Guide to SPSS for Windows S13

8/13/2019 Guide to SPSS for Windows S13

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GuidetoSPSSDr.JohnRuscio p.1of53

GuidetoSPSSforWindows

Dr.JohnRuscio

TheCollegeofNewJersey

Updated: 1/22/2013

SPSSversion19

Thisguideisdesignedtoassiststudentstakingintroductorylevelcoursesinresearch

methodologyandstatisticsaswellasstudentsengagedinotherresearchexperiencesthatinvolvedata

analysis. Thisisnotcopyrightedmaterialandyoumaysave,print,copy,ordistributeit. Thisguideis

organizedintosevenchaptersandtwoappendices. Thefirsttwochaptersdealwithpreliminary

issues,andtheremainingfivechapterscontaininformationaboutusingSPSStomanageandanalyze

data. ThefirsttwoappendiceshelpwithhandcalculationsforcommonlyusedstatisticsthatSPSSdoes

notprovideandthethirdcontainsguidelinesthathelptodetermineanadequatesamplesizewhen

planningastudy.

1. NotationalConventions

Fonts

SymbolsandStatisticalAbbreviations

2. OverviewOfSampleData

3. DataManagement

SettingUpAnSPSSDataFile

UsingSPSSSyntax: PullDownMenus

andCommandSyntax

CreatingNewVariables

Computing

Recoding

IfStatements

NormalizingData

SelectingCases

4. DescriptiveStatistics

Descriptives

FrequenciesExamine

5. Correlation/RegressionAnalyses

Scatterplots

Correlation

Regression

6. ComparingMeans

OneSampletTest

IndependentGroupstTest

RelatedSamplestTest

IndependentGroupsANOVA

RelatedSamplesANOVA

FactorialANOVA

7. ChiSquareAnalyses

2GoodnessofFitTest

2TestofIndependence

AppendixA: CalculatingCohensd

AppendixB: TablesofqValuesforTukeysHSD

AppendixC: EffectSizeandStatisticalPower


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1. NOTATIONALCONVENTIONS

1.1Fonts

TermsthatrefertoSPSSvariablenamesorSPSScommandsappearintheCour i er f ont .

SPSSoutputwascopiedandpastedintothisguideandretainstheformattingusedbySPSS.

1.2SymbolsandStatisticalAbbreviations

Statisticstextsvaryintheiruseofsymbolsandstatisticalabbreviations. Thisguidewillfollow

therulesofAPAstyle(seetheAPAPublicationManual,6thed.,2009,forfulldetails). Statistical

abbreviationsareitalicized,butGreeklettersarenot. (NotethattheGreekalphabetisavailablein

WordyoucanfinditbypressingAltISforinsert,symbolandthenscrollingthroughthefont

options). Unlessotherwisenoted,thefollowingsymbolsandabbreviationsrefertosamplestatistics

ratherthanpopulationparameters:

N=samplesize;n=subsamplesize

M=mean;=populationmean

SD=standarddeviation

Mdn=median

IQR=interquartilerange

SE=standarderror

r=correlationcoefficient(Pearsons)

rpb=pointbiserialcorrelation

rS=Spearmansrho

=phicoefficientSEest=standarderroroftheestimate

df=degreesoffreedom

p=pvalue

=alphalevel

b,a=regressioncoefficients(slope,intercept)

=standardizedregressioncoefficient(slope)

t=tvalue

d=Cohensd(effectsize)

F=Fratio

2=etasquared(effectsize)

2

=chisquare=phi(effectsize)


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2. OVERVIEWOFSAMPLEDATA

Eachprocedureisdescribedandillustratedthroughanalysisofasampledataset,soitmightbe

helpfultounderstandsomethingaboutthesedatawhenexaminingtheoutputinthisguide. These

datacomefromastudyinwhich106studentscompletedsomebackgroundquestionnairesandthen

engagedinajudgmenttask. Thebackgroundquestionnairesincludedthefollowingmeasures:

DemographicdataAseriesofquestionsthatincludedage(inyears),sex(codedas1=male,2=

female),whetherornotvariousmathematicalcourseshadbeentaken(al gforalgebra,geofor

geometry,t r i gfortrigonometry,cal cforcalculus,statcforstatisticscourses,other forother

math/statcourses,andmat hforthetotalnumberofmath/statcourses).

NeedforCognitionScale18itemsthatassesstheextenttowhichindividualsenjoyengagingin

effortful,complexthought. Eachitemisratedona5pointLikertscale,andhalftheitemsarereverse

scored. Variablesinthedatafilearenc1ton18(responsestothe18items),severalreversescored

items(e.g.,nc3r,nc4r,),ncs (NeedforCognitionScalescore,computedasthemeanofthe

availableitemssomeparticipantshadmissingdataonasmallnumberofitems),andncs_group(whetherthescalescorewasabove[2]orbelow[1]themedianforthesample).

Foreachofaseriesof100hypotheticalcases,participantswereprovidedwithasetof

quantitativepredictorsandaskedtomakeapredictionofacriterionvariable. Foreachcase,theywere

alsoaskedtoprovidearangeofvaluessuchthattheywere75%confidentthatthecorrectvaluefell

withintheirrange. Participantsweregiveninstructionsingroupsofupto10butcompletedthetask

individually. Thenatureoftheinformationprovidedforeachcasewasmanipulatedthroughrandom

assignmenttofourexperimentalconditions(codedas1to4inthegroupvariableasfollows):

1. 4S=fourstrongcuesfourquantitativepredictors,eachstronglycorrelatedwiththecriterion

butindependentofoneanother

2. 2S=twostrongcuesanalogousto4Scondition

3. 2S+3W=twostrongplusthreeweakcuessametwopredictorsasin2Scondition,with

additionofthreepredictorsonlyweaklycorrelatedwiththecriterion(andindependentofone

another)

4. 2S+6W=twostrongplussixweakcuesanalogoustothe2S+3Wcondition

Alsomanipulatedviarandomassignmentwassocialaccountability: Onehalfofthe

participantsweretoldinadvancethattheywouldbeaskedtoexplainandjustifytheirjudgment

strategyattheendofthetask,theotherhalfwasnotheldaccountableinthisway. Thisiscodedinthe

account variableas1=accountable,0=notaccountable.

Usingthejudgmentdata,anumberofperformancemeasureswascalculatedforeach

participant:

ConsistencyofjudgmentsThiswascalculatedasthepredictabilityofaparticipantsjudgments

usingastatisticalequation(technically,itwasthevalueofRobtainedforthemodelinwhichthe

availablecuesservedaspredictorsandtheparticipantsjudgmentsservedascriterion). Thisconsi s

variablecouldtakeonvaluesrangingfromthepoorestconsistency(0)toperfectconsistency(1).


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AccuracyofjudgmentsThiswascalculatedasthecorrelationbetweenaparticipantsjudgments

andthecriterionvalues. Eachaccuracymeasurecouldrangefromchancelevelguessing(0)toperfect

accuracy(1);negativevaluesarealsopossible,andtheserepresentperformanceworsethanchance.

Accuracywasmeasuredacrossthefirst100cases(ach100)aswellaswithinfivesuccessiveblocksof

20casesapiece(ach1=cases120,ach2=cases2140,,ach5=cases81100).

ConfidenceThiswascalculatedintwodistinctways. First,theaveragewidthofeach

participantsconfidenceintervalswascomputed. Higherconfidenceisindicatedbynarrowerintervals,

hencelowervaluesoftheci _wi dt hvariablereflectgreaterlevelsofconfidence. Second,the

proportionofconfidenceintervalsthatcontainedtheactualcriterionvaluewascalculated. Thiswas

measuredacrossthefirst100cases(conf 100)aswellaswithinfivesuccessiveblocksof20casesapiece

(conf 1=cases120,conf 2=cases2140,,conf 5=cases81100). Thislattertypeofconfidence

measureshouldbeinterpretedasfollows: scoresbelow.75indicateoverconfidence(participantswere

askedtoget75%correctbutachievedlessthanthis),scoresof.75indicateappropriateconfidence,and

scoresabove.75indicateunderconfidence.


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3. DATAMANAGEMENT

3.1SettingUpAnSPSSDataFile

PriortoenteringanydataintoSPSS,itishelpfultoorganizeandpreparethedatafile. SPSS

requiresthatdatabeenteredsuchthateachrowcontainsdataforonehumanoranimalparticipantand

eachcolumncontainsdataforonevariable. Forexample,anindependentvariablemanipulated

betweensubjectswouldbeenteredusingacolumnthatcontainsnumericalcodesindicatingthe

conditiontowhicheachparticipantwasassigned. Anindependentvariablemanipulatedwithin

subjectswouldrequireusingmultiplecolumnstocontainthedatafortheexperimentalconditions(e.g.,

ifparticipantscompletedamemorytaskatthreepointsintime,thiswouldrequirethreecolumnsto

recordperformanceatthesetimes).

EachvariablemustbegivenanSPSSvariablename,anditishelpfultoassignvariablelabels,

valuelabels,andmissingdataindicatorsaswell. Theeasiestwaytoenterallofthisinformationisto

usetheVariableViewportionofthedatafile(clickonthetabtowardthelowerleftcornerofthedata

screentoenablethisview).1. VariablenamesInthe1stcolumn(Name),enterthevariablenames,oneperrow. Variable

namesshouldbeasshortaspossible,becauseyouwilltypetheseoften.

2. VariablelabelsInthe5thcolumn(Label),enteravariablelabelforeachvariable. Thisisyour

opportunitytoassignamorelengthyanddescriptivelabeltoeachvariable,andyouwillnotbe

requiredtotypethesewhenyouanalyzethedata. SPSSwillusethesevariablelabelswhenever

outputisgenerated,soassigningclearlabelswillhelpyoutomakesenseofyourresults.

3. ValuelabelsInthe6thcolumn(Values),clickwithinacellandthenclickonthebutton

thatappearstoopenawindowforenteringvaluelabels. Thisisdonetoassigndescriptive

labelstonumericalcodesusedforcategoricalvariables. Forexample,ifyouenteredsexusing

thecodesof1and2torepresentmalesandfemales,respectively,youcanassignvaluelabelsso

thatintheoutputfileSPSSwilllabelthesegroupsverballyratherthannumerically. Thisisvery

importantbecauseyoumightforgetwhatcodeswereusedatthestageofdataentrylateron

whenyouanalyzethedata. Inthevaluelabelswindow,enteranumericalcodeinthevalue

space,thenaverballabelinthelabelspace,andclickaddtoaddthistothelistofvalue

labels.Whenallofyourlabelsareentered,clickOKtoclosethiswindow.

4. MissingdataindicatorsInthe7thcolumn(Missing),youcanindicatewhatvalue(s),ifany,

indicatemissingdata. Bydefault,SPSSwillassumethatblankcellsinthedatafilearemissing

data,soyoudonotneedtoenteracodetorepresentmissingvalues. However,sometimesthe

reasonwhydataaremissingisitselfcodedandenteredintothedatafile. Forexample,ifyouusedacodeof8toindicatethataparticipantwrotesomethingillegibleandacodeof9to

indicatethataparticipantskippedthequestion,youwouldneedtoalertSPSSthatthesevalues

shouldnotbeincludedinanyanalysestheyarethereforotherpurposes,suchasselectively

includingorexcludingcaseswithmissingdatainanalysesofothervariables. Toindicate

missingvalues,clickwithinacellandthenclickonthebuttonthatappearstoopena

windowforenteringcodesthatrepresentmissingvalues;theuseofthiswindowisself

explanatory.


