Abstract
This work compares four tests of significance for the equality of two binomial proportions. Tests are compared with regard to their expected significance probabilities under H oand their Bahadur efficiencies under various alternatives. Two tests that are advocated by supporters of conditioning on the total number of successes, Fisher's exact and the Yates-corrected X2tests, are outperformed by two less conservative methods, the mid-P-value and the uncorrected X2 tests.
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