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| p1 and p2 are the proportions in groups 1 and 2 being compared, ratio is the ratio of sizes of group 1 to group 2, ntot is the ''total'' sample size and alpha is the (two-tailed) type I error. The program then outputs the power. | p1 and p2 are the proportions in groups 1 and 2 being compared, delta is the ratio of sizes of group 1 to group 2, ntot is the ''total'' sample size and alpha is the (two-tailed) type I error. The program then outputs the power. |
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| /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. |
/alpha p1 p2 delta n1. BEGIN DATA. .05 0.19 0.09 1 167 .05 0.39 0.25 1 100 END DATA. |
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| 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). |
get m /variables=alpha p1 p2 delta n1 /missing=omit. |
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| compute p11=m(:,1). compute p12=m(:,2). compute p21=m(:,3). compute p22=m(:,4). compute ntot=m(:,5). compute alpha=m(:,6). |
compute p1=make(1,1,0). compute p2=make(1,1,0). compute delta=make(1,1,0). compute n1=make(1,1,0). compute alpha=m(:,1). compute p1=m(:,2). compute p2=m(:,3). compute delta=m(:,4). compute n1=m(:,5). |
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| 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'. |
compute n2=delta*n1. compute #pbar= (n1*p1 + n2*p2) / (n1+n2). compute #z2= ( (p1-p2) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2. compute oddsr = ( n1*p1*n2*(1-p2) ) / ( n1*(1-p1)*n2*p2 ). compute power=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z2). exe. formats n1 (f7.0) n2 (f7.0) alpha (f5.2) p1 (f5.2) p2 (f5.2) power (f5.2). variable labels n1 'Sample Size 1' /n2 'Sample Size 2' /alpha 'Alpha' /p1 'Proportion 1' /p2 'Proportion 2' /oddsr 'Odds Ratio' /power 'Power'. |
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| /variables=p1 p2 ratio alpha ntot power /title "Power for given sample size for an Odds Ratio from a 2x2 table of proportions" . |
/variables=n1 n2 alpha p1 p2 oddsr power /title "Independent group proportions power for given sample sizes" . |
[ADJUST THE EXAMPLE INPUT AS DESIRED; THEN COPY AND PASTE INTO A SPSS SYNTAX WINDOW AND RUN; OUTPUT BOTH TO SPREADSHEET AND OUTPUT WINDOW].
This program uses the difference in proportions (or equivalently the odds ratio) as the effect size, see http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d.
p1 and p2 are the proportions in groups 1 and 2 being compared, delta is the ratio of sizes of group 1 to group 2, ntot is the total sample size and alpha is the (two-tailed) type I error. The program then outputs the power.
DATA LIST free /alpha p1 p2 delta n1. BEGIN DATA. .05 0.19 0.09 1 167 .05 0.39 0.25 1 100 END DATA. matrix. get m /variables=alpha p1 p2 delta n1 /missing=omit. compute alpha=make(1,1,0). compute p1=make(1,1,0). compute p2=make(1,1,0). compute delta=make(1,1,0). compute n1=make(1,1,0). compute alpha=m(:,1). compute p1=m(:,2). compute p2=m(:,3). compute delta=m(:,4). compute n1=m(:,5). end matrix. compute n2=delta*n1. compute #pbar= (n1*p1 + n2*p2) / (n1+n2). compute #z2= ( (p1-p2) /sqrt( #pbar*(1-#pbar)*( (1/n1) + (1/n2) ) ) )**2. compute oddsr = ( n1*p1*n2*(1-p2) ) / ( n1*(1-p1)*n2*p2 ). compute power=1-ncdf.chisq(idf.chisq(1-alpha,1),1,#z2). exe. formats n1 (f7.0) n2 (f7.0) alpha (f5.2) p1 (f5.2) p2 (f5.2) power (f5.2). variable labels n1 'Sample Size 1' /n2 'Sample Size 2' /alpha 'Alpha' /p1 'Proportion 1' /p2 'Proportion 2' /oddsr 'Odds Ratio' /power 'Power'. report format=list automatic align(center) /variables=n1 n2 alpha p1 p2 oddsr power /title "Independent group proportions power for given sample sizes" .