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This paper reviews the problems that bedevil the selection of an appropriate test for the analysis of a 2 × 2 table. In contradiction to an earlier paper, the author now argues the case for the use of Fisher's exact test. It is noted that all test statistics for the 2 × 2 table have discrete distributions and it is suggested that it is irrational to prescribe an unattainable fixed significance level. The use of mid-P is suggested, if a formula is required for prescribing a variable tail probability. The problems of two-tail tests are discussed
Graham Upton (1992) studied this question.