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On the Power of Fisher's Combination Test for Two Stage Sampling in the Presence of Nuisance Parameters
Author(s) -
Banik N.,
Köhne K.,
Bauer P.
Publication year - 1996
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710380103
Subject(s) - statistics , mathematics , sample size determination , power (physics) , exact test , sample (material) , sampling (signal processing) , statistical power , power analysis , nuisance , algorithm , computer science , chromatography , chemistry , thermodynamics , physics , cryptography , filter (signal processing) , law , computer vision , political science
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.