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TheNeedforDiagnostics,289

Non-ParametricANOVATests:TheKruskal–WallisTest,289 TermsandConcepts,292

DataLabandExamples(withSolutions),293

DataLab:Solutions,294

10FACTORIALANOVA297

ExtensionsofANOVA,297

ANCOVA,298

MANOVA,299

MANCOVA,299

FactorialANOVA,299

InteractionEffects,299

SimpleEffects,301

2XANOVA:AnExample,302

CalculatingFactorialANOVA,303

TheHypothesesTest:InterpretingFactorialANOVAResults,306

EffectSizefor2XANOVA:Partial �� 2 ,308

DiscussingtheResults,309 UsingSPSS® toAnalyze2XANOVA,311

SummaryChartfor2XANOVAProcedures,319 TermsandConcepts,319

DataLabandExamples(withSolutions),320

DataLab:Solutions,320

11CORRELATION329

TheNatureofCorrelation,330

TheCorrelationDesign,331

Pearson’sCorrelationCoefficient,332

PlottingtheCorrelation:TheScattergram,334 UsingSPSS® toCreateScattergrams,337 UsingExceltoCreateScattergrams,339

CalculatingPearson’s r ,341

The Z ScoreMethod,342

TheComputationMethod,344

TheHypothesisTestforPearson’s r ,345

EffectSize:theCoefficientofDetermination,347

Diagnostics:CorrelationProblems,349

CorrelationUsingSPSS® andExcel,352

NonparametricStatistics:Spearman’sRankOrderCorrelation(rs ),358 TermsandConcepts,363

DataLabandExamples(withSolutions),364 DataLab:Solutions,365

APPENDICES

AppendixASPSS® BASICS509 UsingSPSS® ,509 GeneralFeatures,510 ManagementFunctions,513 AdditionalManagementFunctions,517

AppendixBEXCELBASICS531 DataManagement,531 TheExcelMenus,533 UsingStatisticalFunctions,541 DataAnalysisProcedures,543 MissingValuesand“0”ValuesinExcelAnalyses,544 UsingExcelwith“RealData”,544

AppendixCSTATISTICALTABLES545

TableC.1: Z -ScoreTable(ValuesShownarePercentages–%),545

TableC.2:ExclusionValuesforthe T -Distribution,547

TableC.3:Critical(Exclusion)ValuesfortheDistributionof F ,548

TableC.4:Tukey’sRangeTest(Upper5%Points),551

TableC.5:Critical(Exclusion)ValuesforPearson’sCorrelation Coefficient, r ,552

TableC.6:CriticalValuesofthe �� 2 (Chi-Square)Distribution,553

REFERENCES555 Index557

PREFACE

Thestudyofstatisticsisgainingrecognitioninagreatmanyfields.Inparticular, researchersinthesocialandhealthsciencesnoteitsimportanceforproblemsolving anditspracticalimportanceintheirareas.Statisticshasalwaysbeenimportant,for example,amongthosehopingtoentercareersinmedicinebutmoresonowdueto theincreasingemphasison“ScientificInquiry&ReasoningSkills”aspreparationfor theMedicalCollegeAdmissionTest(MCAT).Sociology,alwaysrelyingonstatistics andresearchforitscoreemphases,isnowincludedintheMCATaswell.

Thisbookfocusessquarelyontheproceduresimportanttoanessentialunderstandingofstatisticsandhowitisusedintherealworldforproblemsolving.Moreover,my discussioninthebookrepeatedlytiesstatisticalmethodologywithresearchdesign (seethe“companion”volumemycolleagueandIwrotetoemphasizeresearchand designskillsinsocialscience;AbbottandMcKinney,2013).

Iemphasizeappliedstatisticalanalysesandassuchwilluseexamplesthroughoutthebookdrawnfrommyownresearchaswellasfromnationaldatabaseslike GSSandBehavioralRiskFactorSurveillanceSystem(BRFSS).Usingdatafrom thesesourcesallowstudentstheopportunitytoseehowstatisticalproceduresapply toresearchintheirfieldsaswellastoexamine“realdata.”Acentralfeatureofthe bookismydiscussionanduseofSPSS® andMicrosoftExcel® toanalyzedatafor problemsolving.

