statistical tests for categorical data

Statistical tests for categorical dataDr. S. A. Rizwan, M.D.

PublicHealthSpecialistSBCM, JointProgram– Riyadh

MinistryofHealth,KingdomofSaudiArabia

Learningobjectives

Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh

• Examinetherelationshipbetweencategoricalvariables

• Constructacontingencytablefortwocategoricalvariables

• Describetheapproachtostatisticaltestingofcategoricalvariables

Revise:Categoricalvariables


• Categorical(qualitative)

• Nominal(noorder)• Dichotomous,binary,binomial• Polychotomous

• Ordinal(ordered)

• Answers“what?”• Qualitativedataiscategorised

Revise:Categoricalvariables


Revise:Prerequisitesforatest


• Howmanyvariablesarethere?

• Whatisthenatureofdependentandindependentvariable?

• Howmanycategoriesarethereinthecategoricalvariable?

• Doesthecontinuousvariablefollownormaldistribution?

• Isthereanypairinginthedata/variables?

Revise:DV,IV,Paireddata


Statisticaltests:Bivariate

SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!

Forunpaireddata Forpaireddata

• IfassumptionsforChisquarearemet• Chi-square(>=2levels)

• IfassumptionsforChisquareNOTmet• Fisher’sexact(>=2levels)

• Ifthegroupsarepaired• McNemar (if2levels)• RMlogisticregression (if>2levels)• Interrater reliabilityanalysis

Statisticaltests:Multivariate

SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh

Forunpaireddata Formatcheddata

Demystifying statistics!

• IfDVisbinaryand>1IV• Binarylogisticregression

• IfDVispolychotomousand>1IV• Multinomiallogisticregression

• IfDVisordinaland>1IV• Ordinalregression

• Ifthegroupsarematched• Conditionallogisticregression

• Ifrepeatedmeasurements• RMlogisticregression

Statisticaltests:Special


Forstratifieddata

• Cochran-Mantel-Haenszel test

Statisticaltests:Special


Fororderedcategoricalvariable

• ChisquaretestfortrendPassed Failed Total

R1 100 78 178

R2 175 173 348

R3 42 59 101

Total 317 310 627

Measuresofassociation


• Oddsratio• Relativerisk• Interrater reliabilityanalysis

Contingencytable


• Usedinbivariatesituations• Usecounts,notpercentages• Noone-sidedtests• Eachsubjectcountedonlyonce• Explainsignificantfindings

Someselectedtopics


• Coveredinotherclasses• Chisquaretest• Cochran-Mantel-Haenszel test• Regression

• Inthisclasswewillcoverbasicsof:• Fisher’sexacttest• McNemar test• Interrater reliabilityanalysis(Agreementstatistics)

Thoughtexercise1


• Inastudyaresearchertestedaperfumeon9ratsandusedwaterasthecontrolon9otherrats.Amongtheperfumegroup1ratshowedrestlessnesswhereasamongthecontrolgroup4ratsshowedrestlessness.Determineifthereisanassociationbetweenperfumeandrestlessness.

Thoughtexercise2


• 22pairsoftwinswereenrolledinthestudy.Oneofthetwinssmoked,theotherdidn’t.Thetwinswerefollowedtoseewhichtwindiedfirst.For17pairsoftwins,thesmokingtwindiedfirstandfor5pairsoftwins,thenon-smokingtwindiedfirst.

Thoughtexercise3


• All100pathologicalslideswereobservedby2pathologists.Theweresupposedtoclassifythediseaseasmild,moderateandsevere.Pathologist1classified60,30,10andpathologist2classified50,30,20asmild,moderateandsevere.Bothpathologistsagreedthat44weremild,20weremoderateand6weresevereanddisagreedontheremainingslides.Calculatetheagreementbetweenthetwopathologists.

Fisher’sexacttest


• Usedintheplaceofchisquaretestforindependencewhenthecellcountsaresparse

• Morethan20%ofthecellshaveexpected frequenciesof<5

Fisher’sexacttest


Fisher’sexacttest


• 6possibletablesfortheobservedmarginaltotals:9,9,5,13.

• p-valueiscalculatedbysummingallprobabilitieslessthanorequaltotheprobabilityoftheobservedtable

Fisher’sexacttest


• Theobservedtable(TableII)hasprobability=0.132

• P-valuefortheFisher’sexacttest=Pr (TableII)+Pr (TableV)+Pr(TableI)+Pr (TableVI)

• =0.132+0.132+0.0147+0.0147=0.293

McNemar test


• Whendataarepairedandtheoutcomeofinterestisaproportion,theMcNemar Testisused

• Pair-Matcheddatacancomefrom• Case-controlstudieswhereeachcasehasamatchingcontrol

(matchedonage,gender,race,etc.)• Twinsstudies– thematchedpairsaretwins

• Before- Afterdata• Outcomeispresence(+)orabsence(-)ofsomecharacteristic

measuredonthesameindividualattwotimepoints

McNemar test:matchedcase-control


• a- numberofcase-controlpairswherebothareexposed• b- numberofcase-controlpairswherethecaseisexposedandthe

controlisunexposed• c- numberofcase-controlpairswherethecaseis• unexposedandthecontrolisexposed• d- numberofcase-controlpairswherebothareunexposed• Thecountsinthetableforacase-controlstudyarenumbersofpairs

notnumbersofindividuals.

McNemar test:before-afterstudy


• a- numberofsubjectswithcharacteristicpresentbothbeforeandaftertreatment

• b- numberofsubjectswherecharacteristicispresentbeforebutnotafter

• c- numberofsubjectswherecharacteristicispresentafterbutnotbefore

• d- numberofsubjectswiththecharacteristicabsentbothbeforeandaftertreatment.

McNemar test


• Calculatedusingthecountsinthe‘b’and‘c’cellsofthetable

• ThesamplingdistributionChi-squaredistribution,thedegreesoffreedom=1

• Foratestwithalpha=0.05,thecriticalvaluefortheMcNemar statistic=3.84.

McNemar test


McNemar test


• CriticalvalueforChi-squaredistributionwith1df =3.84,pvalue=0.01

• Conclusion:Asignificantlydifferentproportionofsmokingtwinsdiedfirstcomparedtotheirnon-smokingtwinindicatingadifferentriskofdeathassociatedwithsmoking(p=0.01)

Agreementstatistics


• Manytypesofagreementstatistics dependingon• Datatype• Typeofrepetition• Internalconsistency

Agreementstatistics


• Cohen’skappa

• Measurestheagreementbetweentworaters whoeachclassifyNitemsintoCmutuallyexclusivecategories

• Usedwhenresponsesarecategorical

Agreementstatistics


Agreementstatistics


𝐾𝑎𝑝𝑝𝑎 =0.70 − 0.411 − 0.41 = 0.491

Advancedlearning


• Chisquaretestfortrend• Specialcasesoflogisticregression• Repeatedmeasureslogisticregression• Weightedkappa• Othermeasuresofagreementanalysis

Takehomemessages


• Manyapproachesareavailableforanalysingcategoricaldata• Chooseamethodappropriateforyourproblem• Checkthattheassumptionsofthemethodarevalid• Makeconclusionsbasedontheresultsofthetest

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statistical tests for categorical data

Health & Medicine