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.) Bob Porter, Robert J. Porter, Ph.D. Clinical and Consulting Psychologist 308 East Oak Street Tampa, FL, 33603 Office Phone: 813-810-8110 813-225-5678 FAX www.mindspring.com/~rjporter -----Original Message----- From: Dirk Janssen [mailto:dirkj at rz.uni-leipzig.de] Sent: Tuesday, April 22, 2003 8:08 PM To: r-help at stat.math.ethz.ch Subject: [fisher exact vs. simulated chi-square (Dirk Janssen Dear All, I have a problem understanding the difference between the outcome of a fisher exact test and a chi-square test (with simulated p.value). For some sample data (see below), fisher reports p=.02337. The normal chi-square test complains about "approximation may be incorrect", because there is a column with cells with very small values. I therefore tried the chi-square with simulated p-values, but this still gives p=.04037. I also simulated the p-value myself, using r2dtable, getting the same result, p=0.04 (approx). Why is this substantially higher than what the fisher exact says? Do the two tests make different assumptions? I noticed that the discrepancy gets smaller when I increase the number of observations for column A3. Does this mean that the simulated chi-square is still sensitive to cells with small counts, even though it does not give me the warning? Thanks in advance, Dirk Janssen
fisher exact vs. simulated chi-square
2 messages · Bob Porter, Thomas Lumley
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