Throughoutmyteachingandresearchcareer,Ihavedevelopedanapproachto helpingstudentsunderstanddifficultstatisticalconceptsinanewway.Ifindthatthe greatmajorityofstudentsarevisuallearners,soIdevelopeddiagramsandfigures overtheyearsthathelpcreateaconceptualpictureofthestatisticalproceduresthat areoftenproblematictostudents(likesamplingdistributions!).

Anotherreasonforwritingthisbookwastogivestudentsawaytounderstandstatisticalcomputingwithouthavingtorelyoncomprehensiveandexpensivestatistical softwareprograms.SincemoststudentshaveaccesstoMicrosoftExcel,Idevelopeda step-by-stepapproachtousingthepowerfulstatisticalproceduresinExceltoanalyze dataandconductresearchineachofthestatisticaltopicsIcoverinthebook.1

Ialsowantedtomakethosecomprehensivestatisticalprogramsmoreapproachabletostatisticsstudents,soIhavealsoincludeda“hands-on”guidetoSPSSin parallelwiththeExcelexamples.Insomecases,SPSShastheonlymeanstoperform somestatisticalprocedures,butinmostcases,bothExcelandSPSScanbeused.

Herearesomeofthefeaturesofthebook:

1.Emphasisonthe interpretationoffindings.

2.Useof clearexamplesfrommyexistingandformerresearchprojectsandlarge databasestoillustratestatisticalprocedures.“Real-world”datacanbecumbersome,soIintroducestraightforwardproceduresandexamplesinordertohelp studentsfocusmoreoninterpretationoffindings.

3.Inclusionofa datalabsectionineachchapterthatprovidesrelevant,clear examples.

4. Introductiontoadvancedstatisticalproceduresinchaptersections(e.g., regressiondiagnostics)andseparatechapters(e.g.,multiplelinearregression) forgreaterrelevancetoreal-worldresearchneeds.

5.Strengtheningofthe connectionbetweenstatisticalapplicationandresearch designs.

6.Inclusionofdetailedsectionsineachchapterexplaining applicationsfrom ExcelandSPSS.

IuseSPSS2 (versions22and23)screenshotsofmenusandtablesbypermission fromtheIBM® Company.IBM,theIBMlogo,ibm.com,andSPSSaretrademarks orregisteredtrademarksof InternationalBusinessMachinesCorporation,registeredinmanyjurisdictionsworldwide.Otherproductandservicenamesmightbe trademarksofIBMorothercompanies.AcurrentlistofIBMtrademarksisavailable ontheWebat“IBMCopyrightandtrademarkinformation”atwww.ibm.com/legal/

1 OnelimitationtoteachingstatisticsprocedureswithExcelisthatthedataanalysisfeaturesaredifferent dependingonwhethertheuserisa“Mac”userora“PC”user.IamusingthePCversion,whichfeatures a“DataAnalysis”suiteofstatisticaltools.ThisfeaturemaynolongerbeincludedintheMacversionof Excel.

2 SPSSscreenreprintsthroughoutthebookareusedcourtesyofInternationalBusinessMachinesCorporation,©InternationalBusinessMachinesCorporation.SPSSwasacquiredbyIBMinOctober2009.

PREFACE xvii

copytrade.shtml.MicrosoftExcelreferencesandscreenshotsinthisbookareused withpermissionfromMicrosoft.IuseMicrosoftExcel® 2013inthisbook.3

IuseGSS(2014)dataandcodebookforexamplesinthisbook.4 TheBRFSS SurveyQuestionnaireandDataareusedwithpermissionfromtheCDC.5

3 ExcelreferencesandscreenshotsinthisbookareusedwithpermissionfromMicrosoft®

4 Smith,TomW.,PeterMarsden,MichaelHout,andJibumKim.GeneralSocialSurveys,1972–2012 [machine-readabledatafile]/PrincipalInvestigator,TomW.Smith;CoprincipalInvestigator,PeterV.Marsden;CoprincipalInvestigator,MichaelHout;SponsoredbyNationalScienceFoundation.NORCed. Chicago:NationalOpinionResearchCenter[producer];Storrs,CT:TheRoperCenterforPublicOpinion Research,UniversityofConnecticut[distributor],2013.1datafile(57,061logicalrecords) + 1codebook (3432pp.).(NationalDataProgramfortheSocialSciences,No.21).

