The Chernoff Modification of the Fisher Exact Test for the Difference of Two Binomial Probabilities

To test the difference of two binomial probabilities, we will apply the Fisher exact test modified by Chernoff (2002), which will be called CMF test. The key idea is to use the P-value of Fisher exact test as a test statistic and this makes it possible to apply the Fisher exact test for more general problems. The numerical comparison with the likelihood ratio test and the Bayes test are also conducted and we find that the performance of CMF test is close to that of the likelihood ratio test and it is satisfactory in various situations. We also give a Kullback-Leibler information number of the margins to for the testing problems which justify the stability of P-values of CMF test.