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Abstract A modified exact test is proposed for 2×2 contingency tables. This test, which is based on a less conservative definition of the concept of significance (STONE, 1969) is compared with a modified form of Pearson's X 2 test and with Tocher's randomized exact (UMPU) test. The sizes of the new test lie near the nominal 0.05 levels while those of the X 2 test usually exceed the nominal level, sometimes by a factor of 2 or more. The power of the modified test is usually close to that of the UMPU test.
Michelle Haber (1986) studied this question.