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Onceyouhavesetupthedatafile,switchtotheDataView(clickonthistabtowardthe

lowerleftofthedatascreentoenablethisview)andenterthedata.Whenenteringcategoricaldata,be

carefultousethenumericalcodesthatyoudefinedinyourvaluelabels. Also,besuretohandle

missingdataappropriately(e.g.,leaveacellblankorenteranumericalcodedefinedasmissingfora

certainreason). Itisrecommendedthatyousaveyourdatafileregularlytominimizethelossofdataif

theprogram,computer,ornetworkcrasheswhileyouareusingSPSS.

Ifyouaccidentallyenterdataintocolumnsthatdonotcorrespondtovariablesthatyouhave

definedforyourdatafile,highlightthecolumnsbyselectingthemusingthepointeratthelevelofthe

columnheadersandpressdelete. (Thesametechniqueisusefulifyoucreateanewvariablebutlater

decidenottoretainit.) Likewise,ifyouaccidentallyenterdataforrowsthatdonotcorrespondtocases

inthedatafile,youcanhighlighttherowsbyselectingthemattheleveloftherowheadersandpress

delete.

Whenalldataareentered,itisimportantthatyouchecktheaccuracyofyourdataentry. Itmay

betemptingtoproceedimmediatelytotheplanneddataanalyses,butthiscanyielderroneousresultsif

youhavemadeanymistakeswhenenteringthedata. Thereislittlechancethatyouwillnoticethese

mistakesunlessyoulookforthemcarefully. Therearemanywaystocheckfordataentrymistakes,but

noneisaseffectiveaspairingupwithsomeoneelsesuchthatoneofyoureadsoffthedatafromthe

originalsourceandtheotheronechecksthatthismatcheswhatwasenteredintoSPSS. Eventhisisnot

foolproof,butifdoneconscientiouslyyoucanidentifyandcorrectallormostmistakesfairlyeasily.

3.2UsingSPSS: PullDownMenusandCommandSyntax

SPSScontainspulldownmenusthatprovideaccesstomostoftheprogramstools.

Alternatively,youcantypecommandsastext,orsyntax. Thelattermayseemtedious,butthereare

manyadvantagestousingsyntax;themoreoneworkswithdata,themoretheshortcomingsofusing

pulldownmenusbecomeapparent. Inthisguide,pulldownmenusarenotdescribed. Belowisan

overviewofreasonswhyIwouldrecommendthatyoufamiliarizeyourselfwithSPSSsyntaxanduseit

foryourdatamanagementandanalysis:

1. Youcansavearecordofwhatyouhavedone.Whereasyouarelikelytoforgetthepreciseoptions

thatyouselectedfrompulldownmenusandinthewindowsthatappeartorunananalysis,a

syntaxfilewillprovideanexactrecordofyourwork. Thiscanbehelpfullaterwhenwriting

aboutthemethodsandresultsofastudy. Inaddition,ifyouneedtorerunananalysis(e.g.,if

youcollectmoredata,orifyouneedtorespondtoconstructivecriticismbymodifyingyour

analysisplaninsomeway),itsmucheasiertoreopenasavedsyntaxfilethantostartfrom

scratchusingpulldownmenusandwindows.

2. Youcancopyandpastecommands. Beingconfrontedwiththemanychoicesrequiredtoexecutecommandsviapulldownmenusandwindowscanbeabitoverwhelming,whereascopyinga

commandandinsertingyourownvariablesisaneasywaytogetstarted. Also,whenyoure

doingaseriesofsimilaranalyses,copyingandpastingthecommandsiseasierthanworking

throughthepulldownmenusandwindowsrepeatedly,makingminorchangeseachtime.

3. Youcanperformmanydatamanagementtasksmuchmoreeasily. Formanypurposes,itissimpler

andfastertotypecommandsthantousethepulldownmenusandwindows. Forexample,

whenreversescoringitemsand/orcomputingscalescoresfromindividualitems,theequations


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aremucheasiertotypethantopointandclickintoplaceoneelementatatime. Likewise,

recodingortransformingdatatocreatenewvariablesformanyotherpurposesisconsiderably

easierusingsyntaxthanpulldownmenusandwindows.

ThesearejustafewofthesignificantadvantagestolearninghowtouseSPSSsyntax.How

doesitwork? Hereareafewgeneralrules:

1. Syntax

is

entered

into

a

plain

text

file. YoucancreateanewoneoropenanexistingoneviatheFilemenu. Aswhenworkingwithadatafile,itisrecommendedthatyousaveyoursyntax

fileregularlytoavoidlosingworkintheeventofacomputerproblem. Becausedifferentfile

extensionsareusedforSPSSdata(.sav)andsyntax(.sps)files,youcanassignthesamefile

nametoeachwhentheycorrespondtothesamestudy. Forexample,youcansavethedataas

PsychProject.savandthesyntaxasPsychProject.sps. Youcanalsocopyandpastetext

fromotherplaces,suchasSPSShelpwindows,intoyourownsyntaxfiles.

2. Capitalizationisnotimportant. SPSSwillignorethedistinctionbetweenupper andlowercase

letters. Capitalizeasyoulike,ornotatall.

3. Indentationandspacingarenotimportant. UsersfamiliarwitholderversionsofSPSSwillbeused

toidentifyingthebeginningofanewcommandbyplacingitontheleftmargin,with

subsequentlinesofacommandindented. SPSSnolongerrequiresthis,andyouarefreeto

indent(ornot)anylines,atyourdiscretion. Likewise,youcanleavespaceswithinorbetween

linesasyouseefit.

4. Useanasterisktoplacesnotesinthesyntaxfile. Likeanyotherprogrammingenvironment,SPSS

allowsyoutoaddyourownnotesandcommentsinafilethatwillnotbeexecutedas

commands. Todothis,beginalinewithatleastoneasterisk(*). Anythingthatfollowsan

asteriskwillbeignoredbySPSS.

5. Eachcommandmustbefollowedbyaperiod. SPSSdoesrequirethatyouendeachcommandwitha

period.Notethatacommandmayspanmultiplelines,inwhichcaseasingleperiodshouldappearattheendofthefinalline,notoneachline.

6. Commandsarenotexecutedasyoutypethem. Simplytypingacommandintoasyntaxfilewillnot

causeSPSStotakeanyaction. YouhavetoruncommandsforSPSStoexecutethem. Thereare

manywaystorunoneormorecommands. Perhapsthesimplestistohighlightthemandthen

pressCtrlR(orthegreentrianglenearthetopofthescreen). Therearealsoseveralself

explanatoryoptionsavailablefromtheRunmenuofasyntaxwindow.Whencommands

modifyadatafile(e.g.,whenyoucomputenewvariables),itisuptoyouwhethertosavethe

datafilewiththesechangestheyarenotautomaticallysaved.

Thisguidewillpresentthesyntaxforcommonlyusedcommands,andthereareseveralwaysto

learnmoreaboutSPSScommands. Ifyoufindatoolonapulldownmenuandwouldliketoknow

howtouseitviasyntaxinstead,onceyouhavemadetherequiredselectionsinthewindow(s)toget

theproceduretorunclickonthePastebuttoninsteadoftheOKbutton. Thiswilltranslateyour

selectionsintotheappropriateSPSScommandandplaceitintothesyntaxwindow. Then,youcan

savethesyntaxforfutureuse,modifyit,orcopyandpasteittorunaseriesofsimilaranalyses. In

addition,SPSSprovidesawealthofhelpfulinformationinavarietyofformsthatyoucanexplore

usingtheHelpmenu. Forexample,selectingCommandSyntaxReferencewillopenadetailed


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PDFfilethatdescribesandillustratesallavailableSPSScommandsinanindexedandcrossreferenced

format.

3.3CreatingNewVariables

Therearemanycircumstancesunderwhichyoumightwanttocreatenewvariables,andSPSS

providesmanywaystodothis. Forexample,thesampledatasetcontainsresponsestothe18itemsontheNeedforCognitionScale,andthesewereusedtocomputeascalescore. Someoftheitemswere

wordednegatively,meaningthattheyhadtobereversescoredbeforecombiningthemwithother

itemstocomputethescalescore. Forsomepurposes,itwashelpfultoassignparticipantstohigh and

lowscoringgroupsonthescale,andacommandisavailabletorecodevaluestoformanewvariable.

Asanotherexample,thetotalnumberofmath/statscourseswascalculatedbyaddingtogethervalues

foraseriesofvariablescorrespondingtoindividualcourses.

Insomesituations,youmightwanttotransformavariabletochangetheshapeofits

distributionsothatitbetterapproximatesnormalityandmeetstheassumptionsofastatisticaltest.

Almostanylogicalormathematicalexpressionthatyoucandevisetotransform,recode,orcomputea

newvariablefromexistingdatacanbeimplementedusingSPSS. Afewofthemostusefulcommands

willbeoutlinedbelow.

3.3.1Computing. Thecomput ecommandallowsyoutocreateanewvariableusingmostany

mathematicalorlogicalexpressionthatyoucanspecify.Manymathfunctionsarebuiltin,including

notonlythestandardarithmeticoperators,butalsoexponentsandroots,logarithms,andmanyothers.

Hereisasamplingofsimplemathematicaltransformationsofoneormoreofthevariablesfromthe

sampledatasetthatwasdescribedearlier(forsimplicity,thenewvariableisnamedyineachcase,but

ofcourseyouwoulduseadifferentnameforeachnewvariableyoucreate):

Command Operation

compute y = al g + geo + t r i g . sumofthethreevariables,whichwouldrepresenthow

manyofthethreehadbeentaken

comput e y = 6 nc3 . thisreversescorestheitem(i.e.,51,42,33,24,

and15)

compute y = al g * t r i g . productofthevariables(whichwouldbe1forthosewho

tookbothcourses,0otherwise)

comput e y = ncs / 5 . ratioofncs scoretothehighestpossiblescore

comput e y = ncs ** 3 . cubeofncs ;the** operatormeansraisetothepowerof

comput e y = ncs ** ( 1/ 3) . cuberootofncs

comput e y = sqr t ( ncs) . squarerootofncs (equivalenttoncs ** ( 1/ 2) )

comput e y = l n(ncs) . natural(basee)logarithmofncs

compute y = exp( ncs) . exponent(basee)ofncs

comput e y = l g10(ncs) . base10logarithmofncs


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comput e y = 10 ** ncs . exponent(base10)ofncs

Onewidelyusedfunctionprovidesashortcutforaveragingseveralothervariables. Thisis

especiallyhelpfulwhencreatingscalescoresusingindividualitems:

comput e y = mean( nc1, nc2, nc3r , nc4r , nc5r , nc6, nc7r , nc8r , nc9r , nc10,nc11, nc12r , nc13, nc14, nc15, nc16r , nc17r , nc18) .

Bydefault,themeanfunctionwillreturnamissingvalueforanycasethatismissingdataononeor

morevariablesinvolvedinacomputation.However,youcanallowthemeantobecalculatedevenifa

caseismissingdataononeormorevariables. Oneruleofthumbistorequirethatdatabeavailablefor

approximately80%oftheitems(ormore)tocalculatethemean,otherwisethenewvariableisgivena

missingvalue. Forexample,80%ofthe18itemsontheNeedforCognitionScaleisabout14items:

comput e y = mean. 14( nc1, nc2, nc3r , nc4r , nc5r , nc6, nc7r , nc8r , nc9r , nc10,nc11, nc12r , nc13, nc14, nc15, nc16r , nc17r , nc18) .

