Sample Size - vanbelle.org

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2SampleSizeThe rstquestionfacedbya statisticalconsultant,andfrequentlythela st,is, Howmany subjects(animals,units)doI need? , TypeII error, andone sidedversustwo questionistosettlethetypeofvariable(endp oint)theconsulteehasinmind:Isit continuous,discrete,orsomethingelse?Forc ontinuousmeasurementsthenormaldistributi onisthedefaultmodel,fordistributionswith binaryoutcomes, samplesizecalculation,foroneortwo groups,are:TypeI Error( )Probabilityofrejectingthenullhypothesis whenit is trueTypeII Error( )Probabilityofnotrejectingthenullhypothe siswhenit is falsePower=1 Probabilityofrejectingthenullhypothesisw henit is false 20and 21Variancesunderthenullandalternative hypothe ses(maybethesame) 0and 1Meansunderthenullandalternative hypothesesn0andn1Samplesizesintwo groups(maybethesame)Thechoiceofthealtern ative hypothesisis they knew thevalueofthealternative hypothesis,they wouldnotneedtodothestudy. Thereis alsodebateaboutwhichis thenullhypothesisandwhichis the2728SAMPLESIZEPSfragreplacementsH0: 0 1= 0H1: 0 1= 0 =2 =2S:E:= q2nS:E:= q2nR CriticalValuePower= 1 y0 y1|{z} |{z}0+z1 =2 q2n z1 sidedalternative,equalvariancesundernull andalternative , siteis safeorhazardousasthenullhypothesis?

28 SAMPLE SIZE PSfrag replacements H0: 0 1 = 0 H1: 0 1 = 0 =2 =2 S:E:=˙ q 2 S:E:=˙ n q 2 n R Critical Value Power=1 y 0 y 1 | {z } |{z} 0+z1 =2˙ q 2 n 2z1 ˙ q n Fig. 2.1 Sampling model for two independent sample case.

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