[R] Fisher's Exact Test

[Simon Fear]

Probably Kurt Hornik, the author of this package, will have already
replied to this. The ctest package has indeed been recently updated (and
a bug was fixed in the windows binary to boot). Though not immediately
an R question, I wanted to comment on Peter's

>Mind you, there's a paper by Yates lying somewhere in my "must read
>some time" stack where he argues that the 2 * p procedure is more
>correct...

which becomes an R question if your think that there is such a thing as
Kurt's package being "correct". Try this definition of a P value: the
probability, under the null hypothesis, of observing data as, or more,
extreme than that actually observed. If you buy this frequently
quoted/paraphrased definition, and I suggest most people would, then you
should go with latest version of ctest, i.e. summing the probabilities
of all tables with probability of occurrence less than or equal to the
probability of that observed (under the null hypothesis). BUT if you
want your P value to be such that in the long run your type I error is
exactly what you quote, then you use the double-one-sided P. (Actually
you should use double-one-sided-MID-P to get even closer to stated type
I error asymptotically overall, though for certain null hypothesis
values you then sometimes under-quote.)

I ended up suggesting to Kurt that if he finds himself with masses of
spare time on his hands (yes, joke) he include all these via options
since some people get quite passionate about which one is "correct". The
idea of a P value is to quantify to what extent the data are
"consistent" with the null which begs the question of what we mean by
"consistent" (that's according to Cox and Hinkley, anyway). I reckon if
one procedure gave you "significance" and another didn't, you wouldn't
have strongly established the result under anybody's definitions.

Simon Fear
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