Byusingmean. 14ratherthanmean,thisrequiresthatsomeonehadrespondedtoatleast14outofthe

18variablestocalculatethescalescore,orelsethepersonsscalescoreislistedasmissing. Iftherewere100itemsonaquestionnaire,youmightcalculatethemeanusingmean. 80torequirethatdatabe

presentfor80%ofthevariables.

Inadditiontomathfunctions,thecomputecommandwillalsohandlelogicalexpressions,

whichareevaluatedastrue=1andfalse=0. Forexample,supposethatyouwantedtocreateanew

variablethatisscoredas1forwomenaged20+and0foreveryoneelseinthedatafile:

comput e y = ( sex = 2) and ( age >= 20) .

Noticethattherearetwologicalexpressionshere,oneforsexandoneforage. Eachisevaluatedas

true=1andfalse=0,thentheresultsarecombinedusingand

toyieldanoverallscoreof1iftheentireexpressionistrueand0iffalse. SPSSwillrecognizethelogicaloperatorsofand,or,andnot .

Finally,notethatyoucancombinelogicalandmathematicaloperatorsandfunctions. For

example,theandinthepreviouscommandlinecouldbereplacedwith* ;multiplyingtwological

expressionsisequivalenttodeterminingwhethertheyarebothtrue. Asalesstrivialexample,suppose

thatyouwanttoscoreaquizthatcontains5multiplechoiceitems,withcorrectanswersofB,C,A,D,

andA,respectively. Ifthedatawereenteredintovariablesnamedx1tox5,withletterresponses

codedusingnumbers,thescoringcommandwouldbe:

comput e qui z = ( x1 = 2) + ( x2 = 3) + ( x3 = 1) + ( x4 = 4) + ( x5 = 1) .

Thiscombinestheevaluationoflogicalexpressions(i.e.,x1 = 2istrueforsomeonewhoansweredthefirstitemcorrectly,falseotherwise)andamathematicalexpression(i.e.,summingtheresultsfromthe

fivelogicalexpressions,eachofwhichyieldsavalueof0or1). Theresultingqui zvariablewould

containthenumberofitemsthateachpersonansweredcorrectly,from0to5.

3.3.2Recoding. Ther ecodecommandishelpfulwhenyouwanttoreassignvaluesfroman

existingvariabletocreateanewversionofthevariable. Forexample,ifyouhaveacategoricalvariable


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inwhichsomecategorieswereusedinfrequently,youmaywishtocombinethemforanalysis. Or,for

certainpurposesyoumightwanttosplitcaseswhovaryalongacontinuousvariableintocategories.

Ther ecodecommandrequiresthatyouspecifyanexistingvariable,aseriesofconditionsbywhich

valuesarerecoded,andthenthenewvariabletobecreated. Forexample,hereishownc3couldbe

reversescoredtocreateanewvariablenamednc3r :

r ecode nc3 ( 1 = 5) ( 2 = 4) ( 3 = 3) ( 4 = 2) ( 5 = 1) i nto nc3r .

Thisisequivalenttothecommandcomput e nc3r = 6 nc3andillustratestheuseofparentheses

tospecifyeachconditionforrecodingvalues. Hereisanexampleinwhichsomeinfrequentvaluesare

combinedinanewversionofavariable:

r ecode math ( 2, 3 = 1) ( 4 = 2) ( 5, 6, 12 = 3) i nto math3 .

Thistakesavariablethatcontainssomeinfrequentvalues(e.g.,fewstudentstook2,6,or12math

courses)andtransformsitintoanewvariablewiththreegroupsthataresufficientlylargetoperform

statisticalcomparisons: Everyonewhotook2or3mathcourses(n=18),4mathcourses(n=56),and5

ormoremathcourses(n=31).

SPSSwillalsorecognizethenotationofl oandhi torepresentthelowestandhighestvalueson

avariableaswellasthrutoindicatearangeofvalues. Forexample,scoresontheNeedforCognition

Scale(ncs)variedfrom1.611to4.611,andwith50%ofscoresbelow3.6and50%above3.6. Youcould

calculateanewvariablethatindicateswhetherornoteachcasescoredabovetheMdnasfollows:

r ecode ncs ( l o t hr u 3. 59 = 1) ( 3. 60 t hr u hi = 2) i nt o ncs_grp .

Thenewvariablencs_gr pisadichotomizedversionoftheoriginallycontinuousvariablencs .

Finally,SPSSalsorecognizesthenotationofel se,suchthatyoucanincludeacatchall

categoryinther ecodecommandforvaluesnotidentifiedinearlierconditions. Forexample,the

earlierexampleofrecodingthenumberofmathcoursesintothreecategoriescouldbesimplifiedas

follows:

r ecode math ( 2, 3 = 1) ( 4 = 2) ( el se = 3) i nt o math3 .

Thefinalconditionwouldincludeeveryonewhohadtakenanumberofcoursesotherthan2,3,or4

inthiscase,5,6,or12andincludetheminthe3rdcategory.

Afinalnoteonther ecodecommand: Technically,youarenotrequiredtofollowtheseriesof

parentheseswithi nt oandanewvariablename. However,ifyouleavethisoffSPSSwilloverwrite

theoriginalvariablewiththetransformedvalues. Itisrecommendedthatyouneverdothisbecause(a)

youmaywishtousetheoriginaldataforotherpurposesand(b)youmightforgetthattheoriginaldatahasbeenrecoded. Creatinganewvariableissafest,preventingthereentryormisinterpretationof

datathathasbeenrecoded.

3.3.3IfStatements. Anotherwaytocreatenewvariablesistousethei fcommand.Whenever

aspecifiedlogicalexpressionistrue,acalculationisperformed. Forexample,youcancombine

responsesacrossmultiplevariables(e.g.,sexandage)toclassifyindividuals:


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i f ( sex = 1) and (age < 20) sex_age = 1 .

i f ( sex = 1) and (age >= 20) sex_age = 2 .

i f ( sex = 2) and (age < 20) sex_age = 3 .

i f ( sex = 2) and (age >= 20) sex_age = 4 .

Thisseriesofcommandswouldyieldanewvariable,sex_age,thatvariesacrossfourcategories: 1=

youngermen,2=oldermen,3=youngerwomen,4=olderwomen.

Thecomputationaloptionsfollowingthelogicalexpressionarethesameasthoseforthe

comput ecommand. Inotherwords,youcanspecifyaconditionandthenindicateassimpleor

complexacomputationasyouliketotakeplacewhenconditionisevaluatedastrue. Aswiththe

comput ecommand,thecomputationcaninvolvemathematicaloperatorsorfunctions,logical

expressionsandoperators,oracombinationofthese.

Asafinalnoteonthecreationofnewvariables,theoptionsavailableusingthecomput e,

r ecode,andi f commandsarenotmutuallyexclusive. Often,youcanachievethesameresultsusing

differentcommands,butoneapproachmaybesimplerormoreintuitive. Forexample,supposethat

thevariablecl assiscodedas1=freshman,2=sophomore,3=junior,4=senior. Eachofthefollowingcommands(orblocksofcommands)createsanewvariableuppercl ass torepresent

whetherornotastudentisajunior/senior(codedas1)orafreshman/sophomore(codedas0):

comput e uppercl ass = ( cl ass = 3) or ( cl ass = 4) .

comput e uppercl ass = ( cl ass >= 3) .

r ecode cl ass ( 1 = 0) ( 2 = 0) ( 3 = 1) ( 4 = 1) i nt o uppercl ass .

r ecode cl ass ( 1, 2 = 0) ( 3, 4 = 1) i nt o upper cl ass .

i f ( cl ass = 1) upper cl ass = 0 .i f ( cl ass = 2) upper cl ass = 0 .i f ( cl ass = 3) upper cl ass = 1 .i f ( cl ass = 4) upper cl ass = 2 .

i f ( cl ass = 1) or ( cl ass = 2) upper cl ass = 0 .i f ( cl ass = 3) or ( cl ass = 4) upper cl ass = 1 .

i f ( cl ass = 3) upper cl ass = 1 .

3.4NormalizingData

Sometimes,avariablesdistributiondeviatessubstantiallyfromnormality(e.g.,extreme

positiveornegativeskew),andthiscanbeproblematicwhenastatisticaltestassumesthatthe

populationdistributionisnormal. Ifthereareasmallnumberofoutliersorextremescores,thenthese

mightberemovedpriortoanalysis(seesection3.5forhowtoselectorremovecasesforanalysis). If

valuesspanasmallnumberofscores,suchasresponsestoanitemwitha5pointratingscale,there

maybenowaytotransformthedatatobetterapproximatenormality. Providedthatvaluesspana

largenumberofscores,therearemanytransformationsthatmayhelptobetterapproximatenormality.

Forexample,forapositivelyskewedvariable,onemighttrytakingthesquarerootorlogarithmofthe


12/53


originalscores. Atransformationthatcanworkextremelywellistoconverttozscoresthrough

percentiles(oftenreferredtoasapercentiletransformation). Essentially,eachoftheoriginalscoresis

convertedtoapercentile,andthenthispercentileisconvertedtothezscoreatthatpercentile. This

ignoressometechnicaldetailsinvolvinghowtohandlethemostextremescores,becausezscoresfor

percentilesof0and100areundefined. Inthetechniquedescribedbelow,themethodthatSPSSlabels

asRankitisused;seetheSPSSmanualforinformationaboutthisandotheroptions.

SPSScannormalizedatausingthepercentiletransformationwithther ankcommand. For

example,thevariablerepresentingjudgmentaccuracyforthefirst100casesexhibitedamodestamount

ofnegativeskewinitsdistribution(seehistogramontheleft,below). Thefollowingcommand

transformsthisintoanewvariablenamedach100n(thenwasaddedtoindicatethatitisa

normalizedversionoftheoriginalvariable):

r ank vars = ach100/ f r acti on = r anki t/ normal i nt o ach100n .

Allthatyouneedtospecifyisthenameofyouroriginalvariable(here,thatwasach100)andthenew

variablethatwillcontainthetransformedvalues(here,thatwasach100n). Thenewvariableapproximatesanormaldistributionveryclosely(seehistogramontheright,below). Inparticular,

thereisnoskewthedistributionnowisperfectlysymmetric.

Acc uracy , 100 cases

0.6000.5000.4000.3000.2000.1000.000

Frequency

25

20

15

10

5

0

Accurac y, 100 cases

Mean =0.379 Std. Dev. =0.087N =106

Normal Score of ach100 using Rankit's Formula

3.00002.00001.00000.0000-1.0000-2.0000-3.0000

Frequency

12.5

10.0

7.5

5.0

2.5

0.0

Normal Score of ach100 using Rankit's Formula

Mean =-6.90E-6 Std. Dev. =0.9987N =106

Onefinalnoteonthepercentiletransformation: Inadditiontonormalizingdata,italso

standardizes. Intheexampleshownabove,notethatfortheoriginalvariable(ach100),M=.38and

SD=.09,whereasforthetransformedvariable(ach100n),M=.00andSD=1.00(notethatSPSSuses

scientificnotationforverysmallorverylargevaluestheMof6.90E6forthenormalizedvariableis

equivalentto.0000069). Normalizingisachievedbytransformingtoadistributionwhoseshape

approximatesnormality,andstandardizingisachievedbytransformingtoadistributionwhoseM=0

andSD=1.Normalizingandstandardizingareseparateanddistinctprocesses,butthepercentile

transformationhappenstoachievebothofthese.