5 CentersforDiseaseControlandPrevention(CDC). BehavioralRiskFactorSurveillanceSystemSurveyQuestionnaire.Atlanta,Georgia:U.S.DepartmentofHealthandHumanServices,CentersforDisease ControlandPrevention,2013andCentersforDiseaseControlandPrevention(CDC). BehavioralRiskFactorSurveillanceSystemSurveyData.Atlanta,Georgia:U.S.DepartmentofHealthandHumanServices, CentersforDiseaseControlandPrevention,2013.

suchlargeamountsofinformationbeenavailabletoassistresearchersandpolicy makersunderstandwidespreadpublicthinkingandbehavior.Onthechallengeside howeverareseveraldifficultquestions:

• Howaresuchdatatobeexamined?

• Docurrentsocialsciencemethodsandprocessesprovideguidancetoexamining datasetsthatsurpasshistoricaldata-gatheringcapacity?

• Arebigdatarepresentative?

• Dodatasetssolargeobviatetheneedforprobability-basedresearchanalyses?

• Dodecisionmakersunderstandhowtousesocialsciencemethodologytoassist intheiranalysesofemergingdata?

• Willthedecisionsemergingfrombigdatabeusedethically,withinthecontext tosocialscienceresearchguidelines?

• Willeffectsizeconsiderationsovershadowquestionsofsignificancetesting?

Socialscientistscanrelyonexistingstatisticalmethodstomanageandanalyze bigdata,butthe wayinwhichtheanalysesareusedfordecisionmakingwillchange. Onetrendisthatpredictionmaybehailedasamoreprominentmethodforunderstandingthedatathantraditionalhypothesistesting.Wewillhavemoretosayabout thisdistinctionlaterinthebook,butitisimportantatthispointtoseethatresearchers willneedtoadaptstatisticalapproachesforanalyzingbigdata.

VISUALDATAANALYSIS

Anotheremergingtrendforunderstandingandmanagingtheswellofdataistheuse ofvisuals.Ofcourse,visualdescriptionsofdatahavebeenusedforcenturies.Itis commonlyacknowledgedthatthefirst“piechart”waspublishedbyPlayfair(1801). Playfair’sexampleinFigure1.1comparesthedynamicsofnationsovertime.

Figure1.1comparednationsusingsize,color,andorientationovertime.Using thismethodforcomparinginformationhasbeenusefulforviewingthepatternsin datanotreadilyobservablefromnumericalanalysis.

Aswithnumericalmethods,however,thereareopportunitiesandchallengesin theuseofvisualanalyses:

• Canvisualmeansbeusedtoconveycomplexmeaning?

• Arethere“rules”thatwillhelptoinsureastandardwayofcreating,analyzing, andinterpretingsuchvisualinformation?

• Willvisualanalysesbecomedivorcedfromnumericalanalysissothatobservers havenowayofobjectivelyconfirmingthemeaningoftheimages?

Severalvisualdatasoftwareanalysisprogramshaveappearedoverthelastseveral years.Simplyrunninganonlinesearchwillyieldseveralpossibilitiesincludingmany thatofferfree(initial)programsforcatalogingandpresentingdatafromtheuser.I offeroneveryimportantcaveat(seethefinalbulletpointearlier),whichisthatitis

Figure1.1 WilliamPlayfair’spiechart. Source:https://commons.wikimedia.org/wiki/File :Playfair_piecharts.jpg.Publicdomain.

importanttoperformvisualdataanalysisinconcertwithnumericalanalysis.Aswe willseelaterinthebook,itiseasytointentionallyorunintentionallymisleadreaders usingvisualpresentationswhenthesearedivorcedfromnumericalstatisticalmeans thatdiscussthe“significance”and“meaningfulness”ofthevisualdata.

