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Type the odd letters out: scieNce GATHeRS knowledge fAster tHAN SOCIeTY GATHErS wisdom

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 here) as an effect size in regressions including one-way anovas as a special case.

From Cohen (1988) it follows R-squareds of 0.02, 0.13 and 0.26 are suggested conventions for small, medium and large effect sizes in regressions featuring continuous predictors. R-squareds of 0.01, 0.06 and 0.14 are the small, medium and large effect sizes for a one-way anova.

Alpha is the type I error, df of the effect, dfe, is the total number of degrees of freedom for the effect of interest, df of confounders, dfc, is the total number of degrees of freedom of other predictors in the 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 spreadsheet or on-line calculator or in R.

df for each predictor equals k -1 for a group predictor with k levels or 1 for each continuous predictor.

Miles and Shevlin (2001) also produce some power curves corresponding to the small, medium and large effects above which can also be used to find power using different sample sizes (and vice-versa). 

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 power = 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" .

Reference

Miles J and Shevlin M (2001) Applying regression and correlation. A guide for students and researchers. Sage:London.