13/53


3.5SelectingCases

Often,onewishestoworkwithasubsampleofthedata. Forexample,afterexaminingthe

relationshipbetweenvariablesinthefullsample,onemightrepeattheanalysiswithinasubsample

consistingonlyofmen,andtheninasubsampleconsistingonlyofwomen. Youcanidentifya

subsampleofcasesusinganylogicalexpression,howeversimpleorcomplex. Forexample,specifying

sex = 1willyieldanallmalesubsample,andsex = 2anallfemalesubsample. Thesyntaxforselectingasubsampleforanalysisisasfollows:

t emporary .sel ect i f ( logical expression) .analysis .

Thelogicalexpressionisusedtoidentifyyoursubsample(e.g.,sex = 1orsex = 2),andit

canbeassimpleorcomplexasyoulike. Forexample,multipleconditionscanbespecified,andthe

logicaloperatorsand,or,andnot canbeused. Theanalysisiswhatevercommandyouwishto

performusingasubsampleofdata,typicallyastatisticalanalysis. Thet empor arycommandindicates

thatthesampleshouldberestrictedtothespecifiedsubsampleforonlyoneanalysis. Thisisoptional,

buthighlyrecommended,becauseifyoudonotincludethisyoursamplewillberestrictedforall

subsequentanalyses. Forexample,ifyouusesel ect i f ( sex = 1) withoutprecedingitwith

t empor ary,SPSSwillremoveallcasesforwhichsex 1fromyourdatafile. (Ifyouthensavethe

datafile,youwillhavepermanentlydeletedallbutthemen.) Ifyouproceedtousesel ect i f ( sex

= 2) torepeatananalysisamongwomen,youwillgetanerrormessagebecauseyouhavealready

restrictedthesampletomen.Hence,itissafesttoalwaysuset empor arywithsel ect i f .

Asanexample,youcouldexaminethedistributionofNeedforCognitionScalescoreswithin

eachsexusingthefrequenciescommand(describedinthenextchapter)asfollows:

t emporary .

sel ect i f ( sex = 1) .f r eq var s = ncs

/ per 25 50 75/ st at s al l/ hi st nor mal .

t emporary .sel ect i f ( sex = 2) .f r eq var s = ncs

/ per 25 50 75/ st at s al l/ hi st nor mal .


14/53


4. DESCRIPTIVESTATISTICS

4.1Descriptives

Thedesccommandprovidesaveryconcisetableincludingthevalid(nonmissing)N,

minimumvalue,maximumvalue,M,andSDforoneormorevariables. Forexample,thefollowing

commandwouldprovidedescriptivestatisticsforfourofthevariablesinthesampledatafile;the

outputisshownbelow:

desc var s = age ncs mat h ach100 .

Descriptive Statistics

105 17 31 19.11 1.706

106 1.611 4.611 3.54776 .516049

105 2 12 4.18 1.090

106 .090 .566 .37929 .087445

104

Age (Years)

NCS Score

Total # math courses

Accuracy, 100 cases

Valid N (listwise)

N Minimum Maximum MeanStd.

Deviation

NotethatthevalidNdiffersacrossvariablesbecausetherearemissingdataforsomebutnotallof

them. TheValidN(listwise)indicatesthenumberofcaseswithcompletedataonallvariablesinthe

table. ItisrecommendedthattheshapesofdistributionsbeexaminedtodeterminewhethertheMand

SDareappropriatedescriptivestatisticstosummarizeeachvariable. Forthisreason,anexampleof

howtoreporttheseresultsinAPAstylewillbedelayeduntiltheendofthissection.

Thedescriptivescommandcanbeusedasashortcutforcreatinganewvariableasazscore

transformationofanexistingvariable(aka,forstandardizingavariable). Forexample,usingresultsin

thetableshownaboveonecouldwriteacomputestatementtocalculateanewvariableasthezscore

versionofncs . Alternatively,onecouldusethedescriptivescommand. Thefollowingtwocommands

wouldeachyieldthesamenewvariablezncs :

comput e zncs = ( ncs 3. 54776) / . 516049 .

desc vars = ncs/ save .

4.2Frequencies

Thef reqcommandprovidesnotonlymoredescriptivestatistics,butalso(optionally)ahistogramforeachvariable. Itisrecommendedthatyourequestallstatistics(onthe2ndlineofthe

samplesyntax,below)aswellashistogramswithsuperimposednormalcurves(onthe3rdline)and

quartiles(onthe4thline).Hereisanexample,followedbysampleoutput:

f r eq var s = sex age ncs mat h ach100/ st at s al l/ hi st nor mal/ per = 25 50 75 .


15/53


Theoutputbeginswithatableofdescriptivestatistics,arrangedwithonecolumnpervariable.

ThisincludesthevalidNandnumberofmissingcases,M,Mdn,mode,SD,minimumandmaximum

values,andassortedotherdescriptivestatistics,includingthe25th,50th,and75thpercentiles. Because

thiscommanddoesnotprovidetheIQR,youcaneasilycalculateitasQ3Q1,whereisthe3rdquartile

(75thpercentile)andQ1isthe1stquartile(25thpercentile). Forexample,forthevariablencs,IQR=

3.944443.15278=.79166. AlsonotethatSPSSwillcalculateeverystatisticforeveryvariable,even

whenitmaynotbemeaningful(e.g.,Mofaqualitativevariable)youneedtodecideforyourselfwhichpiecesoftheoutputtousewheninterpretingorreportingyourresults.

Statistics

106 105 106 105 106

0 1 0 1 0

1.74 19.11 3.54776 4.18 .37929

.043 .166 .050123 .106 .008493

2.00 19.00 3.59967 4.00 .39825

2 18 3.556 4 .457

.443 1.706 .516049 1.090 .087445

.196 2.910 .266 1.188 .008

-1.085 3.326 -.644 3.401 -.994

.235 .236 .235 .236 .235

-.838 21.528 .668 24.835 1.247

.465 .467 .465 .467 .465

1 14 3.000 10 .476

1 17 1.611 2 .090

2 31 4.611 12 .566

184 2007 376.062 439 40.204

1.00 18.00 3.15278 4.00 .33868

2.00 19.00 3.59967 4.00 .39825

2.00 20.00 3.94444 5.00 .43768

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness

Std. Error of Skewness

Kurtosis

Std. Error of Kurtosis

Range

Minimum

Maximum

Sum

25

50

75

Percentiles

Sex (1=M 2=F) Age (Years) NCS Score

Total # math

courses

Accuracy,

100 cases

Next,afrequencytableisprovidedforeachvariable. Thisincludesthefrequencyforeach

valueobservedinthedata,thepercentofcasesatthatscore(whichiscalculatedoutofthetotal

numberofcases),thevalidpercentofcasesatthatscore(calculatedaftermissingdataareexcluded),

andthecumulativepercent(basedonvalidpercents).

Sex (1=M 2=F)

28 26.4 26.4 26.4

78 73.6 73.6 100.0

106 100.0 100.0

male

female

Total

ValidFrequency Percent Valid Percent

CumulativePercent


16/53


Age (Years)

9 8.5 8.6 8.6

35 33.0 33.3 41.9

24 22.6 22.9 64.8

20 18.9 19.0 83.8

15 14.2 14.3 98.1

1 .9 1.0 99.01 .9 1.0 100.0

105 99.1 100.0

1 .9

106 100.0

17

18

19

20

21

2231

Total

Valid

SystemMissing

Total

Frequency Percent Valid PercentCumulative

Percent

NCS Score

1 .9 .9 .9

1 .9 .9 1.9

1 .9 .9 2.8

1 .9 .9 3.8

1 .9 .9 4.71 .9 .9 5.7

2 1.9 1.9 7.5

4 3.8 3.8 11.3

7 6.6 6.6 17.9

3 2.8 2.8 20.8

1 .9 .9 21.7

3 2.8 2.8 24.5

1 .9 .9 25.5

2 1.9 1.9 27.4

2 1.9 1.9 29.2

6 5.7 5.7 34.9

4 3.8 3.8 38.7

2 1.9 1.9 40.6

1 .9 .9 41.5

8 7.5 7.5 49.1

1 .9 .9 50.0

4 3.8 3.8 53.8

3 2.8 2.8 56.6

4 3.8 3.8 60.4

2 1.9 1.9 62.3

5 4.7 4.7 67.0

1 .9 .9 67.9

4 3.8 3.8 71.7

5 4.7 4.7 76.4

3 2.8 2.8 79.2

6 5.7 5.7 84.9

5 4.7 4.7 89.6

1 .9 .9 90.6

3 2.8 2.8 93.4

3 2.8 2.8 96.2

2 1.9 1.9 98.1

1 .9 .9 99.1

1 .9 .9 100.0

106 100.0 100.0

1.611

2.389

2.444

2.667

2.7062.824

2.833

2.889

2.944

3.000

3.056

3.111

3.167

3.222

3.278

3.333

3.389

3.444

3.500

3.5563.588

3.611

3.667

3.722

3.778

3.833

3.882

3.889

3.944

4.000

4.056

4.111

4.118

4.167

4.222

4.333

4.389

4.611

Total

Valid

Frequency Percent Valid P ercentCumulative

Percent


17/53



3 2.8 2.9 2.9

15 14.2 14.3 17.1

56 52.8 53.3 70.5

28 26.4 26.7 97.1

2 1.9 1.9 99.0

1 .9 1.0 100.0105 99.1 100.0

1 .9

106 100.0

2

3

4

5

6

12Total

Valid

SystemMissing

Total


Percent

Thetableforach100wasomittedbecauseeachparticipanthadauniqueaccuracyscore;hence,

thetablecontained106entries,eachwithafrequencyof1.

Finally,ahistogramisprovidedforeachvariable. Thisincludesasuperimposednormalcurve

generatedusingthemeanandstandarddeviationforthatvariable,whichcanbehelpfulinassessing

theextenttowhichavariablesdistributionisnormal.NotethatSPSSwillprovideahistogram(with

normalcurve)evenforqualitativedata(e.g.,sex),whentheshapeofadistributionmaybe

meaningless.

2.42.11.81.51.20.90.6

Sex (1=M 2=F)

100

80

60

40

20

0

Frequency

Mean =1.74 Std. Dev. =0.443N =106

Sex (1=M 2=F)


18/53


3027242118

Age (Years)

40

30

20

10

0

Frequency

Mean =19.11 Std. Dev. =1.706N =105

Age (Years )

4.0002.000

NCS Score

25

20

15

10

5

0

Frequency

Mean =3.54776 Std. Dev. =0.516049N =106

NCS Score


19/53


121086420


60

50

40

30

20

10

0

Frequency

Mean =4.18 Std. Dev. =1.09N =105


0.6000.5000.4000.3000.2000.1000.000

Acc uracy, 100 cases

25

20

15

10

5

0

Frequency

Mean =0.37929 Std. Dev. =0.087445N =106

Accu racy, 100 cases

Thefrequenciescommandprovidesadequateoutputtodescribedata,becauseyoucanevaluate

theshapesofdistributionsforquantitativevariablestodeterminethemostappropriatedescriptivestatisticstoreport.

