statistical tests for data involving quantitative data
TRANSCRIPT
Statistical tests for quantitative dataDr. S. A. Rizwan, M.D.
PublicHealthSpecialistSBCM, JointProgram– Riyadh
MinistryofHealth,KingdomofSaudiArabia
Learningobjectives
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Describetheapproachtostatisticaltestinginvolvingquantitativevariables
Revise:Categoricalvariables
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• Numerical(Quantitative)
• Continuous• Interval• Ratio
• Answers“howmany?”• Quantitativedataismeasured
Revise:Categoricalvariables
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Revise:Prerequisitesforatest
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Howmanyvariablesarethere?
• Whatisthenatureofdependentandindependentvariable?
• Howmanycategoriesarethereinthecategoricalvariable?
• Doesthecontinuousvariablefollownormaldistribution?
• Isthereanypairinginthedata/variables?
Statisticaltests:Bivariate
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Forunpaireddata:Parametric Forunpaireddata:Non-parametric
• Categorical(2levels)vs.Quantitative• Independent samplesttest
• Categorical(>2levels)vs.Quantitative• OnewayANOVA
• Categorical(2levels)vs.Quantitative• MannWhitneyUtest(akaWilcoxonranksumtest)
• Categorical(>2levels)vs.Quantitative• Kruskal Wallis
Statisticaltests:Bivariate
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Forpaireddata:Parametric Forpaireddata:Non-parametric
• Categorical(2levels)vs.Quantitative• Pairedttest
• Categorical(>2levels)vs.Quantitative• RepeatedmeasuresANOVA
• Categorical(2levels)vs.Quantitative• Wilcoxonsignranktest
• Categorical(>2levels)vs.Quantitative• Friedmantest
Statisticaltests:Bivariate
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Parametric Non-parametric
• Quantitativevs.Quantitative• Pearson’scorrelation
• Quantitativevs.Quantitative• Simplelinearregression
• Quantitativevs.Quantitative• Spearman’s rankcorrelation
Statisticaltests:Multivariate
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Forunpaireddata ForpairedorRMdata
Demystifying statistics!
• IfDVisquantitativeand>1IV• Multiplelinearregression
• IfDVisquantitativeand>1IV• GLM
Measuresofassociation
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• Correlationcoefficient• Regressioncoefficient
Someselectedtopics
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• Coveredinotherclasses• Ttestsanditstypes• Correlation• Regression
• Inthisclasswewillcoverbasicsof:• Mann-WitneyUtest• KruskalWallistest• Wilcoxonsignedranktest• Friedman’stest
Thoughtexercise1
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• Atotalofn=10participantsarerandomizedtoreceiveeitherthenewdrugoraplacebo.Participantsareaskedtorecordthenumberofepisodesofshortnessofbreathovera1weekperiod.Isthereadifferenceinthenumberofepisodesinparticipantsreceivingthenewdrugascomparedtothosereceivingtheplacebo?
Thoughtexercise2
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• Threedietsarecompared,5%,10%,15%protein
• Thealbuminlevelsofparticipantsfollowingeachdietareshown
• Isthereisadifferenceinserumalbuminlevelsamongsubjectsonthethreedifferentdiets?
Thoughtexercise3
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• Atotalof8childrenwithautismenroll inthestudyandtheamountoftimethateachchildisengagedinrepetitivebehavior duringthreehourobservationperiodsaremeasuredbothbeforetreatmentandthenagainaftertakingthenewmedicationforaperiodof1week. Thedataareshown.
• Isthereanyimprovedinthechildren?
Thoughtexercise4
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• Fourresidentsaregiventhreesamplesofkahwa preparedbythreedifferentpersons.Theyscorethequalityofthekahwa innumericalterms.Thedataisshown.
• Isthereisadifferencebetweenthe3typesofkahwa?
Mann–WhitneyUtest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• AlsoknownasWilcoxonRankSumTest• Anonparametricprocedurethatdeterminesifrankedscores(i.e.,ordinaldata)intwoindependentgroupsdiffer
• Alsousedtoanalyze intervalorratioscalevariablesthatarenotnormallydistributed
• Someinterpretthistestascomparingthemediansbetweenthetwopopulations
• H0:Thetwopopulationsareequalversus• H1:Thetwopopulationsarenotequal
Mann–WhitneyUtest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Atotalofn=10participantsarerandomizedtoreceiveeitherthenewdrugoraplacebo.Participantsareaskedtorecordthenumberofepisodesofshortnessofbreathovera1weekperiodfollowingreceiptoftheassignedtreatment.Thedataareshownbelow.
• Isthereadifferenceinthenumberofepisodesinparticipantsreceivingthenewdrugascomparedtothosereceivingtheplacebo?
