Approximations are found for the distribution of the standard criterion used to compare two observed proportions, when the reference set is generated by independent samples from binomial populations with the same parameter. The results are applied to study the overall performance of the continuity correction in 2×2 tables. Previous tentative conclusions are confirmed, to the effect that the correction is not appropriate for the reference set stated.
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R. L. Plackett (1964) studied this question.