A Discussion on the Fisher Exact Test

I begin with a note of dissent. The Fisher-Yates conditional test for the 2 × 2 categorical data is called “exact” not because the test is “based on the theories of R.A. Fisher” but because the computation of the attained level of significance (the P-value) requires no mathematical approximation beyond what is already involved in the choice of the statistical model. The normal test is inexact because the null distribution of the test statistic TN is N(0,1) only as an approximation.