[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: r-help 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 non-centrality parameter in which case it is a sensible
thing to have available since it is essentially the signal-to-noise ratio.
Actually the MLE is the F-statistic but the maximum *marginal* likelihood
estimate (based on the marginal distribution of the F-statistic 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 non-central
chi-squared and non-central 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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