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

Since Fisher's exact test is conducted conditional on the observed value of the margin, there are two kinds of the exact power, the conditional and the unconditional exact power. The conditional exact power is computed at a given value of the margin whereas the unconditional exact power is calculated by incorporating the uncertainty of the margin. Although the sample size is determined based on the unconditional exact power, the actual power which Fisher's exact test has is the conditional power after the experiment is finished. This paper investigates differences between the conditional and unconditional exact power of Fisher's exact test. We conclude that such discrepancy is a disadvantage of Fisher's exact test.