I want to ascertain the basis of the table ranking,

i.e. the meaning of "extreme", in Fisher's Exact Test

as implemented in 'fisher.test', when applied to RxC

tables which are larger than 2x2.

One can summarise a strategy for the test as

1) For each table compatible with the margins

of the observed table, compute the probability

of this table conditional on the marginal totals.

2) Rank the possible tables in order of a measure

of discrepancy between the table and the null

hypothesis of "no association".

3) Locate the observed table, and compute the sum

of the probabilties, computed in (1), for this

table and more "extreme" tables in the sense of

the ranking in (2).

The question is: what "measure of discrepancy" is

used in 'fisher.test' corresponding to stage (2)?

(There are in principle several possibilities, e.g.

value of a Pearson chi-squared, large values being

discrepant; the probability calculated in (2),

small values being discrepant; ... )

"?fisher.test" says only:

In the one-sided 2 by 2 cases, p-values are obtained

directly using the hypergeometric distribution.

Otherwise, computations are based on a C version of

the FORTRAN subroutine FEXACT which implements the

network developed by Mehta and Patel (1986) and

improved by Clarkson, Fan & Joe (1993). The FORTRAN

code can be obtained from

<URL:

http://www.netlib.org/toms/643>.

I have had a look at this FORTRAN code, and cannot ascertain

it from the code itself. However, there is a Comment to the

effect:

c PRE - Table p-value. (Output)

c PRE is the probability of a more extreme table, where

c 'extreme' is in a probabilistic sense.

which suggests that the tables are ranked in order of their

probabilities as computed in (2).

Can anyone confirm definitively what goes on?

With thanks,

Ted.

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Date: 12-Jan-06 Time: 20:19:02

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