🚀 go-pugleaf

Has anyone tested or found that power values reported in Cohen's
STATASTICAL POWER ANALYSIS FOR THE BEHAVIORAL SCIENCES (1977) are
inflated by as much as .1?
I'm finding that we're in agreement on a noncentrality parameter
formula as:

(R**2/(1-R**2))*edf

where R**2 is a squared multiple correlation and edf=N-preds-1.
Using this value in conjunction with the number of predictors
results in a power value obtained from a look up table where
rows represent number of predictors and columns represent
noncentrality values.

For example with a R**2=.71 and ndf=3, edf=8,
(Alpha will always be .05.),  SPSS (from the manova
procedure) and SAS (from the code below) will return
noncentrality parameter=20 and power =.84 (when edf=8).

Cohen's table (noncentrality params by preds) reports .98
as the power estimate.  I've got a bug somewhere, perhaps YOU
can find it in the SAS code below.
Comments,parallel findings are encouraged.
Will post summary if enough responses are reported.

******************SAS APPROACH**************** ;
*data not identical to previous finding ;
data boh ;
do preds= 8 to 12 by 2 ;          *overall 2 separate equations ;
  do rsq=.1 to .5 by .1 ;         *various rsquare values ;
    do n=20 to 120 by 5 ;         *various sample sizes ;
      edf=n-preds-1 ;
      fsq=(rsq/(1-rsq));          *calc cohen's f2 (sect 9.2 & 9.3);
      noncent= fsq*edf ;          *calculation of noncentrality parameter;
      fcrit = finv(.95,preds,edf,0);
      power = 1- probf(fcrit,preds,edf,noncent);
      if power= . then power = 1 ;
      output ;
    end;
  end;
end;
proc print data=boh ;
var rsq n fsq edf preds noncent power fcrit ;

proc sort data=boh ; by preds rsq ;
GOPTIONS DEVICE =xbw ;
SYMBOL1 line=1 i=join v=none ; * c=black;
SYMBOL2 line=2 i=join v=none ; * c=black;
SYMBOL3 line=3 i=join v=none ; * c=black;
SYMBOL4 line=4 i=join v=none ; * c=black;
SYMBOL5 line=5 i=join v=none ; * c=black;
title 'estimated power curves for various rsq values';
PROC GPLOT DATA=boh ;
 plot power*n=rsq ;
 by preds ;


===================================
Richard Cole, Systems Analyst
Computation Center UT Austin
PHONE: (512) 471-3241
BITNET: ccez001@utxvm.cc.utexas.edu
INTERNET: rcole@ccwf.cc.utexas.edu
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