Kudô and Tarumi (1978) proposed a conditional test for testing equivalence of two proportions in 2 × 2 tables by assuming the date collected by a negative binomial sampling. The test is undoubtedly a counterpart of the Fisher exact test, but no comparison has been made of the two tests. In this paper we obtain asymptotic power of the Kudô-Tarumi test and compare it with the Fisher exact test by means of the Pitman asymptotic efficiency. It will be shown that the Kudô-Tarumi test is the most powerful similar test for a risk ratio, whereas the Fisher exact test is, the most powerful similar test for a risk ratio, whereas the Fisher exact test is, as well known, the most powerful similar test for an odds ratio. It is also shown that the Kudô-Tarumi test has higher efficiency than the Fisher exact test in many cases.