Whenoutliersareidentified,itcanbehelpfultocalculatedescriptivestatisticsaftertheremoval

oftheoutliers. Thefollowingcommandsillustratehowtodothisusingt empor aryandsel ect i f :


20/53


t emporary .sel ect i f ( age < 31) .f r eq vars = age

/ st at s al l/ hi st nor mal/ per 25 50 75 .

Statistics

Age (Years)

104

0

19.00

.122

19.00

18

1.246

1.553

.307

.237

-.872

.4695

17

22

1976

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness


Kurtosis

Std. Error of KurtosisRange

Minimum

Maximum

Sum

Age (Years)

9 8.7 8.7 8.7

35 33.7 33.7 42.3

24 23.1 23.1 65.4

20 19.2 19.2 84.6

15 14.4 14.4 99.01 1.0 1.0 100.0

104 100.0 100.0

17

18

19

20

2122

Total

Valid


Percent


21/53


2322212019181716

Age (Years)

40

30

20

10

0

Frequency

Mean =19 Std. Dev. =1.246N =104

Histogram

t emporary .sel ect i f ( mat h < 12) .f r eq vars = mat h

/ st at s al l/ hi st nor mal/ per 25 50 75 .

Statistics


104

0

4.11

.076

4.00

4

.775

.600

-.314

.237

.482

.469

4

26

427

Valid

Missing

N

Mean

Std. Error of Mean

Median

Mode

Std. Deviation

Variance

Skewness


Kurtosis

Std. Error of Kurtosis

Range

Minimum

Maximum

Sum


22/53



3 2.9 2.9 2.9

15 14.4 14.4 17.3

56 53.8 53.8 71.2

28 26.9 26.9 98.1

2 1.9 1.9 100.0

104 100.0 100.0

2

3

4

5

6

Total

Valid

Frequency Percent Valid PercentCumulative

Percent

7654321


60

50

40

30

20

10

0

Frequ

ency

Mean =4.11 Std. Dev. =0.775N =104

Histogram

Forboththeageandmat hvariables,distributionswereapproximatelynormalwhenasingleoutlier

wasremovedfromtheupperendofeachdistribution.Havingremovedtheoutliers,therecalculated

MandSDwouldbeappropriatedescriptivestatistics.

4.3Examine

Theexami necommandalsoprovidesawealthofinformationabouteachvariable,andthereis

someoverlapwiththeoutputofthefrequenciescommand.Notethatthesubcommandrequeststhat

allavailablecasesbeincludedfortheexaminationofeachvariable;ifyouomitthis,thedefaultisto

dropcasesfromtheanalysisiftheyaremissingdataononeormoreofthevariables. Thecommandis:

exami ne age ncs mat h ach100/ mi ssi ng pai r wi se .


23/53


Case Processing Summary

104 98.1% 2 1.9% 106 100.0%

104 98.1% 2 1.9% 106 100.0%

104 98.1% 2 1.9% 106 100.0%

104 98.1% 2 1.9% 106 100.0%

Age (Years)

NCS Score


Accuracy, 100 cases

N Percent N Percent N Percent

Valid Missing Total

Cases

Theoutputbeginswithatablethatsummarizestheextentofmissingdata(above). Inwhat

follows,onlytheoutputforncs ispresentedtoillustratethiscommandandsavespace(thefulloutput

forallvariableswouldbeverylengthy).


106 100.0% 0 .0% 106 100.0%NCS ScoreN Percent N Percent N Percent

Valid Missing Total

Cases

Thetableofdescriptivestatisticsincludesthoseprovidedbythefrequenciescommand,plus

somethatwerenot,includingtheIQR(inthetablebelow,notethattheIQR=.792,thesameaswhat

wascalculatedusingthequartilesprovidedbythefrequenciescommand):

Descriptives

3.54776 .050123

3.44837

3.64714

3.56648

3.59967.266

.516049

1.611

4.611

3.000

.792

-.644 .235

.668 .465

Mean

Lower Bound

Upper Bound

95% Confidence

Interval for Mean

5% Trimmed Mean

MedianVariance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

NCS ScoreStatistic Std. Error

Nextarethegraphicaldisplays: astemandleafplotandaboxplot(akaboxandwhiskersplot).

Theformerisdescribedinmostanystatisticstextandisfairlyselfexplanatory. Inaboxplot,thebox

extendsfromthe1st

to3rd

quartilevaluesinthedata(i.e.,itspanstheIQR),withtheMdnplottedasahorizontallinewithinthebox. Thewhiskersextendfurther,includingthemostextremevalueswithin

1.5IQRofthebox. Anyoutliersorextremescoresareplottedassymbolsevenfurtherout. Inthe

outputshownbelow,boththestemandleafdisplayandtheboxplotsuggestthatalthoughthe

distributionofNCSscalescoresismildlynegativelyskewed,withonecase(#67inthedataset,witha

scoreof1.611)worthcheckingasapossibleoutlieronthelowend,itapproximatesnormalityfairly

well.


24/53


NCS Scor e Stem- and- Leaf Pl ot

Fr equency St em & Leaf

1. 00 Ext r emes ( =


25/53


Theexaminecommandcanbeusedtocomparesubsamplesidentifiedbyacategoricalvariable.

Forexample,thefollowingcommandwouldprovidedescriptivestatisticsandgraphsforncs inthe

fullsampleandthenwithinsubsamplesofmenandwomen:

exami ne ncs by sex/ mi ssi ng pai r wi se .


26/53


5. CORRELATION/REGRESSIONANALYSES

5.1Scatterplots

Priortocalculatingcorrelationcoefficientsorregressionequations,itisimportanttoexamine

therelationshipsbetweenvariables. Ascatterplotdisplaystherelationshipbetweentwovariablesby

plottingadatapointforeachcaseinthesample. Thelocationofeachpointindicatesitsscoresonthetwovariables.Hereisanexampleofascatterplotbetweenconsistency(consi s)andaccuracy

(ach100)ofparticipantsjudgments:

graph/ scat t er pl ot ( bi var ) = consi s wi t h ach100 .

1.0000.8000.600

Consistency (R)

0.600

0.500

0.400

0.300

0.200

0.100

0.000

Accuracy,

100cases

Notethatthefirstvariablethatyouspecify(here,consi s)isplacedonthexaxisandthesecond

variable(here,ach100)isplacedontheyaxis.

Whenyouhaveaseriesofvariablesandwouldliketoexaminescatterplotsbetweenallpairsof

them,youcangenerateascatterplotmatrix. Forexample,thefollowingcommandprovidesa

scatterplotmatrixusingtheaccuracyscoresforthefirstthreeblocksoftrialsinthestudy(ach1,ach2,andach3):

graph/ scat t er pl ot ( mat r i x) = ach1 ach2 ach3 .


27/53


Accuracy, cases 41-60Accuracy, cases 21-40Accuracy, cases 1-20

Accuracy,cases41-60

Accuracy,cases

21-40

Accuracy,cases1-20

Asyoucansee,thismatrixincludesallpairwisecombinationsofvariables. Infact,eachcombinationof

variablesisusedtocreatetwoscatterplotsbyswappingthetwovariablespositionsonthexandy

axes. Forexample,thescatterplotsintheupperrightandlowerleftcellsinvolvethesametwo

variables,buttheirpositionsontheaxesarereversed.

5.2Correlation

Thecorr commandwillcalculatethecorrelationbetweentwovariables,oramatrixofcorrelationsbetweenallpairsofspecifiedvariables.Whenbothvariablesarecontinuous,thisyields

theconventionalPearsonproductmomentcorrelationcoefficient(r).Whenthedataareranked,this

yieldsSpearmansrho(rs).Whenonevariableiscontinuousandtheotherisdichotomous,thisyieldsa

pointbiserialcorrelation(rpb).Whenbothvariablesaredichotomous,thisyieldsaphicoefficient().

Thus,thiscommandisversatileinthatitcanhandlemanytypesofdatabesuretousetheproper

notationwhenreportingtheresults.

Toillustratethebasiccommand,hereishowtocalculateacorrelationbetweentheconsistency

(consi s)andaccuracy(ach100)ofparticipantsjudgments:

corr var s = consi s ach100 .


28/53


Correlations

1 .518

.000

106 106

.518 1

.000

106 106

Pearson Correlation

Sig. (2-tailed)

N

Pearson CorrelationSig. (2-tailed)

N

Consistency (R)

Accuracy, 100 cases

Consistency(R)

Accuracy,100 cases

Evenwhenjusttwovariablesareprovided,SPSSpresentstheresultsinamatrix. Onthediagonal

runningfromtheupperlefttothelowerrightcells,eachcorrelation=1becauseeachofthesecells

crossesavariablewithitself;youshouldignorethese. Youcanalsoignorethevaluesabovethis

diagonalorthevaluesbelowthisdiagonal,becausethesesetsofresultsareidentical(thisiseasyto

verifyinthesimplestcase,shownabove,wherethereareonlytwovariablesandhenceonlyone

correlationalresult.Withinacell,thecorrelationappearsabovethepvalue,followedbythenumberof

casesintheanalysis.TowritetheresultsinAPAformat,rememberthatdf=N2forcorrelations. Theresultsshown

abovecouldbereportedasfollows: Theconsistencyandaccuracyofparticipantsjudgmentswere

statisticallysignificantlycorrelated,r(104)=.52,p


29/53


Noticethatmostofthesecorrelationswerecalculatedusing106cases,butsomewerecalculated

using105casesspecifically,therewasonepieceofmissingdataforach5becauseoneparticipantdid

notcompletethejudgmenttask. Bydefault,SPSSusesapairwisemissingdatatechniqueinwhich

eachcorrelationinamatrixiscalculatedusingasmuchdataaspossible.However,itissometimes

preferabletousealistwisemissingdatatechniqueinwhichanycasethatismissingdataononeor

morevariablesiseliminatedfromallcorrelations. Torerunthesecorrelationsusingthelistwise

missingdatatechnique,itcanbeaddedasanoptionalsubcommandtothecorrelationcommand:

cor r vars = consi s ach1 ach2 ach3 ach4 ach5/ mi ssi ng l i stwi se .

Correlations a

1 .399 .383 .247 .373 .126

.000 .000 .011 .000 .199

.399 1 .475 .396 .167 .103

.000 .000 .000 .089 .295

.383 .475 1 .431 .314 .120

.000 .000 .000 .001 .221

.247 .396 .431 1 .197 .190

.011 .000 .000 .044 .052

.373 .167 .314 .197 1 .003

.000 .089 .001 .044 .975

.126 .103 .120 .190 .003 1

.199 .295 .221 .052 .975

Pearson Correlation

Sig. (2-tailed)

Pearson Correlation

Sig. (2-tailed)

Pearson Correlation

Sig. (2-tailed)Pearson Correlation

Sig. (2-tailed)

Pearson Correlation

Sig. (2-tailed)

Pearson Correlation

Sig. (2-tailed)

Consistency (R)

Accuracy, cases 1-20





Consistency(R)

Accuracy,cases 1-20

Accuracy,cases 21-40




Listwise N=105a.

Inthismatrix,Nisnotpresentedineachcellbecauseitisidenticalforallofthem,asnotedin

thefootnotebeneaththetable.

