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I'm aware of the Fisher exact test, for determining the probability distribution for a $2\times2$ contingency table.

Is there an exact test for a $3\times3$ table? Or is there a way to combine the results of three Fisher tests, for each of the $2\times2$ tables for each pair of variables, so as to give an exact probability?

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@Amzoti is right. Freeman-Halton fits the bill.

On-line calculators:

References:

  • Freeman, G.H. and Halton, J.H. (1951). Note on an exact treatment of contingency, goodness of fit and other problems of significance. Biometrika, 38, pp. 141-149.
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