IMPORTANCEOFSTATISTICSFORTHESOCIALANDHEALTH SCIENCESANDMEDICINE

Thepresenceofsomuchrichinformationpresentsmeaningfulopportunitiesfor understandingmanyoftheprocessesthataffectthesocialworld.Whilemuchof thetimebigdataanalysesareusedforunderstandingbusinessdynamicsandeconomictrends,itisalsoimportanttofocusonthosedatapatternsthatcanaffectthe socialspherebeyondtheseindicators:socialandpsychologicalbehaviorandattitudes,changesinunderstandinghealthandmedicine,andeducationalprogress.These socialindicatorshavebeenthesubjectofagreatdealofanalysesoverthedecades andnowmaymakesignificantadvancesdependingonhowbigdataareanalyzedand managed.Onarelatednote,thesocialsciences(especiallysociologyandpsychology)arenowareasincludedinthenewMedicalCollegeAdmissionTest(MCAT), whichalsoincludesgreateremphasisupon“ScientificInquiry&ReasoningSkills.” Thematerialwewilllearnfromthisbookwillhelptosupportstudyintheseareas foraspiringhealthandmedicalprofessionals.

Inthisbook,Iintendtofocusonhowtouseandanalyzedataofallsizesand shapes.Whilewewillbelimitedinourabilitytodiveintotheworldofbigdatafully, wecanstudythebasicsofhowtorecognize,generate,interpret,andcritiqueanalyses ofdatafordecisionmaking.Oneofthefirstlessonsisthat datacanbeunderstood bothnumericallyandvisually.Whenwedescribeinformation,weareattemptingto

Nightingale(1858)ismostoftenrememberedasthefounderofmodernnursing. Sheisoftenrepresentedinpaintingsas“theladywiththelamp,”sinceshewas knowntowalkamongthebedsidescheckingonthesickandwoundedofthewar. ButNightingalewasalsoanastutestatisticianwhousedstatisticstocapturethedramaticneedinhospitalsduringtheCrimeanWar.Sheiscreditedasbeingoneofthe firsttousea“piechart”(moreaccurately,a“polarchart”).Figure1.3showscomparisonsinheroriginalpolarchartofdifferencesbetweensoldierswhodiedofbattlefield wounds(“red”wedgesnearthecenter)andthosewhodiedfromothercauses(“blue” wedgesmeasuredfromthecenterofthegraph)overtime.Therelationshipbetween thesegroupsfueledNightingale’seffortstoobtainfurtherfundingforsanitaryhospitalconditionssincethosewhodiedofinfectionsweregreaterinnumberthanthose dyingofbattlefieldwounds.

APPROACHOFTHEBOOK

Manystudentsandresearchersareintimidatedbystatisticalprocedures,whichmay beduetofearofmath,problematicmathteachersinearliereducation,orthelackof exposuretoa“discovery”methodforunderstandingdifficultprocedures.Thisbook isanintroductiontounderstandingstatisticsinawaythatallowsstudentstodiscover patternsindataanddevelopingskillatmakinginterpretationsfromdataanalyses.I describehowtousestatisticalprograms(SPSSandExcel)tomakethestudymore understandableandtoteachstudentshowtoapproachproblemsolving.Ordinarily,a firstcourseinstatisticsleadsstudentsthroughtheworldsofdescriptiveandinferential statisticsbyhighlightingtheformulasandsequentialproceduresthatleadtostatistical decisionmaking.Wewilldoallthisinthisbook,butIplaceagooddealmoreattention onconceptualunderstanding.Thus,ratherthanmemorizingaspecificformulaand usingitinaspecificwaytosolveaproblem,Iwanttomakesurethestudentfirst understandsthenatureoftheproblem,whyaspecificformulaisneeded,andhowit willresultintheappropriateinformationfordecisionmaking.

