Comparison of Exact Unconditional Methods for the Difference of Two Binomial Proportions

Abstract

Exact tests based upon the difference of two independent binomial proportions are popularly used and are especially suited for studies with small to moderate sample sizes. In the context of testing for superiority and noninferiority, we apply the confidence region p-value method (Berger and Boos, 1994) in proposing an exact test that has been found to perform better than the standard exact test in many situations. The exact tests use unconditional distributions and the variances of the test statistics are determined via a restricted maximum likelihood method (Farrington and Manning, 1990). Inverting the tests, we derive corresponding confidence intervals and we provide coverage probability and expected length comparisons. These comparisons show that, in many cases, the confidence intervals based upon the proposed exact method have less conservative coverage and shorter lengths when compared to confidence intervals based on the standard exact method.