On a Test of the Difference Between Two Binomial Proportions

Abstract

The problem of testing for the equality of the proportions of two independent binomial populations is covered in the literature by a very extensive research. The most popular procedures are Fisher's exact test and the chi-square test with (or without) Yates's continuity correction. However, testing for a given difference in the proportions received very limited attention. In this article we propose two new test procedures which use hypothesis-dependent variance estimates, and investigate their performances, as well as the performances of the commonly used tests. We show that the proposed tests are more robust in that their actual significance levels are usually closer to the nominal levels than those of the commonly used tests.

Keywords:

• Binomial distribution
• Chi-square test
• Fisher's exact test
• Maximum likelihood estimator
• Small sample testing

Mathematics Subject Classification:

• 62-02
• 62F06
• 62F30