Improved algorithms for closed step-down procedures to test heterogeneity of all subsets of means |
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| Institution: | 1. Department of Pharmaceutical Sciences, College of Pharmacy and AHP, Wayne State University, Detroit, MI 48202, USA;2. Department of Psychiatry and Behavioral Neurosciences, School of Medicine, Wayne State University, Detroit, MI 48202, USA;1. Department of Mathematics & Statistics, McMaster University, 1280 Main Street West, Hamilton, Ont. L8S 4K1, Canada;2. Martin-Luther-Universität Halle-Wittenberg, Institut für Medizinische Epidemiologie, Biometrie und Medizinische Informatik D-06097 Halle, Germany;3. Friedrich-Schiller-Universität Jena, Institut für Medizinische Statistik, Informatik und Dokumentation D-07740 Jena, Germany;1. National Institute of Health Sciences, Osaka Branch, 1-1-43, Hoenzaka, Chuo-ku, Osaka, 540-0006, Japan;2. Safety Research Institute for Chemical Compounds Co., Ltd., 363-24, Shin-ei, Kiyota-ku, Sapporo, Hokkaido, 004-0839, Japan |
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| Abstract: | A common problem in analysis of variance is testing for heterogeneity of different subsets of the full set of k population means. A step-down procedure tests a given subset of p means only after rejecting homogeneity for all sets that contain it. The Peritz and Gabriel closed procedure rejects homogeneity for the subset if every partition of the k means that includes the subset includes some rejected set. The Begun and Gabriel closure algorithm reduces computations, but the number of tests still increases exponentially with respect to the number of complementary means, m=k?p. We propose a new algorithm that tests only the m?1 pairs of adjacent ordered complementary sample means. Our algorithm may be used with analyses of variance test statistics in balanced and unbalanced designs, and with Studentized ranges except in extremely unbalanced designs. Seaman, Levin, and Serlin proposed a more powerful closure criterion that cannot exploit the Begun and Gabriel algorithm. We propose a new algorithm in this case as well. |
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