Byusingstatisticalsoftware,wecanplacemoreattentiononunderstandinghowto interpretfindings.Statisticscoursestaughtinmathematicsdepartments,andinsome socialsciencedepartments,oftenplaceprimaryemphasesontheformulas/processes themselves.Intheextreme,thiscanlimittheusefulnessoftheanalysestothepractitioner.Myapproachencouragesstudentstofocusmoreonhowtounderstandand makeapplicationsoftheresultsofstatisticalanalyses.SPSSandotherstatistical programsaremuchmoreefficientatperformingtheanalyses;thekeyissueinmy approachishowtointerprettheresultsinthecontextoftheresearchquestion.

Beginningwithmyfirstundergraduatecourseteachingstatisticswithconventional textbooks,Ihavespentcountlesshoursdemonstratinghowtoconductstatisticaltests manuallyandteachingstudentstodolikewise.Thisisnotalwaysabadstrategy; performingtheanalysismanuallycanleadthestudenttounderstandhowformulas treatdataandyieldvaluableinformation.However,itisoftenthecasethatthestudentgravitatestomemorizingtheformulaorthestepsinananalysis.Again,there isnothingwrongwiththisapproachaslongasthestudentdoesnotstopthere. The

outcomeoftheanalysisismoreimportantthanmemorizingthestepstotheoutcome. Examiningtheappropriateoutputderivedfromstatisticalsoftwareshiftstheattention fromthenuancesofaformulatothewealthofinformationobtainedbyusingit.

ItisimportanttounderstandthatIdoindeedteachthestudentthenuancesof formulas,understandingwhy,when,how,andunderwhatconditionstheyareused. Butinmyexperience,forcingthestudenttoscrutinizestatisticaloutputfilesaccomplishesthisandteachesthemtheappropriateuseandlimitationsoftheinformation derived.

Studentsinmyclassesarealwayssurprised(ecstatic)torealizetheycanusetheir textbooksandnotesonmyexams.Buttheyquicklyfindthat,unlesstheyreally understandtheprinciplesandhowtheyareappliedandinterpreted,anopenbook isnotgoingtohelpthem.Overtime,theycometorealizethattheanalysesandthe outcomesofstatisticalproceduresaresimplytheingredientsforwhatcomesnext: buildingsolutionstoresearchproblems.Therefore,theirroleismoredetectiveand constructorthannumberjuggler.

Thisapproachmirrorstherecentnationalandinternationaldebateaboutmath pedagogy.Inourrecentbook, WinningtheMathWars (2010),mycolleaguesand Iaddressedtheseissuesingreatdetail,suggestingthat,whiletraditionalwaysof teachingmathareusefulandimportant,theemphasesofreformapproachesarenotto bedismissed.Understandingandmemorizingdetailarecrucial,butproblemsolving requiresadifferentapproachtolearning.

CASESFROMCURRENTRESEARCH

Ifocusonusingreal-worlddatainthisbook.Thereareseveralreasonsfordoingso, primarilybecausestudentsneedtobegroundedinapproachesforusingdatafromthe realworldwithalltheirproblemsand“grittiness.”Whenpeoplerespondtosurveys orinterviews,theyinevitablyfilloutinformationinwaysnotaskedbyinterviewers(e.g.,respondentsmaychoosetwopossibleanswerswhenoneisrequired,etc.). Moreover,transferringdatatoelectronicformmayresultinmiscodedresponsesor categorizationproblems.Researchersalwaysconfronttheseissues,andIbelieveit isimportantforstudentstoleavetheclassroomawareoftherangeofpossibleproblemswithreal-worlddataandpreparedfordealingwiththem.Ofcourse,muchofthe datawewillexaminewillalreadyhavebeenputinstandardforms,butotherresearch issueswillarise(e.g.,howdoIrecategorizedata,assignmissingcases,computenew variables,etc.?).

AnotherreasonIusereal-worlddataistofamiliarizestudentswithcontemporary researchquestionsinthesocialandhealthsciencefields.Classroomdataoftenare contrivedtomakeacertainpointorshowaspecificprocedure,whicharebothhelpful. ButIbelieveitisimportanttodrawthefocusawayfromtheprocedureperseand understandhowtheprocedurewillhelptheresearcherresolvearesearchquestion. Theresearchquestionsareimportant.Policyreflectstheavailableinformationona researchtopic,tosomeextent,soitisimportantforstudentstobeabletogenerate thatinformationaswellastounderstandit.Thisisan“active”ratherthan“passive” learningapproachtounderstandingstatistics.

