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| The effect size used here is the Odds Ratio See http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d which can also be expressed as a difference in proportions. |
The effect size used here is the Odds Ratio See http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d which can also be expressed as a difference in proportions.
DATA LIST free /p1 p2 ratio ntot alpha. BEGIN DATA. 0.19 0.09 1 311 0.05 0.19 0.09 4 311 0.05 0.19 0.09 3 600 0.05 END DATA. compute p11= (p1*ratio)/(1+ratio). compute p12=((1-p1)*ratio)/(1+ratio). compute p21=p2/(1+ratio). compute p22=(1-p2)/(1+ratio). compute oddsr = (p11*p22)/(p21*p12). exe. matrix. get m /variables=p11 p12 p21 p22 ntot alpha /missing=omit. compute p11=make(1,1,0). compute p12=make(1,1,0). compute p21=make(1,1,0). compute p22=make(1,1,0). compute alpha=make(1,1,0). compute p11=m(:,1). compute p12=m(:,2). compute p21=m(:,3). compute p22=m(:,4). compute ntot=m(:,5). compute alpha=m(:,6). end matrix. COMPUTE #chisq1 = (LN(oddsr)/(sqrt((1/p11)+(1/p12)+(1/p21)+(1/p22))))**2. compute #df=1. compute #conf = 1-alpha. compute #chisq=ntot*#chisq1. compute power = 1 - NCDF.CHISQ(IDF.CHISQ(#conf,#DF),#DF,#CHISQ). compute p1=p11/(p11+p12). compute p2=p21/(p21+p22). compute ratio = (p11+p12)/(p21+p22). formats p1 (f5.2) p2 (f5.2) alpha (f5.2) ntot (f5.2) power (f5.2). variable labels p1 'Proportion 1' /p2 'Proportion 2' /ratio 'Ratio group 1 to group 2' /alpha 'Two-Tailed Alpha' /ntot 'Sample Size' /power 'Power'. report format=list automatic align(center) /variables=p1 p2 ratio alpha ntot power /title "Power for given sample size for an Odds Ratio from a 2x2 table of proportions" .
