[R] observed power

[David W]

Two or three years ago there was an extended discussion on
sci.stat.consult concerning "post-hoc power analysis". If
memory serves (since DejaNews is not currently allowing
searches back that far), it was power estimation using the
sample estimate of the variance done after conducting a
"failed" experiment . Some of the contributors did not seem
to understand that the variance was subject to sampling
error. Using the observed interim sample variance to
determine a plausible number of additional subjects would
seem of some use after an experiment of insufficient size
had testing consistent with the null. (With appropriate
regard for adjusting alpha after multiple tests.)  It
doesn't need to be distinguished by a separate term, and any
reasonable interpretation would already be subsumed under
existing interim analysis strategies.

Regards;
David Winsemius

Bill.Venables at CMIS.CSIRO.AU wrote:
> 
> 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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