Diff for "FAQ/power/props" - CBU statistics Wiki
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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. here].
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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.		 p1 and p2 are the proportions in groups 1 and 2 being compared, delta is the ratio group 2 size/group 1 size, n1 is the sample size of group 1 and alpha is the (two-tailed) type I error. The program then outputs the power. Power may also be computed using a [attachment:bin2.xls spreadsheet] or [:FAQ/powppR:in R.]
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[ADJUST THE EXAMPLE INPUT AS DESIRED; THEN COPY AND PASTE INTO A SPSS SYNTAX WINDOW AND RUN; OUTPUT BOTH TO SPREADSHEET AND OUTPUT WINDOW].
 
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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 "Power for Independent proportions given sample sizes" .
exe.
compute #contc= 0.5*((1/n1)+(1/n2)).
compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
compute #z21= ( ( abs(p1-p2)-#contc ) /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,#z21).
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 "Power for Independent proportions given sample sizes (continuity correction)" .

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. here].

p1 and p2 are the proportions in groups 1 and 2 being compared, delta is the ratio group 2 size/group 1 size, n1 is the sample size of group 1 and alpha is the (two-tailed) type I error. The program then outputs the power. Power may also be computed using a [attachment:bin2.xls spreadsheet] or [:FAQ/powppR:in R.]

[ADJUST THE EXAMPLE INPUT AS DESIRED; THEN COPY AND PASTE INTO A SPSS SYNTAX WINDOW AND RUN; OUTPUT BOTH TO SPREADSHEET AND OUTPUT WINDOW]. 

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 "Power for Independent proportions given sample sizes" .
exe.
compute #contc= 0.5*((1/n1)+(1/n2)).
compute #pbar= (n1*p1 + n2*p2) / (n1+n2).
compute #z21= ( ( abs(p1-p2)-#contc ) /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,#z21).
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 "Power for Independent proportions given sample sizes (continuity correction)" .

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