Is Fisher ’ s exact test very conservative ?

There are various two-tailed test versions of Fisher’s exact test for analyzing a 2~ 2 table. In this paper, the optimal version is selected on the basis of the concept of mean power (arranging in order from the smallest to the largest hypergeometrical probability, and in the case of a tie, arranging in order from the largest to the smallest value of the odds-ratio), and this selection is as valid when considering it as a conditional test as it is when considering it as an unconditional test. The comparison of the power of the version selected (with one and two tails), with that of the more common unconditional tests (Barnard, 1947, and McDonald et al., 1977) shows that the loss of power produced by using Fisher’s test is very slight in the majority of situations, and this is acceptable in return for the greater ease of computation and a more generic validity (for all types of sample).