Anotheroptioncansimplifyacorrelationmatrixwhenyouareonlyinterestedincertain

pairingsofvariables. Forexample,supposethatyouwouldliketoknowhowstronglyconsistency

correlateswitheachofthefiveaccuracyscores,butyouarenotinterestedinhowstronglytheaccuracy

scorescorrelatewithoneanother. Thematrixabovecontainsall15correlationsbetweenpairsof

variables,butyouonlywantedthe5correlationsbetweenconsistencyandtheaccuracyscores. To

obtainonlythecorrelationsyouwant,youcanspecifyoneormorevariablestoformtherow(s)ofa

matrix,followedbythetermwi t handthenoneormorevariablestoformthecolumn(s)ofamatrix,as

follows:

cor r vars = consi s wi t h ach1 ach2 ach3 ach4 ach5/ mi ssi ng l i stwi se .

Correlations a

.399 .383 .247 .373 .126

.000 .000 .011 .000 .199

Pearson Correlation

Sig. (2-tailed)

Consistency (R)

Accuracy,cases 1-20





Listwise N=105a.


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5.3Regression

Ther egr essi oncommandcalculatesalinearregressionequation. Thereisaremarkable

varietyofoptionsavailableinSPSSregressionanalyses,andforthesakeofsimplicityonlysimple

linearregressionwillbedescribedherethesimplereferstotheinclusionofasinglepredictor

variable. Toperformaregressionanalysis,youneedtospecifythedependentvariableandthe

predictorvariable. Forexample,thefollowingcommandcalculatesaregressionequationusingconsistencyofjudgments(consi s)topredictaccuracyofjudgments(ach100,whichserveshereas

thedependentvariable):

r egr essi on/ dep ach100/ ent er consi s .

Thisgeneratesaconsiderableamountofoutput. First,therewillbeatablelabeledVariables

Entered/Removedthatnotesthevariableenteredasapredictorandtheoneservingasthedependent

variable:

Variables Entered/Removed b

Consistency (R)

a . Enter

Model1

VariablesEntered

VariablesRemoved Method

All requested variables entered.a.

Dependent Variable: Accuracy, 100 casesb.

Next,atablelabeledModelSummarywilldisplaythecorrelationbetweenthepredictorand

dependentvariable(listedasR,butbecausethisissimplelinearregressionitisequivalenttoPearsons

r;notethatthisvalueisidenticaltowhatwasobtainedaboveinthefirstcorrelationalanalysis). This

tablealsoincludesthecoefficientofdetermination(r2,listedhereasRSquare),anadjustedvalueofthisstatisticthatestimateswhatr2wouldlikelybeinanewsample(AdjustedRSquare),andthe

standarderroroftheestimate(SEest,listedasStd.ErroroftheEstimate),whichrepresentsthetypical

amountoferrorinpredictingthedependentvariableusingtheregressionequationbasedonthe

predictorvariable:

Model Summary

.518a .269 .262 .075143

Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), Consistency (R)a.

Thenexttable,labeledANOVA,canbeignored;itsresultsareredundantwiththoseinthe

tablethatfollows.


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ANOVAb

.216 1 .216 38.195 .000a

.587 104 .006

.803 105

Regression

Residual

Total

Model

1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), Consistency (R)a.

Dependent Variable: Accuracy, 100 casesb.

Thefinaltable,labeledCoefficients,containstheresultsthattypicallyaremostusefulina

regressionanalysis:

Coefficients a

-.231 .099 -2.332 .022

.689 .111 .518 6.180 .000

(Constant)

Consistency (R)

Model

1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: Accuracy, 100 casesa.

Theregressioncoefficients(b=slope,a=intercept)usedtoconstructthebestfittingregressionequation

areshowninthecolumnlabeledBunderUnstandardizedCoefficients. Inthiscase,b=.689anda

=.231,sotheregressionequationcouldbewrittenasfollows:

PredictedAccuracy=.689Consistency.231

Alternatively,ifthepredictoranddependentvariablesweretransformedintozscores,theintercept

couldbedroppedfromtheequation,andthecoefficientforthepredictor(slope)wouldequalthe

correlation:

z(PredictedAccuracy)=.518z(Consistency)

Whenstandardized,theslopeisknownas,anditisalsolistedinthetableshownabove. Finally,the

pvalueforthiscoefficientisshowninthetableundertheSig.heading.Whenwritingupregression

resultsinAPAstyle,thevalueofandparesufficient: =.52,p


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6. COMPARINGMEANS

6.1OneSampletTest

Thiscommandallowsyoutotestwhetherthemeanobservedinyoursample,usedasan

estimateofapopulationmean,differsfromaspecifiedpopulationmean. Thecommand,t - tes t,is

followedbyasubcommandonwhichyouspecifythepopulationmean()thatrepresentsthenull

hypothesis(thisisthet est val onthe2ndline,below)andthenanothersubcommandonwhichyou

listoneormoredependentvariablestotest(ach100,intheexampleshownbelow). Ifyoudonot

specify,SPSSusesadefaultt est val of0. Ifyoulistmultipledependentvariables,aseparateone

samplettestisperformedforeach(asshowninthesecondcommandandsetofoutputprovided

below).

t - t e s t/ t est val = 0/ var s = ach100 .

TheoutputbeginswithatablelabeledOneSampleStatisticsthatprovidesbasicdescriptive

statisticsforthedependentvariable(s),includingthevalidN,M,SD,andSEoftheM:

One-Sample Statistics

106 .37929 .087445 .008493Accuracy, 100 cases

N MeanStd.

DeviationStd. Error

Mean

NextisatablelabeledOneSampleTestthatcontainstheactualttestresults,includingthet

value,df(whichisN1forthistypeofttest),pvalue(listedunderSig.(2tailed));thevalueofis

alsolistedastheTestValue(inthiscase,itis0):

One-Sample Test

44.657 105 .000 .379288 .36245 .39613Accuracy, 100 casest df Sig. (2-tailed)

MeanDifference Lower Upper

95% ConfidenceInterval of the

Difference

Test Value = 0

SPSSdoesnotcalculateameasureofeffectsize,butitiseasytocomputeCohensdbyhand(see

AppendixAforformulasandAppendixCforadditionalinformation). InAPAstyle,onemightreport

theseresultsasfollows: Theaccuracyofparticipantsjudgments,assessedasthecorrelationbetweeneachparticipantsjudgmentsandthecriterionvalues(M=.38,SD=.09),wasstatisticallysignificantly

betterthanchance(=.00),t(105)=44.66,p


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t - t e s t/ t est val = 0/ vars = ach1 ach2 ach3 .

One-Sample Statistics

106 .43105 .158472 .015392

106 .61701 .124916 .012133

106 .39030 .106211 .010316




N Mean

Std.

Deviation

Std. Error

Mean

One-Sample Test

28.005 105 .000 .431050 .40053 .46157

50.854 105 .000 .617007 .59295 .64106

37.834 105 .000 .390300 .36984 .41076




t df Sig. (2-tailed)Mean

Difference Lower Upper


Difference

Test Value = 0

Becauseeachofthesetestsyieldedstatisticallysignificantresults,onecouldreporttheresults

moreconciselyinasinglesentenceratherthanusingthreerepetitivesentencesformattedliketheone

forthepreviousanalysis. Forexample: Foreachofthefirstthreeblocksof20trials,theaccuracyof

participantsjudgments(Ms=.43,.62,.39andSDs=.16,.12,.11,respectively)exceededchance(=.00),

eacht(105) 28.01,eachp2.72.

6.2IndependentGroupstTest

Thiscommandteststhenullhypothesisthatthemeansofthepopulationsfromwhichtwogroupsweredrawnareequal. Toperformtheindependentgroupsttest,thecommand,t - tes t,is

followedbythespecificationofthetwogroupstobecomparedandthenasubcommandonwhichyou

listoneormoredependentvariablestotest. Ifyoulistmultipledependentvariables,aseparate

independentgroupsttestisperformedforeach(asshowninthesecondcommandandsetofoutput

providedbelow). Inthefollowingexample,groupsaredefinedbythesexvariable,withthe

specificationthatthegroupsareidentifiedbythecodesof1and2(whichcorrespondtomenand

women);accuracy(ach100)islistedastheonlydependentvariable.

t - t est gr oups = sex( 1, 2)/ var s = ach100 .

TheoutputbeginswithatablelabeledGroupStatisticsthatprovidesbasicdescriptive

statisticsforthedependentvariable(s)includingthevalidN,M,SD,andSEoftheMforthetwo

groupsbeingcompared:


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Group Statistics

28 .35359 .088279 .016683

78 .38851 .085837 .009719

Sex (1=M 2=F)

male

female

Accuracy, 100 cases

N MeanStd.

DeviationStd. Error

Mean

ThisisfollowedbyatablelabeledIndependentSamplesTestthatcontainstheactualttest

results. Notethatthetvalue,df(whichisN2forthistypeofttest),andpvalue(listedunderSig.(2

tailed))areprovidedtwice. Thetoprowassumesthatvariancesinthetwopopulationsareequal(i.e.,

thehomogeneityofvarianceassumptionissatisfied),andthebottomrowdoesnotassumethis.

Levenestestforequalityofvariancesisonewaytodeterminewhethertheassumptionissatisfied,and

thereforewhichrowofthetabletousewheninterpretingandreportingthetestresults. Specifically,

Levenestestevaluatesanullhypothesisofequalvariances. IfthepvalueforLevenestestissmall

(e.g.,below=.05),thishypothesiswouldberejectedandonewouldnotassumeequalvariances;the

bottomrowwouldprovidetheappropriateresults. IfthepvalueforLevenestestislarge(e.g.,above

=.05),onewouldfailtorejectthehypothesisofequalvariancesandthereforeusethetoprowofthe

table.

Independent Samples Test

.011 .917 -1.833 104 .070 -.034928 .019052 -.072708 .002852

-1.809 46.556 .077 -.034928 .019308 -.073780 .003924

Equal variancesassumed

Equal variancesnot assumed

Accuracy, 100 cases

F Sig.

Levene's Test forEquality of Variances


DifferenceStd. ErrorDifference Lower Upper


Difference

t-test for Equality of Means

Inthiscase,thepvalueforLevenestestiswellabove=.05,soonecansafelyassumeequal

variancesandusethetoprowoftheoutput. SPSSdoesnotcalculateameasureofeffectsize;seeAppendixAfordetailsonhowtocalculateCohensd. TheseresultscouldbereportedinAPAstyleas

follows: Therewasnostatisticallysignificantdifferenceintheaccuracyofjudgmentsmadebymen

(M=.35,SD=.09)andwomen(M=.39,SD=.09),t(104)=1.83,p=.070,d=0.40.

Whentheassumptionofequalvariancesisnotsatisfiedandtheresultsaredrawnfromthe

bottomrowofthetable,thisshouldbenotedforreaders. Inotherwords,readerspresumethatthe

homogeneityofvarianceassumptionwassatisfiedunlesstoldotherwise. Hereishowthewriteup

woulddifferifequalvarianceshadnotbeenassumed: Usingatestprocedurethatadjustsforunequal

variances,therewasnostatisticallysignificantdifferenceintheaccuracyofjudgmentsmadebymen

(M=.35,SD=.09)andwomen(M=.39,SD=.09),t(46.56)=1.81,p=.077,d=.40.

Hereisanexampleofoutputforacommandthatrequestsaseriesofthreeindependentgroupstteststotestforsexdifferencesinaccuracyscoresateachofthefirstthreeblocksoftrials:

t - t est gr oups = sex( 1, 2)/ vars = ach1 ach2 ach3 .


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Group Statistics

28 .37374 .160267 .030288

78 .45162 .153674 .017400

28 .59253 .129848 .024539

78 .62579 .122760 .013900

28 .37409 .116504 .022017

78 .39612 .102438 .011599

Sex (1=M 2=F)male

female

male

female

male

female




N MeanStd.

