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1、February17,2011StatisticalalgorithmsfortheCalculatorinReviewManager5.1GeorgiaSalantiOnBehalfoftheStatisticalMethodsGroupoftheCochraneCollaborationTestvalues(Zandttestscores)andp-valuesWhatisusuallydescribedas‘distribution’invarioussoftwareisthecumulativeprobabilityfunction,thati
2、sthefunctionthatmapsatestvalue(t-testvalueorzvalue,herecalledtandz)toaprobability.Thesefunctionsaredenotedhereaspt(forthet-distribution)andpnorm(forthenormaldistributionassociatedwiththeztest).Thep-valuecanbecalculatedas(-(
3、
4、))(1)(-(
5、
6、))(2)wheredfarethedegreesoffreedom(seebelowo
7、nhowtocalculatethese).Theinverseofthefunctionsptandpnorm(denotedqtandqnormrespectively,‘q’standsforthequantiles)mapsthep-valuetoavalueoft-testorz-test(denotedastandz)usingthefollowingfunctions(-)(3)(-)(4)Thesignoftorzineachcasecanbeobtainedfromthedifferencebetweenthetwomeans(oro
8、nemeancomparedtozero)forcontinuousdataandfromthesignsoflog(OR)orlog(RR)orRDforbinarydata.ContinuousDataCalculationsforonegroup(experimentalorcontrol)DatastructureGroupsizeMeanResponseStandardDeviationExperimentalN1Mean1SD1ControlN2Mean2SD2ForexperimentalThefollowingformulaeareus
9、edinthecalculationsofvariousstatisticsTocalculatethestandarderror1February17,2011√Tocalculatethet-testvalueforcomparingonemeanwithzeroasP-value1andttest1canbecalculatedfromequations(1)and(3)withdf=N1-1((
10、
11、))()Let’scallfthe‘confidencelevel’.Thatisf=0.90,0.95or0.99dependingonwhati
12、sselectedbytheuser.Upperandlowerlimitsforthef%ConfidenceInterval(CI)aregivenby()WhenN1,Mean1andSD1needtobeestimatedfromacombinationoftwo(sub)groupswithsamplesizes,meansandstandarddeviationsNA,MeanA,SDA,NB,MeanB,SDBthefollowingformulaeapplyN1=NA+NB()()√where()Note:Theformulaeabov
13、eholdonlywhengroupsAandBareindependent;soitcannotbeusedtoestimateforchangescores(combiningpreandpostmeasurementsforthesamegroup).ForcontrolAllformulaedescribedforexperimentalholdforMean2,SD2,SE2,N2,ttest2,pvalue22February17,2011CalculationsforMeanDifferenceThecalculationsassocia
14、tedwithmeandifference(MD)anditsstandarderror(SE
