In testing 2×2 contingency tables with one marginal total fixed, so-called Fisher-Yates exact test has the size well below the nominal level α, which results in a substantial loss of power. In this paper we evaluate this loss in terms of sample size required to obtain the same power as by the randomized UMP unbiased test, which is theoretically the best. Further, some modifications in the use of Binomial Probability Paper for this problem are proposed. Numerical examinations are also made.
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