DataLabsareaveryimportantpartofthiscoursesincetheyallowstudentsto takechargeoftheirlearning.Thisistheheartofdiscoverylearning.Understandinga statisticalprocedureintheconfinesofaclassroomisnecessaryandhelpful.However, learningthatlastsisbestaccomplishedbystudentsdirectlyengagingtheprocesses withactualdataandobservingwhatpatternsemergeinthefindingsthatcanbeapplied torealresearchproblems.

Somepracticeproblemsmayusedatacreatedforclassroomuse,butreal-world datafromactualresearchdatabaseswillenableadeepeningofunderstanding.Inadditiontonationaldatabases,Iuseresultsfrommyownresearchforclassroomlearning. Ineverycase,researchersknowthattheywilldiscoverknottyproblemsandunusual, sometimesidiosyncratic,informationintheirdata.Ifstudentsarenotexposedtothis real-worldaspectofresearch,itwillbeconfusingwhentheyengageinactualresearch beyondtheconfinesoftheclassroom.

Inthiscourse,wewillhaveseveraloccasionstocompleteDataLabsthatpose researchproblemswithactualdata.StudentstakewhattheylearnfromthebookmaterialandconductastatisticalinvestigationusingSPSSandExcel.Then,theyhavethe opportunitytoexaminetheresults,writeresearchsummaries,andcomparefindings withthesolutionspresentedattheendofthebook.

Theprojectlabsalsointroducestudentstotwosoftwareapproachesforsolvingstatisticalproblems.Thesearequitedifferentinmanyregards,aswewillsee inthechaptersthatfollow.SPSSprovidesadditionaladvancedprocedureseducationalresearchersutilizeformorecomplexandextensiveresearchquestions.Excel iswidelyaccessibleandprovidesawealthofinformationtoresearchersaboutmany statisticalprocessestheyencounterinactualresearch.TheDataLabsprovidesolutionsinbothformatssothestudentcanlearnthecapabilitiesandapproachesofeach.

Thisbookmakesuseofpublicallyavailableresearchdata.TheGeneralSocialSurveyorGSS1 isanationallyrepresentativesurveydesignedtobepartofaprogramof socialresearchtomonitorchangesinAmericans’socialcharacteristicsandattitudes. FundedthroughtheNationalScienceFoundationandadministeredbytheNational OpinionResearchCenter(NORC),theGSShasbeenadministeredannuallyorbiannuallysince1972.Asageneralsurvey,theGSSasksavarietyofquestionsonaseries oftopicsdesignedtotracktheopinionsofAmericansoverthelastfourdecades. Otherdatabaseswewilluseinthebookincludethefollowing:

• TheCentersforDiseaseControlandPrevention(CDC)conductstheBehavioral RiskFactorSurveillanceSystem(BRFSS)asahealth-relatedtelephonesurvey tomeasureAmericanresidents’healthconditions,healthbehaviors,anduseof preventativeservices.2

1 TomW.Smith,PeterMarsden,MichaelHout,andJibumKim.GeneralSocialSurveys,1972–2012 [machine-readabledatafile]/PrincipalInvestigator,TomW.Smith;CoprincipalInvestigator,PeterV. Marsden;CoprincipalInvestigator,MichaelHout;SponsoredbyNationalScienceFoundation.–NORC ed.–Chicago:NationalOpinionResearchCenter[producer];Storrs,CT:TheRoperCenterforPublic OpinionResearch,UniversityofConnecticut[distributor],2013.1datafile(57,061logicalrecords) + 1 codebook(3432pp.).--(NationalDataProgramfortheSocialSciences,No.21).

2 CentersforDiseaseControlandPrevention(CDC)(2013). BehavioralRiskFactorSurveillanceSystemSurveyData.Atlanta,Georgia:U.S.DepartmentofHealthandHumanServices,CentersforDisease ControlandPrevention.

