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1、WhenToUseFisher’sExactTestbyKeithM.Bower,M.S.ReprintedwithpermissionfromtheAmericanSocietyforQualitySixSigmapractitionersoccasionallyconductstudiestoassessdifferencesbetweenitemssuchasoperatorsormachines.Whentheexperimentaldataaremeasuredonacontinuousscale(measuringnozzl
2、ediameterinmicrons,forexample),aproceduresuchas1“Student’s”two-samplet-testmaybeappropriate.Whentheresponsevariableis22recordedusingcounts,however,KarlPearson’sχtestmaybeemployed.2Butwhenthenumberofobservationsobtainedforanalysisissmall,theχtestmayproducemisleadingresult
3、s.Amoreappropriateformofanalysis(whenpresentedwitha2*2contingencytable)istouseR.A.Fisher’sexacttest.ExampleOntheLateShowWithDavidLetterman,thehost(David)andtheshow’smusicaldirector(PaulShaffer)frequentlyassesswhetherparticularitemswillorwillnotfloatwhenplacedinatankofwat
4、er.Let’sassumeLettermanguessedcorrectlyforeightofnineitems,andShafferguessedcorrectlyforonlyfouritems.Let’salsoassumealltheitemshavethesameprobabilityofbeingguessed.Figure1GuessedcorrectlyGuessedincorrectlyTotalLetterman819Shaffer459Total126182Youwouldtypicallyusetheχtes
5、twhenpresentedwiththecontingencytableresultsin2Figure1.Inthiscase,theχtestassesseswhattheexpectedfrequencieswouldbeifthenullhypothesis(equalproportions)wastrue.Forexample,iftherewerenodifferencebetweenLettermanandShaffer’sguesses,youwouldexpectLettermantohavebeencorrects
6、ixtimes(seeFigure2).Thisiscalculatedas(9*12)/18=108/18=6.Figure2Rows:PlayerColumns:ResultCorrectIncorrectAllDavid8196.003.009.00Paul4596.003.009.00All1261812.006.0018.00Chi-Square=4.000,DF=1,P-Value=0.0462cellswithexpectedcountslessthan5.0CellContents--CountExpFreq2There
7、sultingp-value,0.046,fromtheχtestindicatesthereisastatisticallysignificantdifference(attheα=0.05level)inthesuccessratesbetweenLettermanandShaffer.2AsFisherdiscusses,however,“Thetreatmentoffrequenciesbymeansofχisanapproximation,whichisusefulforthecomparativesimplicityofth
8、ecalculations.The3exacttreatmentissomewhatmorelaborious,thoughnecessaryincasesofdoubt.”Somepractitioner
