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Since Fisher’s exact test is conducted conditional on the observed value of the margin, there are two kindsof the exact power, the conditional and the unconditional exact power. The conditional exact power iscomputed at a given value of the margin whereas the unconditional exact power is calculated by incorpo-rating the uncertainty of the margin. Although the sample size is determined based on the unconditionalexact power, the actual power which Fisher’s exact test has is the conditional power after the experimentis nished. This paper investigates di erences between the conditional and unconditional exact power ofFisher’s exact test. We conclude that such discrepancy is a disadvantage of Fisher’s exact test. Keywords: Conditional test, sample size determination, homogeneity, binomial. 1. Introduction In this paper we focus on testing the homogeneity of two independent binomial proportions whenthe sample size is small. When the sample size is large enough, the normal approximation to thebinomial distribution may be employed. However, when the sample size is small, such approximationmay not be valid and Fisher’s exact test is often employed as an alternative. The main advantageof exact tests (including Fisher’s exact test) is that it is guaranteed to control type I error ratesunder the nominal level.A key feature of Fisher’s exact test is that the test is conducted conditional on the observed valueof the margin. Therefore, there are two kinds of the exact power, the conditional and unconditionalexact power. The conditional exact power is computed at a given value of the margin whereas theunconditional exact power is calculated by incorporating the uncertainty of the margin. The samplesize should be determined based on the unconditional exact power, because a value of the margin isnot observed yet before an experiment is conducted. However, after the experiment is nished, theactual power which Fisher’s exact test has is the conditional power, because the test is a conditionaltest. Since in general the conditional exact power is not as same as the unconditional exact power,the actual power (the conditional exact power) which Fisher’s exact test has after the experiment

The Comparison of the Unconditional and Conditional Exact Power of Fisher's Exact Tes