyhowgoodlookingtheywere–ratingswerehighregardlessoflooks.Nowlookatthemenwhoweredullards.Womenratedthesedatesaslowregardlessofhowattractivethemanwas.Inotherwords,ratingsfordullardswereunaffectedbylooks:evenagoodlookingmangetslowratingsifheisadullard.So,basically,theattractivenessofmenmakesnodifferenceforhighcharisma(allratingsarehigh)andlowcharisma(allratingsarelow).Finally,let’slookatthemenwhowereaveragelycharismatic.Forthesemenattractivenesshadabigimpact–attractivemengothighratings,andunattractivemengotlowratings.Ifamanhasaveragecharismathengoodlookswouldpullhisratingup,andbeinguglywouldpullhisratingsdown.AsuccinctwaytodescribewhatisgoingonwouldbetosaythattheLooksvariableonlyhasaneffectforaveragelycharismaticmen.
Guided Example A clinical psychologistwas interested in the effects of antidepressants and cognitive behaviour therapy on suicidalthoughts.Fourpeoplediagnosedwithdepressiontookpartinfourconditions:placebotabletwithnotherapyforonemonth,placebotabletwithcognitivebehaviourtherapy(CBT)foronemonth,antidepressantwithnotherapyforonemonth,andantidepressantwithcognitivebehaviourtherapy(CBT)foronemonth.Theorderofconditionswasfullycounterbalancedacrossthe4participants.Participantsrecordedthenumberofsuicidalthoughtstheyhadduringthefinalweekofeachmonth.
Table3:DatafortheeffectofantidepressantsandCBTonsuicidalthoughts
Drug: Placebo AntidepressantTherapy: None CBT None CBT
Andy 70 60 81 52
3. Looks * Charisma
Measure: MEASURE_1
89.600 2.099 84.852 94.34887.100 2.152 82.231 91.96951.800 1.093 49.327 54.27388.400 2.634 82.442 94.35868.900 1.882 64.642 73.15847.000 1.183 44.323 49.67786.700 1.719 82.810 90.59051.200 1.724 47.299 55.10146.100 .971 43.903 48.297
Charisma123123123
Looks1
2
3
Mean Std. Error Lower Bound Upper Bound95% Confidence Interval
Attractiveness
Attractive Average Ugly
Mea
n R
atin
g
0
20
40
60
80
100
High Charisma Some Charisma Dullard
©Prof.AndyField,2016 www.discoveringstatistics.com Page15
Zoë 66 52 70 40
Zach 56 41 60 31
Arlo 68 59 77 49
Mean 65 53 72 43
TheSPSSoutputyougetforthesedatashouldlooklikethefollowing:
Within-Subjects Factors
Measure: MEASURE_1
PLNONEPLCBTANTNONEANTCBT
THERAPY1212
DRUG1
2
DependentVariable
Descriptive Statistics
65.0000 6.2183 453.0000 8.7560 472.0000 9.2014 443.0000 9.4868 4
Placebo - No TherapyPlacebo - CBTAntidepressant - No TherapyAntidepressant - CBT
MeanStd.
Deviation N
Mauchly's Test of Sphericityb
Measure: MEASURE_1
1.000 .000 0 . 1.000 1.000 1.0001.000 .000 0 . 1.000 1.000 1.0001.000 .000 0 . 1.000 1.000 1.000
Within Subjects EffectDRUGTHERAPYDRUG * THERAPY
Mauchly'sW
Approx.Chi-Squa
re df Sig.
Greenhouse-Geiss
erHuynh-Fe
ldtLower-bo
und
Epsilona
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables isproportional to an identity matrix.
May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests aredisplayed in the Tests of Within-Subjects Effects table.
a.
Design: Intercept Within Subjects Design: DRUG+THERAPY+DRUG*THERAPY
b.
