ThebitestcommandisabetterversionoftherstformofprtestinthatitgivesexactpvaluesResearchersshouldusebitestwhenpossibleespeciallyforsmallsamplesseeRbitestOptions Main bygroupvarspeciesanume ID: 523920
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2prtest—Testsofproportions Thebitestcommandisabetterversionoftherstformofprtestinthatitgivesexactp-values.Researchersshouldusebitestwhenpossible,especiallyforsmallsamples;see[R]bitest.Options � Main �by(groupvar)speciesanumericvariablethatcontainsthegroupinformationforagivenobservation.Thisvariablemusthaveonlytwovalues.Donotconfusetheby()optionwiththebyprex;bothmaybespecied.level(#)speciesthecondencelevel,asapercentage,forcondenceintervals.Thedefaultislevel(95)orassetbysetlevel;see[U]20.7Specifyingthewidthofcondenceintervals.countspeciesthatintegercountsinsteadofproportionsbeusedintheimmediateformsofprtest.Intherstsyntax,prtestiexpectsthat#obs1and#p1arecounts—#p1#obs1—and#p2isaproportion.Inthesecondsyntax,prtestiexpectsthatallfournumbersareintegercounts,that#obs1#p1,andthat#obs2#p2.Remarksandexamplesstata.comTheprtestoutputfollowstheoutputofttestinprovidingalotofinformation.Eachproportionispresentedalongwithacondenceinterval.Theappropriateone-ortwo-sampletestisperformed,andthetwo-sidedandbothone-sidedresultsareincludedatthebottomoftheoutput.Foratwo-sampletest,thecalculateddifferenceisalsopresentedwithitscondenceinterval.Thiscommandmaybeusedforbothlarge-sampletestingandlarge-sampleintervalestimation. Example1:One-sampletestofproportionIntherstform,prtesttestswhetherthemeanofthesampleisequaltoaknownconstant.Assumethatwehaveasampleof74automobiles.Wewishtotestwhethertheproportionofautomobilesthatareforeignisdifferentfrom40%..usehttp://www.stata-press.com/data/r13/auto(1978AutomobileData).prtestforeign==.4One-sampletestofproportionforeign:Numberofobs=74 Variable MeanStd.Err.[95%Conf.Interval] foreign .2972973.0531331.1931583.4014363 p=proportion(foreign)z=-1.8034Ho:p=0.4Ha:p0.4Ha:p!=0.4Ha:p&#x-532;0.4Pr(Zz)=0.0357Pr(|Z|&#x-531;|z|)=0.0713Pr(Z&#x-531;z)=0.9643Thetestindicatesthatwecannotrejectthehypothesisthattheproportionofforeignautomobilesis0.40atthe5%signicancelevel. 4prtest—Testsofproportions .prtesti30.445.67Two-sampletestofproportionsx:Numberofobs=30y:Numberofobs=45 Variable MeanStd.Err.z�P|z|[95%Conf.Interval] x .4.0894427.2246955.5753045y .67.0700952.532616.807384 diff -.27.1136368-.4927241-.0472759 underHo:.1169416-2.310.021 diff=prop(x)-prop(y)z=-2.3088Ho:diff=0Ha:diff0Ha:diff!=0Ha:diff&#x-531;0Pr(Zz)=0.0105Pr(|Z||z|)=0.0210Pr(Z&#x-531;z)=0.9895 Storedresultsprtestandprtestistorethefollowinginr():Scalarsr(z)zstatisticr(P #)proportionforvariable#r(N #)numberofobservationsforvariable#MethodsandformulasSeeAcock(2014,155–161)foradditionalexamplesoftestsofproportionsusingStata.Alarge-sample100(1� )%condenceintervalforaproportionpisbpz1� =2r bpbq nanda100(1� )%condenceintervalforthedifferenceoftwoproportionsisgivenby(bp1�bp2)z1� =2s bp1bq1 n1+bp2bq2 n2wherebq=1�bpandziscalculatedfromtheinversecumulativestandardnormaldistribution.Theone-tailedandtwo-tailedtestsofapopulationproportionuseanormallydistributedteststatisticcalculatedasz=bp�p0 p p0q0=nwherep0isthehypothesizedproportion.Atestofthedifferenceoftwoproportionsalsousesanormallydistributedteststatisticcalculatedas