Iemphasize“practicalsignificance”(effectsize)inthisbookaswellasstatistical significance.Inmanyways,thisisamorecomprehensiveapproachtouncertainty, sinceeffectsizeisameasureof“impact”intheresearchevaluation.Itisimportant tomeasurethelikelihoodofchancefindings(statisticalsignificance),buttheextent ofinfluencerepresentedintheanalysesaffordstheresearcheranothervantagepoint todeterminetherelationshipamongtheresearchvariables.

CoverageofStatisticalProcedures

Thestatisticalapplicationswewilldiscussinthisbookare“workhorses.”Thisisan introductorytreatment,soweneedtospendtimediscussingthenatureofstatisticsand basicproceduresthatallowyoutousemoresophisticatedprocedures.Wewillnotbe abletoexamineadvancedproceduresinmuchdetail.Iwillprovidesomereferences forstudentswhowishtocontinuetheirlearningintheseareas.Hopefully,asyou learnthecapabilityofSPSSandExcel,youcanexploremoreadvancedprocedures onyourown,beyondtheendofourdiscussions.

Somereadersmayhavetakenstatisticscourseworkpreviously.Ifso,myhopeis thattheyareabletoenrichwhattheypreviouslylearnedanddevelopamorenuanced understandingofhowtoaddressproblemsineducationalresearchthroughtheuseof SPSSandExcel.Whetherreadersarenewtothestudyorexperiencedpractitioners, myhopeisthatstatisticsbecomesmeaningfulasawayofexaminingproblemsand debunkingprevailingassumptionsinthesocialandhealthsciences.

Often,well-intentionedpeoplecan,throughignoranceofappropriateprocesses, promoteideasthatmaynotbetrue.Further,policiesmightbeofferedthatwouldhave anegativeimpacteventhoughthepolicywasnotbasedonsoundstatisticalanalyses. Statisticsaretoolsthatcanbemisusedandinfluencedbythevalueperspectiveofthe wielder.However,policiesareoftengeneratedintheabsenceofcompellingresearch. Studentsneedtobecome“researchliterate”inordertorecognizewhenstatistical processesshouldbeusedandwhentheyarebeingusedincorrectly.

morecomplexthancanbeexplainedbytwovariables.Wethereforemustbeable to“see”patternsamongdatausingbothnumericalandvisualmeansthatunderlie seeminglysimplerelationships.

AswewilldiscussinChapter11,thereisabigdifferencebetween“correlation”and“causation.”Thisstatisticaladagehelpstopointoutthecomplexityof understandingthepatternsamongvariables.Justbecausetwovariablesarestrongly statisticallyrelateddoesnotmeanthatthereisacausalrelationshipbetweenthem. Causalityisdifficulttoprove.Inordertounderstandtheapparentcausalrelationship morefully,wemustlookat othervariablesthatmighthaveameaningfulbut“hidden” relationshipwithboth“visible”variables.Researchersusetheterm“spuriousness”to describewhetheranapparentrelationshipbetweentwovariablesmightbetheinfluenceofvariablesnotintheanalysis.Anexampleofspuriousnessistherelationship betweenicecreamconsumptionandcrime.1

Thereisapositiverelationshipbetweenratesoficecreamconsumptionandcrime; whenoneincreases,sodoestheother.Shouldweconcludethenthaticecreamconsumptionleadstocriminalbehaviorinacausalway?Spuriousnessmeansthatthere maynotatrueorgenuinerelationshipbetweenfactorsevenifitlookslikethereis. Some unobservedorunnoticedvariablemayberelatedtobothofthevariableswe can“see”(inthisexampleicecreamconsumptionandcrime),whichmaymakeit appearthatthe“visible”variableshaveacause–effectrelationship.

Inthisexample,icecreamconsumptionincreasesascrimeincreases;and, consequently,whencrimeincreases,sodoestheconsumptionoficecream.These twovariablesappeartobeconsistentlyrelatedtoeachother.Theyprobablydo nothaveacausalrelationship,however,sincebothicecreamconsumptionand crimearerelatedtoathirdfactor:temperature.Whentemperaturesrise,icecream consumptionincreases(peopleeatmoreicecreaminthesummerthanwinter).Also, whentemperaturesrise,crimeincreases.Ifweincludetheseadditionalrelationships inourstudy,thenwecanseethattheapparentcausalrelationshipbetweenicecream consumptionandcrimeisprobablyreallymoreanissueoftheweather;bothofthe variablesare“linked”bytemperature.

