FAQ/power/props - CBU statistics Wiki

Upload page content

You can upload content for the page named below. If you change the page name, you can also upload content for another page. If the page name is empty, we derive the page name from the file name.

File to load page content from
Page name
Comment
WHat wOrd is made by the captiaL lettErs?

location: FAQ / power / props

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)" .