Tests of Within-Subjects Effects
Measure: MEASURE_1
9.000 1 9.000 1.459 .3149.000 1.000 9.000 1.459 .3149.000 1.000 9.000 1.459 .3149.000 1.000 9.000 1.459 .314
18.500 3 6.16718.500 3.000 6.16718.500 3.000 6.16718.500 3.000 6.167
1681.000 1 1681.000 530.842 .0001681.000 1.000 1681.000 530.842 .0001681.000 1.000 1681.000 530.842 .0001681.000 1.000 1681.000 530.842 .000
9.500 3 3.1679.500 3.000 3.1679.500 3.000 3.1679.500 3.000 3.167
289.000 1 289.000 192.667 .001289.000 1.000 289.000 192.667 .001289.000 1.000 289.000 192.667 .001289.000 1.000 289.000 192.667 .001
4.500 3 1.5004.500 3.000 1.5004.500 3.000 1.5004.500 3.000 1.500
Sphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-bound
SourceDRUG
Error(DRUG)
THERAPY
Error(THERAPY)
DRUG * THERAPY
Error(DRUG*THERAPY)
Type IIISum of
Squares dfMean
Square F Sig.
©Prof.AndyField,2016 www.discoveringstatistics.com Page16
® EnterthedataintoSPSS.
® Savethedatainafilecalledsuicidaltutors.sav.
® Conduct the appropriate analysis to seewhether the number of suicidal thoughtspatientshadwassignificantlyaffectedbythetypeofdrugtheyhad,thetherapytheyreceivedortheinteractionofthetwo..
Whataretheindependentvariablesandhowmanylevelsdotheyhave?
YourAnswer:
Whatisthedependentvariable?
YourAnswer:
Whatanalysishaveyouperformed?
YourAnswer:
1. DRUG
Measure: MEASURE_1
59.000 3.725 47.146 70.85457.500 4.668 42.644 72.356
DRUG12
Mean Std. ErrorLowerBound
UpperBound
95% ConfidenceInterval
2. THERAPY
Measure: MEASURE_1
68.500 3.824 56.329 80.67148.000 4.546 33.532 62.468
THERAPY12
Mean Std. ErrorLowerBound
UpperBound
95% ConfidenceInterval
3. DRUG * THERAPY
Measure: MEASURE_1
65.000 3.109 55.105 74.89553.000 4.378 39.067 66.93372.000 4.601 57.358 86.64243.000 4.743 27.904 58.096
THERAPY1212
DRUG1
2
Mean Std. ErrorLowerBound
UpperBound
95% ConfidenceInterval
Type of Therapy
No Therapy CBTN
umbe
r of S
uici
dal T
houg
hts
0
20
40
60
80
PlaceboAntidepressant
©Prof.AndyField,2016 www.discoveringstatistics.com Page17
Describetheassumptionofsphericity.Hasthisassumptionbeenmet?(QuoterelevantstatisticsinAPAformat).
YourAnswer:
ReportthemaineffectoftherapyinAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?
YourAnswer:
Reportthemaineffectof‘drug’inAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?
YourAnswer:
ReporttheinteractioneffectbetweendrugandtherapyinAPAformat.Isthiseffectsignificantandhowwouldyouinterpretit?
©Prof.AndyField,2016 www.discoveringstatistics.com Page18
YourAnswer:
In your own time … Task 1 Thereisalotofconcernamongstudentsastotheconsistencyofmarkingbetweenlecturers.Itisprettycommonthatlecturersobtainreputationsforbeing‘hardmarkers’or ‘lightmarkers’butthere isoften littletosubstantiatethesereputations. So, a groupof students investigated the consistencyofmarkingby submitting the sameessay to fourdifferentlecturers.Themarkgivenbyeachlecturerwasrecordedforeachofthe8essays.Itwasimportantthatthesameessayswereusedforalllecturersbecausethiseliminatedanyindividualdifferencesinthestandardofworkthateachlecturerwasmarking.Thedataarebelow.
® EnterthedataintoSPSS.
® Savethedatainafilecalledtutor.sav.
® Conducttheappropriateanalysistoseewhetherthetutorwhomarkedtheessayhadasignificanteffectonthemarkgiven.
® Whatanalysishaveyouperformed?
® ReporttheresultsinAPAformat?
® Do the findings support the idea that some tutorsgivemoregenerousmarks thanothers?
TheanswerstothistaskareonthecompanionwebsiteformySPSSbook.
