A Comparison of Alternative Tests for the 2 × 2 Comparative Trial

Abstract

SUMMARY This paper considers twenty-two alternative tests which have been suggested for testing the null hypothesis Pi = P2 in a 2 x 2 comparative trial. Attention is confined to the case where the null hypothesis is true. The dependence of the tests on m and n, the sample sizes, and on p, the common binomial parameter, is investigated. Amongst other results it is shown that the exact test of Fisher, and the corresponding Yates correction to Pearson's X2 test, give tests which are both extremely conservative and inappropriate. The uncorrected X2 test performs well. On both empirical and theoretical grounds, the preferred test is the scaled version (N- 1)/N X2.