DeviationStd. Error

Mean

Independent Samples Test

.063 .803 -2.275 104 .025 -.077889 .034238 -.145784 -.009993

-2.230 46.006 .031 -.077889 .034930 -.148199 -.007578

.307 .581 -1.212 104 .228 -.033270 .027459 -.087721 .021182

-1.180 45.464 .244 -.033270 .028202 -.090056 .023516

1.021 .315 -.941 104 .349 -.022030 .023412 -.068456 .024396

-.885 42.907 .381 -.022030 .024886 -.072220 .028160




Equal variances

not assumed






F Sig.

Levene's Test forEquality of Variances


DifferenceStd. ErrorDifference Lower Upper


Difference

t-test for Equality of Means

Foreachofthesetests,thehomogeneityofvarianceassumptionappearstobesatisfied

Levenestestyieldedapvalueabove=.05. Theresultscouldbereportedasfollows: Accuracyof

judgmentwascalculatedwithinblocksof20trials,theaccuracyscoresforthefirstthreeblockswere

testedforsexdifferences.Womensjudgments(M=.45,SD=.15)werestatisticallysignificantlymore

accuratethanmensjudgments(M=.37,SD=.16)forthefirstblock,t(104)=2.28,p=.025,d=0.50.

Therewasnostatisticallysignificantsexdifferenceateitherthesecondblock(mensM=.59,SD=.13;

womensM=.63,SD=.12),t(104)=1.21,p=.228,d=0.27,orthethirdblock(mensM=.37,SD=.12;womensM=.40,SD=.10),t(104)=.94,p=.349,d=0.21.

6.3RelatedSamplestTest

Thiscommandteststhenullhypothesisthatthemeansofthepopulationsfromwhichtwo

relatedsamplesweredrawnareequal.Mostoften,thetwosamplesconsistofdifferentmeasures

collectedwithinthesamesampleofparticipantsinarepeatedmeasuresdesign,akaawithinsubjects

design. Dataforsomerelatedsamplesttestscomefrommatcheddesigns,wherepairsofindividuals

intwogroupsarematchedtooneanotherandtreatedasrepeatedmeasurements. Toperformthe

relatedsamplesttest,thecommand,t - tes t,isfollowedbythespecificationofpairsofvariableswhosemeanswillbecompared. Ifyoulistmultiplevariables,aseparaterelatedsamplesttestis

performedforeachpairofvariables(asshowninthesecondcommandandsetofoutputprovided

below). Inthefollowingexample,accuracyofjudgmentiscomparedacrossthefirsttwoblocksof

trials:

t - t est pai r s = ach1 ach2 .


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TheoutputbeginswithatablelabeledPairedSamplesStatisticsthatprovidesbasic

descriptivestatisticsforeachvariable,includingthevalidN,M,SD,andSEoftheM:

Paired Samples Statisti cs

.43105 106 .158472 .015392

.61701 106 .124916 .012133



Pair

1

Mean NStd.

DeviationStd. Error

Mean

ThisisfollowedbyatablelabeledPairedSamplesCorrelationsthatyoushouldignore. This

displaysthecorrelationbetweenthetwovariables,whichisonlyindirectlyrelevanttoarelated

samplesttestandisusuallynotreported. Inparticular,donotmistakethepvalueinthistableforthe

resultsofthettest,whichispresentedinthefinaltable,labeledPairedSamplesTest.

Paired Samples Correlations

106 .475 .000

Accuracy, cases 1-20 &


Pair

1

N Correlation Sig.

Paired Samples Test

-.185957 .148021 .014377 -.214464 -.157449 -12.934 105 .000Accuracy, cases 1-20 -Accuracy, cases 21-40

Pair1

MeanStd.

DeviationStd. Error

Mean Lower Upper


Difference

Paired Differences

t df Sig. (2-tailed)

Thetestresultst,df(whichisN1forthistypeofttest),andp(underSig.(2tailed))are

providedinthefinalthreecolumnsofthistable. Notethatthistestdoesnotrequiretheassumptionof

homogeneityofvariance,soitissimplerthantheindependentgroupsttesttointerpretandreport.

SPSSdoesnotcalculateameasureofeffectsize;seeAppendixAfordetailsonhowtocalculateCohens

dbyhand. Inthiscase,theresultscouldbereportedasfollows: Theaccuracyofjudgmentsmade

duringthefirstblockof20trials(M=.43,SD=.16)increasedbyastatisticallysignificantamountinthe

secondblock(M=.62,SD=.12),t(105)=12.93,p


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Paired Samples Correlation s

106 .475 .000

106 .397 .000

106 .432 .000

Accuracy, cases 1-20 &Accuracy, cases 21-40

Pair1

Accuracy, cases 1-20 &Accuracy, cases 41-60

Pair2

Accuracy, cases 21-40 &


Pair

3

N Correlation Sig.

Paired Samples Test

-.185957 .148021 .014377 -.214464 -.157449 -12.934 105 .000

.040750 .151808 .014745 .011514 .069986 2.764 105 .007

.226707 .124227 .012066 .202782 .250631 18.789 105 .000

Accuracy, cases 1-20 -Accuracy, cases 21-40

Pair1


Pair2


Pair3

MeanStd.

DeviationStd. Error

Mean Lower Upper


Difference

Paired Differences

t df Sig. (2-tailed)

Eachofthethreetestsyieldedstatisticallysignificantdifferences. Theclearestwaytopresent

theseresultswouldbetofocusonthechangefromoneblocktothenext,asfollows: Accuracyof

judgmentwascalculatedwithinblocksof20trials. Accuracyforthefirstblock(M=.43,SD=.16)was

statisticallysignificantlylowerthanaccuracyatthesecondblock(M=.62,SD=.12),t(105)=12.93,p


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Between-Subjects Factors

4 SP 26

2 SP 27

2 SP, 3 WP 27

2 SP, 6 WP 26

1

2

3

4

ExperimentalGroup

Value Label N

ThisisfollowedbyatableofdescriptivestatisticsthatincludestheM,SD,nforeachgroup:


Dependent Variable: Accuracy, 100 cases

.43835 .068524 26

.40403 .056030 27

.33447 .090051 27

.34107 .087998 26

.37929 .087445 106

Experimental Group

4 SP

2 SP

2 SP, 3 WP

2 SP, 6 WP

Total

MeanStd.

Deviation N

NextisanANOVAsummarytable. Thisincludesseveralrowsthatyoucanignore: CorrectedModel,Intercept,Total,andCorrectedTotal. Theonlyrowsyouneedarethoselabeled

group(whichisthefactornameinthisanalysisinyouranalyses,thefactornamewillbedifferent,

butitwillappearinthesamerow[3]ofthetable)andError(theerrortermforthisANOVA,

representingwithingroupsvariance). NotethatthecolumnlabeledSig.,containsthepvalueforthe

Ftest,andthedfthatyouwouldreportcomefromtherowslabeledwithyourfactorsname(here,

group)andErrorinthisexample,thestatisticalresultswouldbereportedasfollows: F(3,102)=

11.24,p


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First,atablelabeledMultipleComparisonspresentstheresultsofallpossiblepairwise

comparisonsofmeans. Thefirsttwocolumnsindicatewhichconditionsarebeingcomparedineach

rowofthetable,andtheSig.columncontainsthepvaluesforeachofthesecomparisons.Whenever

thepvalueislessthanyourpreferredlevel(typically.05),thenullhypothesisofequalityisrejected

andyouconcludethatthesetwogroupsweredrawnfrompopulationswithdifferentmeans. Inthe

presentcase,thefollowingexpressionindicateswhichgroupsdo(anddonot)differfromoneanother

statisticallysignificantly(using=.05):

([4S]=[2S]) ([2S+3W]=[2S+6W])

Inotherwords,conditionswithnoweakcuesdidnotdifferfromoneanother,notdidconditionswith

weakcues,butbothconditionswithnoweakcuesdifferedfrombothconditionswithweakcues. To

writetheresultsofthisANOVAandposthoctestinAPAstyle: Accuracyofjudgmentdiffered

statisticallysignificantlyacrossthefourexperimentallymanipulatedcueconditions,F(3,102)=11.24,p


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Accuracy, 100 c ases

Tukey HSDa,b,c

27 .33447

26 .34107

27 .40403

26 .43835

.989 .370

Experimental Group

2 SP, 3 WP

2 SP, 6 WP

2 SP

4 SP

Sig.

N 1 2

Subset

Means for groups in homogeneous subsets are displayed.Based on Type III Sum of SquaresThe error term is Mean Square(Error) = .006.

Uses Harmonic Mean Sample Size = 26.491.a.

The group sizes are unequal. The harmonic meanof the group sizes is used. Type I error levels arenot guaranteed.

b.

Alpha = .050.c.

6.5RelatedSamplesANOVA

Thisprocedureteststhenullhypothesisthattwoormorerelatedsamplesaredrawnfrompopulationswiththesamemean. Onceagain,usuallyanANOVAisperformedonlywhenthereareat

leastthreemeanstocompare,becausearelatedsamplesttesthandlesthesimplercaseofcomparing

tworelatedsamplesmeans. Thegl mcommandperformsthistypeofANOVA,anditrequiresthe

specificationoftheseriesofvariablesthatcontainthedatafortherelatedsamples(typicallyrepeated

measurementsonthesamecases,butsometimesscoresformatchedsamples). Intheexampleshown

here,theaccuracyscoresforthefirstthreeblocksoftrials(ach1,ach2,andach3)arecompared. The

firstsubcommandisrequired,anditiswhereyouprovidealabelforthesinglefactorintheanalysis

andtellSPSShowmanylevelsthereare. Inthiscase,thelabelofbl ockwasprovidedandthereare

threelevels(ach1,ach2,andach3). Youcanuseanylabelyoulike,solongasitisnotaterm

reservedforSPSSsyntaxoranexistingvariablename. Thislabelwillbeusedintheoutputtoidentify

thetestofthisfactor. Thenextsubcommandrequestsdescriptivestatisticsandameasureofeffectsize

(2),andthefinalsubcommandinformsSPSSthatyouwantittousethedefaultwithinsubjectsdesign.

gl m ach1 ach2 ach3/ wsf act or bl ock ( 3)/ pr i nt desc et asq/ wsdesi gn .

Theoutputisvoluminous,andperhapsthetrickiestpartofworkingwiththistypeofanalysisis

findingtherelevantportionsandignoringtherest. Thefirsttable,labeledWithinSubjectsFactors,

simplysummarizesthelevelsofthefactor. Inthiscase,youcanseethatthebl ockfactorhasthree

levels,andthatSPSSunderstandsthatyouwantedtouseach1,ach2,andach3asthethreelevels:

Within-Subjects Factors

Measure: MEASURE_1

ach1

ach2

ach3

block

1

2

3

DependentVariable


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Thenexttablepresentsdescriptivestatisticsforeachlevelofthefactor,includingitsMandSD:


.43105 .158472 106

.61701 .124916 106

.39030 .106211 106




MeanStd.

Deviation N

BeyondthispointareANOVAresults,calculatedintwoways,plusatestofanassumptionthat

isanalogoustohomogeneityofvariance,calledsphericity. Thedetailsofwhatthisassumption

entails,howitistested,andhowtohandleitarebeyondthescopeofthisguide;agraduatelevel

statisticstextwillprovideinformationonthissubject.Withtheunderstandingthatthisisnotalways

themostappropriatewaytoproceed,whatfollowsisasimplifiedapproachtointerpretingand

reportingtheresultsthatignoresthisassumption.

