Optimal unconditional test in 2×2 multinomial trials

Abstract

The unconditional independence tests in 2×2 tables have been studied in many papers, but only the case of one fixed marginal has received sufficient attention. The case of zero fixed marginals (double dichotomy or 2×2 multinomial trials) is the most complex as regards its computation, and for that reason, less has been written about it, and what there is of more recent date. Of all the different versions proposed on this subject, there is only one comparative study in existence (Haber, Comm. Statist. Simulation 16 (4), 1987, 999–1013) which is limited in various aspects (it covers only a few versions, two-tailed tests and error α=5%, and its methodology could be perfected). This paper compares all the existent relevant versions as well as other new ones, by means of the “mean power” criterion proposed by Martı́n and Silva (Comput. Statist. Data Anal. 17, 1994, 555–574) and which is developed here for the current case. The comparison is carried out for one- and two-tailed tests and for values of α between 0% and 10%, and the authors conclude that although the best methods are Barnard's method and its approximation, the method based on Fisher's mid- p-value is the optimal since it maintains a good balance between the power reached and the computation time required.