Exact Sample Sizes for Use with the Fisher-Irwin Test for 2 x 2 Tables

Gail and Gart (1973) present tables showing the required sample size, n, for the Fisher-Irwin exact conditional test for 2 X 2 tables to achieve a power of at least 0.50, 0.80 and 0.90 against one-sided alternatives at the nominal .05 and .01 significance levels. However, calculations for n > 35 were based on the Arc sine approximation, which was found to underestimate the actual required sample size by as much as 34%. The purpose of this note is to revise the Gail-Gart tables, giving exact sample sizes in all cases. The problem of nominal versus actual significance levels when the underlying probability of response is low is also briefly discussed.