[R] Fisher's Exact Test

[yudi@hermes.ucd.ie]

This is a statistical comment, not R, but I think it'd be of
interest to some in the group.

There have been many thoughtful comments on this topic,
though none is likely to 'solve' the problem of 2-sided P-value
for asymmetric distribution. I find the issue theoretically
embarassing: for any definition you can come up with
a simple uncontrived bothersome example. For what's worth,
there is a paper of mine (jointly with A.Dunne) on 2-sided 
P-value based on the UMPU tests: Statistician, 1996, 397-405. 
**I'm not suggesting we use it in practice though.**

Yates corrected Chi-square for 2x2 table corresponds to
doubling 1-sided p-value, a method that appeared to be
endorsed by Fisher in 1941 (quoted in Yates-1984), though
unfortunately Fisher didn't seem to think very hard on this
issue.

I agree with Simon Fear that for 1-dimensional parameters 
the mid-P-value method is probably most sensible. For
multi-dimensional problems summing the prob's less than
the observed is the most practical, though it would corres-
pond to a biased test.

The lack of resolution probably means there's something
wrong with the idea of 2-sided P-value. (Bayesians say so
for any P-value). At some point we should probably
switch to something like likelihood ratio (and AIC for
multi-dimensional problems). 

-Yudi-

------------------------------
Yudi Pawitan: yudi at ucd.ie
Department of Statistics, UCD
Dublin 4, Ireland
Ph : 353-1-706 7641
Fax: 353-1-706 1186
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