A number of messages have discussed robustness of algorithms for Fisher's
exact test.
I prefer to think of this test in terms of the hypergeometric distribution
(as described in Conover WJ, Practical Nonparametric Statistics (3rd
edition). Wiley 1999.).
The validation of calculation of lower tail/side P for this test is thus
validation of the algorithm used for the hypergeometric distribution.
Factorials need not be calculated.
Validation of two sided P depends upon your point of view with respect to
assumptions about marginal totals. The StatsDirect Fisher's test gives both
summary and expanded versions of the enumeration of probabilities, see
http://www.statsdirect.com or http://www.camcode.com. Large numbers are not
a problem.
Iain Buchan
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