statistical tests for categorical data
TRANSCRIPT
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
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Categorical(qualitative)
• Nominal(noorder)• Dichotomous,binary,binomial• Polychotomous
• Ordinal(ordered)
• Answers“what?”• Qualitativedataiscategorised
Revise:Categoricalvariables
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
Revise:Prerequisitesforatest
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Howmanyvariablesarethere?
• Whatisthenatureofdependentandindependentvariable?
• Howmanycategoriesarethereinthecategoricalvariable?
• Doesthecontinuousvariablefollownormaldistribution?
• Isthereanypairinginthedata/variables?
Revise:DV,IV,Paireddata
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
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
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
Forstratifieddata
• Cochran-Mantel-Haenszel test
Statisticaltests:Special
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
Fororderedcategoricalvariable
• ChisquaretestfortrendPassed Failed Total
R1 100 78 178
R2 175 173 348
R3 42 59 101
Total 317 310 627
Measuresofassociation
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Oddsratio• Relativerisk• Interrater reliabilityanalysis
Contingencytable
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Usedinbivariatesituations• Usecounts,notpercentages• Noone-sidedtests• Eachsubjectcountedonlyonce• Explainsignificantfindings
Someselectedtopics
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Coveredinotherclasses• Chisquaretest• Cochran-Mantel-Haenszel test• Regression
• Inthisclasswewillcoverbasicsof:• Fisher’sexacttest• McNemar test• Interrater reliabilityanalysis(Agreementstatistics)
Thoughtexercise1
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Inastudyaresearchertestedaperfumeon9ratsandusedwaterasthecontrolon9otherrats.Amongtheperfumegroup1ratshowedrestlessnesswhereasamongthecontrolgroup4ratsshowedrestlessness.Determineifthereisanassociationbetweenperfumeandrestlessness.
Thoughtexercise2
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• 22pairsoftwinswereenrolledinthestudy.Oneofthetwinssmoked,theotherdidn’t.Thetwinswerefollowedtoseewhichtwindiedfirst.For17pairsoftwins,thesmokingtwindiedfirstandfor5pairsoftwins,thenon-smokingtwindiedfirst.
Thoughtexercise3
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• All100pathologicalslideswereobservedby2pathologists.Theweresupposedtoclassifythediseaseasmild,moderateandsevere.Pathologist1classified60,30,10andpathologist2classified50,30,20asmild,moderateandsevere.Bothpathologistsagreedthat44weremild,20weremoderateand6weresevereanddisagreedontheremainingslides.Calculatetheagreementbetweenthetwopathologists.
Fisher’sexacttest
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Usedintheplaceofchisquaretestforindependencewhenthecellcountsaresparse
• Morethan20%ofthecellshaveexpected frequenciesof<5
Fisher’sexacttest
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
Fisher’sexacttest
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• 6possibletablesfortheobservedmarginaltotals:9,9,5,13.
• p-valueiscalculatedbysummingallprobabilitieslessthanorequaltotheprobabilityoftheobservedtable
Fisher’sexacttest
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• 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
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Whendataarepairedandtheoutcomeofinterestisaproportion,theMcNemar Testisused
• Pair-Matcheddatacancomefrom• Case-controlstudieswhereeachcasehasamatchingcontrol
(matchedonage,gender,race,etc.)• Twinsstudies– thematchedpairsaretwins
• Before- Afterdata• Outcomeispresence(+)orabsence(-)ofsomecharacteristic
measuredonthesameindividualattwotimepoints
McNemar test:matchedcase-control
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• a- numberofcase-controlpairswherebothareexposed• b- numberofcase-controlpairswherethecaseisexposedandthe
controlisunexposed• c- numberofcase-controlpairswherethecaseis• unexposedandthecontrolisexposed• d- numberofcase-controlpairswherebothareunexposed• Thecountsinthetableforacase-controlstudyarenumbersofpairs
notnumbersofindividuals.
McNemar test:before-afterstudy
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• a- numberofsubjectswithcharacteristicpresentbothbeforeandaftertreatment
• b- numberofsubjectswherecharacteristicispresentbeforebutnotafter
• c- numberofsubjectswherecharacteristicispresentafterbutnotbefore
• d- numberofsubjectswiththecharacteristicabsentbothbeforeandaftertreatment.
McNemar test
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Calculatedusingthecountsinthe‘b’and‘c’cellsofthetable
• ThesamplingdistributionChi-squaredistribution,thedegreesoffreedom=1
• Foratestwithalpha=0.05,thecriticalvaluefortheMcNemar statistic=3.84.
McNemar test
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
McNemar test
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• CriticalvalueforChi-squaredistributionwith1df =3.84,pvalue=0.01
• Conclusion:Asignificantlydifferentproportionofsmokingtwinsdiedfirstcomparedtotheirnon-smokingtwinindicatingadifferentriskofdeathassociatedwithsmoking(p=0.01)
Agreementstatistics
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Manytypesofagreementstatistics dependingon• Datatype• Typeofrepetition• Internalconsistency
Agreementstatistics
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
• Cohen’skappa
• Measurestheagreementbetweentworaters whoeachclassifyNitemsintoCmutuallyexclusivecategories
• Usedwhenresponsesarecategorical
Agreementstatistics
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
Agreementstatistics
SBCM, Joint Program – RiyadhSBCM, Joint Program – RiyadhDemystifying statistics!
𝐾𝑎𝑝𝑝𝑎 =0.70 − 0.411 − 0.41 = 0.491
Advancedlearning
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Chisquaretestfortrend• Specialcasesoflogisticregression• Repeatedmeasureslogisticregression• Weightedkappa• Othermeasuresofagreementanalysis
Takehomemessages
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Manyapproachesareavailableforanalysingcategoricaldata• Chooseamethodappropriateforyourproblem• Checkthattheassumptionsofthemethodarevalid• Makeconclusionsbasedontheresultsofthetest