[R] observed power
Bill.Venables@CMIS.CSIRO.AU
Bill.Venables at CMIS.CSIRO.AU
Sat Jan 27 03:07:57 CET 2001
Peter Dalgaard BSA [mailto:p.dalgaard at biostat.ku.dk] wonders:
 Sent: Saturday, 27 January 2001 1:29
 To: Mark M. Span
 Cc: rhelp at stat.math.ethz.ch
 Subject: Re: [R] observed power


 "Mark M. Span" <span at psy.uva.nl> writes:

 > Is there a way to obtain the observed power of an aov()?
 >
 > I perform an aov with one between and one within factor,
 > and would like to know the observed power of the tests,
 > both for the main effect and the interaction. I found the
 > package 'hpower', but sense there is a more convenient
 > possibility. Is there?
 >
 > thanks
 >
 > Mark M. Span

 What's "observed power"? If you mean the item that SPSS has by that
 name, I think you first have to convince us that that is a sensible
 thing to calculate...
If you ever do find out, Peter, let me know too, please. I was puzzled, but
a bit worried about showing my ignorance... I can only imagine it means an
estimate of the noncentrality parameter in which case it is a sensible
thing to have available since it is essentially the signaltonoise ratio.
Actually the MLE is the Fstatistic but the maximum *marginal* likelihood
estimate (based on the marginal distribution of the Fstatistic itself) is
of more interest as it is closer to unbiased. In the case of the multiple
correlation coefficient, for example, this is (practically) what people call
the "adjusted R^2" statistic, where the adjustment is essentially a bias
correction. You can come up with simple analogues for noncentral
chisquared and noncentral F of course, but they are again just simple
linear adjustments, unless you really want to get flash. (I wrote a couple
of papers on this stuff in the 70s so I have a kind of nostalgic affinity
for it...)
I would be more interested in these quantities optionally appearing
routinely on summary tables than, for example, the cute 'significance
stars'. But as for calling them the "observed power", I would definitely
caution against that. It encourages entirely the wrong idea of what power
really is. (For example, it is a function, not a quantity, and you don't
ever "observe" it in practice.)
Bill Venables.

Bill Venables, CSIRO/CMIS Environmetrics Project
Email: Bill.Venables at cmis.csiro.au
Phone: +61 7 3826 7251
Fax: +61 7 3826 7304
Postal: PO Box 120, Cleveland, Qld 4163, AUSTRALIA
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