FAQ/power/owanova - CBU statistics Wiki

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Type the odd characters out in each group: abz2a 125t7 HhHaHh year.s 5433r21 worl3d

Revision 17 as of 2007-03-05 15:44:32

location: FAQ / power / owanova

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

This program uses R-squared, the multiple correlation, as the effect size, which may also be expressed as Cohen's f= R-sq/(1-R-sq) (see http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d) as an effect size in regressions including one-way anovas as a special case.

From Cohen(1977, 1992) it follows R-squareds of 0.01, 0.0588 and 0.138 are suggested conventions for small, medium and large effect size.

Alpha is the type I error, g is the number of groups in a (between subjects) one-way anova or, alternatively, one more than the number of predictor variables in a multiple regression, ntot is the total sample size and rsq is the multiple correlation. The program then outputs the power. Power computation may also be done using a [attachment:reg.xls spreadsheet.]

DATA LIST free
/alpha dfreg dfc ntot rsq. 
BEGIN DATA. 
.05 2 0 40  0.3
END DATA. 
matrix.
get m /variables=alpha g ntot rsq  /missing=omit.
compute alpha=make(1,1,0).
compute dfreg=make(1,1,0).
compute dfc=make(1,1,0).
compute ntot=make(1,1,0).
compute rsq=make(1,1,0).
compute alpha=m(:,1).
compute dfreg=m(:,2).
compute dfc=m(:,3).
compute ntot=m(:,4).
compute rsq=m(:,5).  
end matrix.
COMPUTE POWanov = 1 - NCDF.F(IDF.F(1-ALPHA,DFREG,NTOT-DFREG-DFC-1),DFREG,NTOT-DFREG-DFC-1,NTOT*RSQ/(1-RSQ)).
EXE.
formats ntot (f7.0) alpha (f5.2) dfreg (f5.2) dfc (f5.2) rsq (f5.2) power (f5.2).
variable labels ntot 'Total Sample Size' /alpha 'Alpha' /dfreg 'Df effect' /dfc 'Df confounders' /rsq 'R-squared' /power 'Power'.
report format=list automatic align(center)
  /variables=ntot alpha dfreg dfc rsq power 
  /title "Power in a multiple regression for given total sample size" .