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 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 spreadsheet or in R.

An example uses marginal probabilities to compute cell probabilities in a 2x2 table to give inputs for a power analysis.

[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)" .```

None: FAQ/power/props (last edited 2013-03-08 10:17:40 by localhost)