Tests of Significance for 2 × 2 Contingency Tables

Fisher's exact test, and the approximation to it by the continuity-corrected X 2 test, have repeatedly been attacked over the past 40 years, recently with the support of extensive computer exercises. The present paper argues, on commonsense grounds, supported by simple examples, that these attacks are misconceived, and are mainly due to uncritical acceptance of the Neyman-Pearson approach to tests of significance, the use of nominal levels, and refusal to accept the arguments for conditioning on the margins.Two-sided tests have also added to the confusion; it is argued that the best definition of a two-sided probability is twice the observed one-tail probability.

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