Asymptotic and Exact Two-Sample Poisson Tests

Abstract

The Poisson distribution is popular in modeling a rare events in various fields such as biology, commerce, quality control, and so on. Many applications involve a comparison of two treatment groups based on two independent random samples drawn from Poisson distributions. In this study, the asymptotic power function and sample size formula of two types of Wald test are derived. Moreover, two exact testing procedures are introduced and investigated as well. The required sample size of the exact procedures can be found numerically. Through intensive numerical studies, the validity of these tests is justified. The performance of the two asymptotic tests are found to depend on the fraction of the two sample sizes and they tend to generate conclusions that are too liberal. In contrast, the two exact tests lead to more satisfactory statistical conclusions. Moreover, the asymptotic sample size formulae provide adequate approximations to the required sample size for the exact approach. A data set of breast cancer patients is analyzed for illustration.