Mann–WhitneyUtest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
where R1 = sum of the ranks for group 1 and R2 = sum of the ranks for group 2.
Mann–WhitneyUtest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Inourexample,U=3(smallerofthetwoUs).Isthisevidenceinsupportofthenullorresearchhypothesis?
• ThecriticalvalueofUcanbefoundinthetable.Todeterminetheappropriatecriticalvalueweneedsamplesizes(n1=n2=5)andourtwo-sidedlevelofsignificance(α=0.05).
• Thecriticalvalueis2,andthedecisionruleistorejectH0 ifU < 2.• WedonotrejectH0 because3>2.
Kruskal Wallistest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• NonparametrictesttocompareoutcomesamongmorethantwoindependentgroupsistheKruskal Wallistest.
• Usedtocomparemediansamongkcomparisongroups(k>2)• DescribedasanANOVAwiththedatareplacedbytheirranks.
• Thenullandresearchhypothesesarestatedasfollows:• H0:Thekpopulationmediansareequalversus• H1:Thekpopulationmediansarenotallequal
Kruskal Wallistest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Threedietsarecompared,rangingfrom5%to15%protein,andthe15%proteindietrepresentsatypicalAmericandiet.Thealbuminlevelsofparticipantsfollowingeachdietareshownbelow
• Isthereisadifferenceinserumalbuminlevelsamongsubjectsonthethreedifferentdiets?
Kruskal Wallistest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Wefirstorderthedatainthecombinedtotalsampleof12subjectsfromsmallesttolargest.
• Wealsoneedtokeeptrackofthegroupassignmentsinthetotalsample
Kruskal Wallistest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• TheteststatisticisdenotedHandisdefinedasfollows:
• wherek=thenumberofcomparisongroups,N=thetotalsamplesize,nj isthesamplesizeinthejth groupandRj isthesumoftheranksinthejth group
• InthisexampleR1 =7.5,R2 =30.5,andR3 =40
Kruskal Wallistest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Thecriticalvalueis5.656,thuswerejectH0 because7.52 > 5.656,andweconcludethatthereisadifferenceinmedianalbuminlevelsamongthethreedifferentdiets.
Wilcoxonsignedranktest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Nonparametrictestformatchedorpaireddata• Itisbasedondifferencescores,butinadditiontoanalyzing thesignsofthedifferences(unlikethesigntest),italsotakesintoaccountthemagnitudeoftheobserveddifferences
Wilcoxonsignedranktest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Atotalof8childrenwithautismenroll inthestudyandtheamountoftimethateachchildisengagedinrepetitivebehavior duringthreehourobservationperiodsaremeasuredbothbeforetreatmentandthenagainaftertakingthenewmedicationforaperiodof1week. Thedataareshown
Wilcoxonsignedranktest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• First,wecomputedifferencescoresforeachchild.
Wilcoxonsignedranktest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Wefirstorderthe absolutevaluesofthedifferencescores andassignrankfrom1throughntothesmallestthroughlargestabsolutevaluesofthedifferencescores,
• Assignthemeanrankwhentherearetiesintheabsolutevaluesofthedifferencescores.
Wilcoxonsignedranktest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Thefinalstepistoattachthesigns("+"or"-")oftheobserveddifferencestoeachrankasshownbelow.
Wilcoxonsignedranktest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• TheteststatisticfortheWilcoxonSignedRankTestisW,definedasthesmallerofW+(sumofthepositiveranks)andW- (sumofthenegativeranks).
• Inthisexample,W+=32andW- =4.• ThecriticalvalueofWis6andthedecisionruleistorejectH0 ifW < 6.Thus,werejectH0,because4 < 6.
Friedmantest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Non-parametricalternativetotheone-wayANOVAwithrepeatedmeasures
• Itisusedtotestfordifferencesbetweengroupswhenthedependentvariableisquantitativebutcorrelated
• Itcanalsobeusedforcontinuousdatathathasviolatedtheassumptionsnecessaryofone-wayANOVAwithrepeatedmeasures;forexample,markeddeviationsfromnormality
Friedmantest
Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• distributedaschi-squarewithdf =k– 1,• chqr =4.5• P=0.1054
Advancedlearning
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• RepeatedmeasuresANOVA• GeneralisedLinearModels• Coxregression• Factoranalysis• Longitudinaldataanalysis• Othertypesofregressionmodels• Meta-analysis
Takehomemessages
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Manyapproachesareavailableforanalysingquantitativedata• Chooseamethodappropriateforyourproblem• Checkthattheassumptionsofthemethodarevalid• Makeconclusionsbasedontheresultsofthetest