Table4:Marksof8essaysby4differenttutors
Essay Tutor1(Dr.Field)
Tutor2(Dr.Smith)
Tutor3(Dr.Scrote)
Tutor4(Dr.Death)
1 62 58 63 642 63 60 68 653 65 61 72 654 68 64 58 615 69 65 54 596 71 67 65 507 78 66 67 508 75 73 75 45
©Prof.AndyField,2016 www.discoveringstatistics.com Page19
Task 2 In a previous handout we came across the beer-goggles effect: a severe perceptual distortion after imbibing vastquantitiesofalcohol. Imaginewewantedtofollowthisfindingupto lookatwhatfactorsmediatethebeergoggleseffect.Specifically,wethoughtthatthebeergoggleseffectmightbemadeworsebythefactthatitusuallyoccursinclubs,whichhavedimlighting.Wetookasampleof26men(becausetheeffect isstronger inmen)andgavethemvarious doses of alcohol over four different weeks (0 pints, 2 pints, 4 pints and 6 pints of lager). This is our firstindependentvariable,whichwe’llcallalcoholconsumption,andithasfourlevels.Eachweek(and,therefore,ineachstateofdrunkenness)participantswereaskedtoselectamateinanormalclub(thathaddimlighting)andthenselecta secondmate in a specially designed club that had bright lighting. As such, the second independent variablewaswhethertheclubhaddimorbrightlighting.Theoutcomemeasurewastheattractivenessofeachmateasassessedbyapanelofindependentjudges.Torecap,allparticipantstookpartinalllevelsofthealcoholconsumptionvariable,andselectedmatesinbothbrightly-anddimly-litclubs.ThisistheexampleIpresentedinmyhandoutandlectureinwritinguplaboratoryreports.
® EnterthedataintoSPSS.
® SavethedatainafilecalledBeerGogglesLighting.sav.
® Conducttheappropriateanalysistoseewhethertheamountdrunkandlightingintheclubhaveasignificanteffectonmateselection.
® Whatanalysishaveyouperformed?
® ReporttheresultsinAPAformat?
® Dothefindingssupporttheideathatmateselectiongetsworseaslightingdimsandalcoholisconsumed?
ForanswerslookatthecompanionwebsiteformySPSSbook.
Table5:Attractivenessofdatesselectedbypeopleunderdifferentlightingandlevelsofalcoholintake
DimLighting BrightLighting
0Pints 2Pints 4Pints 6Pints 0Pints 2Pints 4Pints 6Pints
58 65 44 5 65 65 50 33
67 64 46 33 53 64 34 33
64 74 40 21 74 72 35 63
63 57 26 17 61 47 56 31
48 67 31 17 57 61 52 30
49 78 59 5 78 66 61 30
64 53 29 21 70 67 46 46
83 64 31 6 63 77 36 45
65 59 46 8 71 51 54 38
64 64 45 29 78 69 58 65
64 56 24 32 61 65 46 57
55 78 53 20 47 63 57 47
81 81 40 29 57 78 45 42
58 55 29 42 71 62 48 31
63 67 35 26 58 58 42 32
©Prof.AndyField,2016 www.discoveringstatistics.com Page20
49 71 47 33 48 48 67 48
52 67 46 12 58 66 74 43
77 71 14 15 65 32 47 27
74 68 53 15 50 67 47 45
73 64 31 23 58 68 47 46
67 75 40 28 67 69 44 44
58 68 35 13 61 55 66 50
82 68 22 43 66 61 44 44
64 70 44 18 68 51 46 33
67 55 31 13 37 50 49 22
81 43 27 30 59 45 69 35
Task 3 ImagineIwantedtolookattheeffectalcoholhasonthe‘rovingeye’(apparentlyIamratherobsessedwithexperimentsinvolvingalcoholanddating…).The‘rovingeye’effectisthepropensityofpeopleinrelationshipsto‘eye-up’membersof theopposite sex. I took 20men and fitted themwith incredibly sophisticated glasses that could track their eyemovements and recordboth themovement and theobject beingobserved (this is thepoint atwhich it shouldbeapparentthatI’mmakingitupasIgoalong).Over4differentnightsIpliedthesepoorsoulswitheither1,2,3or4pintsofstronglagerinapub.EachnightImeasuredhowmanydifferentwomentheyeyed-up(awomenwascategorizedashavingbeeneyedupiftheman’seyemovedfromherheadtotoeandbackupagain).Tovalidatethismeasurewealsocollectedtheamountofdribbleontheman’schinwhilelookingatawoman.
