fisher exact vs. simulated chi-square
On Wed, 23 Apr 2003, Bob Porter wrote:
The Chi-Square test is based upon the assumption that the sample is large enough to allow approximation of a (nearly symetric) binomial by a normal distribution. (Chi Sqare is z^2). When expected (NOT observed) cells are too small, that suggests a very asymetric binomial and, consequently a poor fit for the assumption. The exact test calculates the exact probability of the observed values, or more extreme ones, given the assumed probabilities generating the expected values. As someone else noted, exact is exact, Chi-square is not (unless, of course, assumptions are exactly met.)
This is true but not the issue. The question was about the difference between the Fisher p.value and a Monte Carlo estimate of the exact p value for the chisquared statisic. -thomas