Withoutconsideringspuriousness,somemightbetemptedtoexplain whythereis acausalrelationshipbetweenicecreamconsumptionandcrime.Forexample,does icecreamleadtofeelingsofgrandeurorapropensityforaggression,whichcauses peopletocommitcrime?Orisitthatgoodicecreamissoexpensivethatpeople commitcrimesinordertosupporttheiricecreamhabit?Whichmakesmostsense? Althoughwecouldcomeupwithseveralreasons(mostlyfanciful)whyoneofthese variablesmightbecausallyrelatedtotheother,weneedtobecautious.

Thissituationleadstooneofthemostprofoundlessonsinsocialscience: objectivityisnecessarytopursueknowledgedispassionately.Ifweassumethereisarelationshipbetweenthingswithoutusingobjectivemeansofassessingthetruthofthe situation,thenwearesimplyimposingasubjectiveunderstandingofthesituationthat isnot“anchored”inscience.Somecallthisthe“procrusteanexercise”referencing themythologicalfigurewhoforcedpeopletoanironbedbyeitherstretchingthemto

1 ThisexampleandexplanationarediscussedinAbbottandMcKinney(2013).

Figure2.1 Thepossiblespuriousrelationshipbetweenicecreamconsumptionandcrime. fitorcuttingofftheexcess.Thus,bynottakinganobjectivestance,wemayhavea tendencytomakeapparentreality“fit”ourmentalpictureorsubjectiveassumptions.

Figure2.1showshowthepossiblerelationshipsamongicecreamconsumption, crime,andtemperature.Thetoppanelshowstheapparentrelationshipbetweenice creamconsumptionandcrime,withatwo-waylineconnectingthevariablesindicatingthatthetwoarehighlyrelatedtooneanother.Thebottompanelshowsthat, whenthethirdvariable(temperature)isintroduced,theapparentrelationshipbetween icecreamconsumptionandcrimedisappears,asindicatedbytheabsenceofaline connectingthem.

Identifyingpotentiallyspuriousrelationshipsisoftenquitedifficultandcomes onlyafterextendedresearch.Theresearchermustknowtheirdataintimatelyinorder tomakethediscovery.AnexampleofthisisastudyIconductedinastudyofindustrialdemocracyseveralyearsago.Itwasgenerallyacceptedinindustryatthetime that,ifworkersweregiventheabilitytoparticipateindecisionmaking,theywould havehigherjobsatisfaction(JS).Thiswasareasonableassumption,givensimilar findingsintheresearchliterature.However,themoreIexaminedmyowndatafrom workersinanelectronicindustry,themoreIquestionedthisassumptionanddecided toexplorethematterfurther.

Inoticedfrominterviewsthatmanyworkers didnotwanttoparticipateindecisionmaking,eventhoughtheyhadtheopportunitytodoso.Ithereforeanalyzed theoriginal“participation–jobsatisfaction”butthistimeaddedvariablesthatmeasuredworkers’attitudestowardtheirworkandadesireformanagement.Througha seriesofanalyses,Ifoundanumberofsurprisingresultsthat“modified”theoriginal assumptionofadirect(andcausal)relationshipbetweenparticipationandJS.Oneof thesefindingswasthataworker’s attitudetowardmanagementhadalottodowith theireventualsatisfactionlevels.Thoseworkerswhoparticipatedindecisionmakingandwhohadapositiveviewofmanagementshowedstrongersatisfactionthan thoseworkerswhodidnotsuchapositiveviewofmanagement.Thus,athirdvariable(viewofmanagement)thatwasnotoriginallyincludedinthesimplerelationship (participation–satisfaction)hadanimpactonthefindings.Thissubsequentanalysis discoveredapatterninthedatathatwasnot“visible”attheoutset.

Ice Cream Consumption

Ice Cream Consumption

Crime

Crime