Table6:Numberofwomen‘eyed-up’bymenunderdifferentdosesofalcohol
1Pint 2Pints 3Pints 4Pints
15 13 18 13
3 5 15 18
3 6 15 13
17 16 15 14
13 10 8 7
12 10 14 16
21 16 24 15
10 8 14 19
16 20 18 18
12 15 16 13
11 4 6 13
12 10 8 23
9 12 7 6
13 14 13 13
12 11 9 12
©Prof.AndyField,2016 www.discoveringstatistics.com Page21
11 10 15 17
12 19 26 19
15 18 25 21
6 6 20 21
12 11 18 8
® EnterthedataintoSPSS.
® SavethedatainafilecalledRovingEye.sav.
® Conducttheappropriateanalysistoseewhethertheamountdrunkhasasignificanteffectontherovingeye.
® Whatanalysishaveyouperformed?
® ReporttheresultsinAPAformat?
® Dothefindingssupporttheideathatmalestendtoeyeupfemalesmoreaftertheydrinkalcohol?
ForanswerslookatthecompanionwebsiteformySPSSbook.
Task 4 Westernpeoplecanbecomeobsessedwithbodyweightanddiets,andbecausethemediaareinsistentonrammingridiculousimagesofstick-thincelebritiesdownintooureyesandbrainwashingusintobelievingthattheseemaciatedcorpsesareactuallyattractive,weallendupterriblydepressedthatwe’renotperfect.Thisgivesevilcorporatetypestheopportunitytojumponourvulnerabilitybymakingloadsofmoneyondietsthatwillapparentlyhelpusattainthebodybeautiful!Well,notwishingtomissoutonthisgreatopportunitytoexploitpeople’sinsecuritiesIcameupwithmy own diet called the ‘Andikins diet’1. The basic principle is that you eat likeme: you eat nomeat, drink lots ofDarjeelingtea,eatshed-loadsofsmellyEuropeancheesewithlotsoffreshcrustybread,pasta,andeatchocolateateveryavailableopportunity,andenjoyafewbeersattheweekend.Totesttheefficacyofmywonderfulnewdiet,Itook10peoplewhoconsideredthemselvestobeinneedoflosingweight(thiswasforethicalreasons–youcan’tforcepeopletodiet!)andputthemonthisdietfortwomonths.TheirweightwasmeasuredinKilogramsatthestartofthedietandthenafter1monthand2months.
Table7:Weight(Kg)atdifferenttimesduringtheAndikinsdiet
BeforeDiet After1Month After2Months
63.75 65.38 81.34
62.98 66.24 69.31
65.98 67.70 77.89
107.27 102.72 91.33
66.58 69.45 72.87
120.46 119.96 114.26
62.01 66.09 68.01
71.87 73.62 55.43
1NottobeconfusedwiththeAtkinsdietobviouslyJ
©Prof.AndyField,2016 www.discoveringstatistics.com Page22
83.01 75.81 71.63
76.62 67.66 68.60
® EnterthedataintoSPSS.
® SavethedatainafilecalledAndikinsDiet.sav.
® Conducttheappropriateanalysistoseewhetherthedietiseffective.
® Whatanalysishaveyouperformed?
® ReporttheresultsinAPAformat?
® Doesthedietwork?
… And Finally, The Multiple Choice Test!
Complete themultiple choice questions forChapter 14 on the companionwebsite to Field(2013):https://studysites.uk.sagepub.com/field4e/study/mcqs.htm.Ifyougetanywrong,re-readthishandout(orField,2013,Chapter14)anddothemagainuntilyougetthemallcorrect.
References Field,A.P.(2013).DiscoveringstatisticsusingIBMSPSSStatistics:Andsexanddrugsandrock'n'roll(4thed.).London:
Sage.
Girden,E.R.(1992).ANOVA:Repeatedmeasures.Sageuniversitypaperseriesonquantitativeapplicationsinthesocialsciences,07-084.NewburyPark,CA:Sage.
Greenhouse,S.W.,&Geisser,S.(1959).Onmethodsintheanalysisofprofiledata.Psychometrika,24,95–112.
Huynh,H.,&Feldt,L.S.(1976).EstimationoftheBoxcorrectionfordegreesoffreedomfromsampledatainrandomisedblockandsplit-plotdesigns.JournalofEducationalStatistics,1(1),69-82.
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.
