confidence intervals: types and calculations

Confidence Intervals: types and calculationDr. S. A. Rizwan, M.D.

PublicHealthSpecialistSBCM, JointProgram– Riyadh

MinistryofHealth,KingdomofSaudiArabia

Learningobjectives

Demystifying statistics! – Lecture 10 SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh

• DescribethevarioussituationsforcalculatingCI• Applytheformulaforcalculatingdifferentsituations

Introduction


• Confidenceintervalscanbecalculatedforanumberofstatistics• Theyallfollowthegeneralformat• Thedifferenceslieintheformulaforstandarderror

StepsincalculatingCI


CIforasinglemean:example


• Example:findCIwhensamplemean=10.2,sd =10.1,N=1055,confidencelevel=95%.

• zisderivedfromthe95%value:whatvalueofzleaves95%inthemiddleand2.5%oneachendofadistribution?• Forp=.975,z=1.96

• Thestandarderroriss/SQRT(n)=10.1/SQRT(1055)=0.31• Upperlimit10.2+1.96*0.31=10.80• Lowerlimit10.2– 1.96*0.31=9.59• Hence,theconfidenceintervalis9.59to10.81

CIforasinglemean:workout


• Welookatastudyof200malesversus200femalesmeanSATscores.ThemeanSATscoreforfemalesis1180withastandarddeviationof5andformales,themeanSATscoreis1160withastandarddeviationof6.

• Forma95%confidenceintervalforthemeanSATscoreforfemalesandmales

CIforasinglemean:workout


Variable Obs Mean Std.Err. [95%Conf. Interval]Females 200 1180 0.35 1179.30 1180.69

Variable Obs Mean Std.Err. [95%Conf. Interval]Males 200 1160 0.42 1159.16 1160.83

CIforasingleproportion:workout


• Astudywasdoneontheproportionofmalesandfemaleswhoparticipateinathletics.480femalesand530malesparticipatedinthestudy,where170femalesand208malesparticipatedinathletics

• Forma95%CIforeachoftheproportionoffemaleandmaleathletes?

CIforasingleproportion:workout


Variable Obs Mean Std.Err. [95%Conf.Interval]Females 480 0.354 0.0218 0.3113 0.3987

Variable Obs Mean Std.Err. [95%Conf.Interval]Males 530 0.392 0.0212 0.3506 0.4354

CIforadifferencein2means


• Thetablebelowsummarizesdatan=3539participantsattendingthe7thexaminationoftheOffspringcohortintheFraminghamHeartStudy.

• Calculatethedifferenceinmeansystolicbloodpressuresbetweenmenandwomen,and95%confidenceintervalforthedifferenceinmeans.



Mean difference = 1.7 (95% CI: 0.44, 2.96)

CIforadifferencein2proportions


• ThefollowingtablecontainsdataonprevalentCVDamongparticipantswhowerecurrentlynon-smokersandthosewhowerecurrentsmokersintheFraminghamOffspringStudy.

• CalculatethedifferenceinprevalentCVDbetweensmokersandnon-smokersanda95%CIconfidenceintervalforthedifference.

CIforadifferencein2proportions


Differenceinprevalence=0.0114(95%CI:-0.0133,0.0361)

CIforrelativerisk


CIforoddsratio


CIforotherpointestimates


• Smallsamplesize(<30)• Matcheddata• Oddsratio• Riskratio• Hazardratio• Regressioncoefficient• Manyotherstatistics

Advancedlearning


• ThemethodsofcalculatingCImaydifferdependingontheformulausedforagivenpointestimateandhencetheCImaydiffer

• MostofthetimeCIandpvaluesagreeinacomparativesituation,butsometimestheydon’t

• InsomesituationsCImaynotbesymmetrical

• Whatarepredictionintervalsanduncertaintyintervals?

Takehomemessages


• Confidenceintervalisoneofthecornerstonesofstatisticalinference

• Eachpointestimatefromasamplerequiresaconfidenceinterval

• RememberthegeneralformatofCI

• RememberthecorrectinterpretationofCIforthegivensituation

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confidence intervals: types and calculations

Health & Medicine