Sample size determination in step-down and step-up multiple tests for comparing treatments with a control |
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| Institution: | 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. Departamento de Medicina Preventiva y Salud Pública, Facultad de Medicina, Universidad Autónoma de Madrid, Instituto de Investigación Hospital Universitario La Paz (IdiPAZ), Madrid, Spain;2. Centro de Investigación Biomédica en Red de Epidemiología y Salud Pública (CIBERESP), Spain;3. Departmento de Medicina Preventiva, Complejo Hospitalario Insular Materno Infantil, Las Palmas de Gran Canaria, Las Palmas, Spain;4. Facultad de Ciencias y Artes, Departamento de Ciencias de la Salud, Universidad Católica «Santa Teresa de Jesús», Ávila, Spain;5. IMDEA Food Institute, CEI UAM+CSIC, Madrid, Spain;6. Division de Medicina Interna, Hospital Universitario Quirón, Madrid, Spain;1. Department of Urban Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;2. Environmental Science Center, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-0033, Japan;1. Mizuki biotech, Co., Ltd., 1-1 Hyakunenkouen, Kurume, Fukuoka 839-0864, Japan;2. Center for Marine Environmental Studies (CMES), Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan;3. Department of Biological and Chemical Systems Engineering, National Institute of Technology, Kumamoto College, 2627 Hirayama-shinmachi, Yatsushiro, Kumamoto 866-8501, Japan;4. Faculty of Agriculture, Ehime University, 3-5-7 Tarumi, Matsuyama, Ehime 790-8566, Japan;5. Faculty of Environmental and Symbiotic Sciences, Prefectural University of Kumamoto, 3-1-100 Higashi-ku, Tsukide, Kumamoto 862-8502, Japan;1. Southampton Statistical Sciences Research Institute, University of Southampton, Southampton SO17 1BJ, UK;2. Department of Mathematics, University of Patras, 26504 Patras, Greece;1. Key Laboratory of Soil Environment and Pollution Remediation, Institute of Soil Science, Chinese Academy of Sciences, Nanjing, 210008, PR China;2. University of Chinese Academy of Sciences, Beijing, 100049, PR China;3. State Key Laboratory of Pollution Control and Resource Reuse, School of the Environment, Nanjing University, Nanjing, 210023, PR China |
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| Abstract: | We address the problem of sample size determination in multiple comparisons of k treatments with a control for step-down and step-up testing, assuming normal data and homogeneous variances. We define power as the probability of correctly rejecting all hypotheses for which the treatment vs. control difference exceeds a specified value. Our paper supplements papers by Hayter and Tamhane (J. Statist. Plann. Inference 27 (1991) 271–290) who solved the problem for one-sided comparisons using the step-down procedure and by Liu (J. Statist. Plann. Inference 62 (1997b) 255–261) who considered the two-sided case using the single-step method. We provide expressions that allow computer evaluation of the power and necessary sample sizes for one- and two-sided tests using either step-down or step-up procedures. Tables are given from which sample sizes to guarantee a specified power can be determined. |
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