Exact attained significance level and sample size methods are developed for use with the unconditional Z statistic in the 2 × 2 contingency table from two independent binomial samples of equal size. The resulting sample sizes tend to be smaller than those required by tables for the exact conditional test. Moreover, the proposed exact Z test is uniformly more powerful than the exact conditional test for α = 0.01, 0.025 and 0.05, and common sample size n = 10(1)150, the only combinations of α and n considered herein. These methods therefore provide an exact approach to unconditional tests which, in contrast to the conditional ones, are easily explained to and understood by non-statisticians. This paper is the first for which sample size calculations are made based on exact unconditional tests for any situation in which no ancillary statistic exists for the nuisance parameter.
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Journal of the Royal Statistical Society. Series A (General)
© 1985 Royal Statistical Society
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