Providedthatyouarewillingtoignorethesphericityassumption,youcanskipthetableslabels

MultivariateTestsandMauchlysTestofSphericity,proceedingstraighttotheANOVAsummary

tablelabeledTestsofWithinSubjectsEffects.

Multivariate Testsb

.788 193.323a 2.000 104.000 .000 .788

.212 193.323a 2.000 104.000 .000 .788

3.718 193.323a 2.000 104.000 .000 .788

3.718 193.323a 2.000 104.000 .000 .788

Pillai's Trace

Wilks' Lambda

Hotelling's Trace

Roy's Largest Root

Effectblock

Value F Hypothesis df Error df Sig.Partial EtaSquared

Exact statistica.

Design: InterceptWithin Subjects Design: block

b.

Mauchly's Test of Spherici ty b

Measure: MEASURE_1

.944 5.940 2 .051 .947 .964 .500

Within Subjects Effectblock

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: block

b.

ThestandardANOVAsummarytableisshownbelow,anditincludesameasureofeffectsize

(2). Onceagain,ifyouarewillingtoignorethesphericityassumption,youcandrawresultsfromthe

firstofthefourrowswithineachcellofthetable(labeledSphericityAssumed).Notethatthedfthat

youneedtoreportappearintherowslabeledwiththewithinsubjectsfactor(here,block)andits

errorterm(here,Error(block)). TheresultsappearingbelowcouldbereportedinAPAstyleas


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follows: Therewasastatisticallysignificantdifferenceinaccuracyofjudgmentsacrossthefirstthree

blocksof20trials,F(2,210)=153.83,p


43/53


6.6FactorialANOVA

Thisprocedureteststhenullhypothesesthatcorrespondtomaineffectsandinteractionsina

factorialANOVAwithstrictlybetweensubjectsfactors. Theuni anovacommandperformsthistype

ofANOVA,anditrequiresthespecificationofthedependentvariable(here,ach100,themeasureof

accuracyofjudgment)andthecategoricalvariablesthatdefineeachfactor(here,groupandaccount,

thetwoindependentvariables). Recommendedsubcommandsrequestdescriptivestatisticsandposthoccomparisonsofmeans.Notethatyoucanrequestposthoctestsforeachfactorinthedesignthat

hasmorethantwolevels. Intheexampleshownbelow,gr oupvariesacrossfourlevelsandaccount

variesacrosstwolevels,soposthoctestswererequestedonlyfortheformer. TukeysHSDisspecified

astheposthoctechnique,butmanyothersareavailable(seetheSPSShelpmaterialsfordetails).

uni anova ach100 by gr oup account/ post hoc gr oup ( t ukey)/ pr i nt desc et asq .

TheoutputbeginswithatablelabeledBetweenSubjectsFactorsthatsummarizesthefactors

andlevelsthatwerespecifiedinthecommand. Youshouldverifythatthisiswhatyouintended.

Between-Subjects Factors

4 SP 26

2 SP 27

2 SP, 3 WP 27

2 SP, 6 WP 26

no 51

yes 55

1

2

3

4

Experimental Group

0

1

Social Accountability

Value Label N

Nextisatableofdescriptivestatisticsthatincludesthen,M,andSDforeachcellofthedesign,

aswellasthemarginalmeans. Iftherewasamaineffectforexperimentalgroups,youwouldusetheMsandSDsforthefourlevelsofthisfactor,whicharepresentedintheTotalrowsforeachlevel:Ms

=.43885,.40403,.33447,and.34107. Iftherewasamaineffectforsocialaccountability,youwoulduse

theMsandSDsforthetwolevelsofthisfactor,whicharepresentedintheTotalnoand

Totalyesrowsnearthebottomofthetable:Ms=.38582and.37323. Iftherewasaninteraction

effect,youwouldusetheeightmeansinthecellsofthetableallrowsthatdonotcontainaTotal.


44/53



Dependent Variable: Accuracy, 100 cases

.43723 .045967 12

.43932 .085086 14

.43835 .068524 26

.42004 .038517 12

.39122 .065338 15

.40403 .056030 27

.35427 .076816 13

.31608 .100077 14

.33447 .090051 27

.34171 .074845 14

.34033 .104775 12

.34107 .087998 26

.38582 .073368 51

.37323 .099029 55

.37929 .087445 106

Social Accountability

no

yes

Total

no

yesTotal

no

yes

Total

no

yes

Total

no

yes

Total

Experimental Group

4 SP

2 SP

2 SP, 3 WP

2 SP, 6 WP

Total

MeanStd.

Deviation N

NextisanANOVAsummarytable. NotethatthecolumnlabeledSig.,containsthepvalue

foreachFtest. Formostpurposes,youcanignoreseveralrowsofthetable,includingthoselabeledCorrectedModel,Intercept,Total,andCorrectedTotal. TherowsthatcontainFtests(and

effectsizes)thatshouldbeinterpretedandreportedincludemaineffects,oneperbetweensubjects

factor(here,groupandaccount ),andinteractions,whichinvolveallmultiplicativecombinationsof

factors(here,theonlyinteractiontermisgroup * account becausethereareonlytwofactors).Note

thatthedfforeachFtestappearontherowwiththeFvalueandtherowlabeledError. Forexample,

statisticalresultsforthegr oupmaineffectwouldbereportedas: F(3,98)=11.04,p


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11.04,p


46/53


7. CHISQUAREANALYSES

7.12GoodnessofFitTest

Thisprocedureteststhenullhypothesisofnodifferencebetweenobservedandexpected

frequenciesacrossaseriesofcategories. Because2isonetypeofnonparametricstatistic,SPSS

implementsitusingitsmoregeneralnpar t est procedure(shortfornonparametrictest). Thefirst

subcommandrequestsa2analysisofaspecifiedcategoricalvariable(here,sex),andthisisfollowed

byasubcommandthatspecifiestheexpectedfrequencies. Onewaytodothisistogenerateexpected

frequenciesbydividingthetotalsamplesizeintoequalsizedcategories. Inthefirstexampleshown

below,thetotalof106casesissplitintoexpectedfrequenciesof53menand53women:

npar t est/ chi square = sex/ expect ed = equal .

Theoutputissimple. Thefirsttableshowstheobservedfrequencies(ObservedN),expected

frequencies(ExpectedN),andthedifferencebetweenthese(Residual):

Sex (1=M 2=F)

28 53.0 -25.0

78 53.0 25.0

106

male

female

Total

Observed N Expected N Residual

Thesecondtableshowsthevalueof2,thedf(numberofcategories1),andpvalue(Asymp.

Sig.).:

Test Statistics

23.585

1

.000

Chi-Squarea

df

Asymp. Sig.

Sex (1=M2=F)

0 cells (.0%) have expected frequencies less than5. The minimum expected cell frequency is 53.0.

a.

InAPAstyle,theseresultswouldbereportedasfollows: Theobservednumbersofmen(n=

28)andwomen(n=78)statisticallysignificantlydifferedfromanequalsplit,2(1,N=106)=23.59,p


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Notethattheexpectedfrequenciesmustbelistedintheorderthatthecategoriesarecoded.

Becausesexiscodedas1=male,2=female,theexpectedfrequencyformenappearsbeforethatfor

women. Theoutputappearsbelow:

Sex (1=M 2=F)

28 35.0 -7.0

78 71.0 7.0

106

male

female

Total

Observed N Expected N Residual

Test Statistics

2.090

1

.148

Chi-Squarea

df

Asymp. Sig.

Sex (1=M2=F)

0 cells (.0%) have expected frequencies less than5. The minimum expected cell frequency is 35.0.

a.

Theseresultswouldbereportedasfollows: Theobservednumbersofmen(n=28)and

women(n=78)didnotdifferstatisticallysignificantlyfromtheexpected1:2ratioofmentowomen,

2(1,N=106)=2.09,p=.148.

7.22TestofIndependence

Thisprocedureteststhenullhypothesisthattwocategoricalvariablesfrequenciesare

distributedindependently.Moreintuitively,thisisatestoftheassociationbetweentwovariables. If

thenullhypothesisofindependenceisrejected,thenknowledgeofascoreononevariablepredictsthe

scoreontheothervariablebetterthanchance. SPSSimplementsthistestusingthecr osst abs

command(shortforcrosstabulations). Thepairofvariablestobetestedforindependenceis

specifiedonthefirstsubcommand;twoadditionalsubcommandsrequesthelpfuloutput(the2

statisticplusobservedandexpectedfrequenciesineachcellofthetableofcrossclassifications).

Intheexampleshownbelow,atestisperformedtodeterminewhethermenandwomen(the

sexvariable,codedas1=male,2=female)wereequallylikelytohavetakenacalculuscourse(the

cal cvariable,codedas1=yes,0=no).WhereasSPSSrequiresthespecificationofexpectedvaluesto

performthe2testforgoodnessoffit,itcalculatestheseautomatically(usingthemarginaltotals)to

performthe2testforindependence.

cr osst abs

/ t abl es = sex by cal c/ st at s = chi sq/ cel l s = count exp .

TheoutputbeginswithaCaseProcessingSummarythatindicateshowmanycases(ifany)

weremissingdata.Here,therewasonlyonecasemissingdata:


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105 99.1% 1 .9% 106 100.0%Sex (1=M 2=F) *Calculus course

N Percent N Percent N Percent

Valid Missing Total

Cases

Thenexttablepresentsthecrossclassificationofcases. Ineachcell,theobservedfrequency(Count)appearsabovetheexpectedfrequency(ExpectedCount);thelatteriscalculatedastherow

totaltimesthecolumntotaldividedbythetotalsamplesize(e.g.,fortheupperrightcell,menwho

tookcalculus,2888/105=23.5).

Sex (1=M 2=F) * Calculus course Crosstabulation

2 26 28

4.5 23.5 28.0

15 62 77

12.5 64.5 77.0

17 88 10517.0 88.0 105.0

Count

Expected Count

Count

Expected Count

CountExpected Count

male

female

Sex (1=M2=F)

Total

no yes

Calculus course

Total

Thedifferencebetweenobservedandexpectedfrequenciesprovidesatestoftheindependence

ofthetwovariables. The2value,df(fromthecrossclassificationtable,numberofrows1times

numberofcolumns1),andpvalueareprovidedinthefinaltable,labeledChiSquareTests.

Usually,thePearsonChiSquareresultsareused.

Chi-Square Tests

2.303b

1 .1291.484 1 .223

2.641 1 .104

.229 .108

2.281 1 .131

105

Pearson Chi-SquareContinuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

Value df Asymp. Sig.

(2-sided)Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

1 cells (25.0%) have expected count less than 5. The minimum expected count is 4.53.

b.

Becausethisisa2testofindependencewithonly1dfinotherwords,thedataforma22

tableyoucancalculate N

2

asameasureofeffectsize;thisisinterpretedusingthesamerulesof

thumbasforr(.10=small,.30=medium,.50=large;seeAppendixCforadditionalinformation).In

thiscase, 1481.105

303.2 . Forthisexample,onecouldreporttheresultsinAPAstyleasfollows:

Menandwomendidnotdifferstatisticallysignificantlyintherelativefrequencywithwhichthey

tookacalculuscourse,2(1,N=105)=2.30,p=.129,=.15.

8/13/2019 Guide to SPSS

Guide to SPSS for Windows S13

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