On the Power of Fisher's Combination Test for Two Stage Sampling in the Presence of Nuisance Parameters

Combination tests for p ‐values are used in meta‐analysis and in multistage testing with adaptive designs (Bauer & Köhne, 1993). The well known combination test due to Fisher is based on the products of p ‐values. The power of this test applied to p ‐values found from stochastically independent samples at two stages of an experiment is calculated. The probability models assumed correspond to the classical t ‐tests for paired comparisons and parallel groups. The loss of power as compared to the optimal t ‐tests in the pooled sample is small even for moderate sample sizes differing over stages, however, with one exception: If in the case of parallel groups the sample sizes are substantially unbalanced over treatments, then the combination of two tests with a nonoptimal sample size allocation exaggerates the loss of power.