Bayesian tests for the balanced two-way analysis of variance model |
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| Institution: | 1. University of Fort Hare, Alice, Ciskei, South Africa;2. Department of Mathematical Statistics, University of the Orange Free state, Bloemfontein 9300, South Africa;1. Urology Research Center, Tehran University of Medical Sciences, Tehran, Iran;2. Women''s College Research Institute, Women’s College Hospital, University of Toronto, Canada;3. Institute of Medical Science, Faculty of Medicine, University of Toronto, Canada;1. School of Pharmacy, Key Laboratory of Molecular Pharmacology and Drug Evaluation (Yantai University), Ministry of Education, Collaborative Innovation Center of Advanced Drug Delivery System and Biotech Drugs in Universities of Shandong, Yantai University, Yantai, 264005, PR China;2. Medicinal Chemistry Research Department, R & D Center (Luye Pharma Group Ltd.), Yantai, 264003, PR China;3. School of Public Health and Management, Binzhou Medical University, Yantai, PR China;4. College of Life Sciences, Yantai University, Yantai, Shangdong, 264005, PR China;1. Pharmacokinetics and Metabolism Division, CSIR-Central Drug Research Institute, Lucknow 226032 India;2. Medicinal and Process Chemistry Division, CSIR-Central Drug Research Institute, Lucknow 226032 India;3. Academy of Scientific and Innovative Research, New Delhi 110001 India;1. Eaton-Peabody Laboratories, Massachusetts Eye and Ear, Boston, MA, USA;2. Department of Otolaryngology—Head and Neck Surgery, Harvard Medical School, Boston, MA, USA;3. Department of Psychiatry, Nash Family Department of Neuroscience, and Friedman Brain Institute, Icahn School of Medicine at Mount Sinai, New York, NY, USA |
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| Abstract: | A Bayesian approach for the balanced two-way analysis of variance is derived. Four hypotheses are considered, namely the existence of neither block nor treatment effect, the existence of block but not treatment effect, the existence of treatment but not block effect, and the existence of both block and treatment effects. Lower bounds on the posterior probability are derived over the class of conjugate priors for the normal model. The hypotheses are further combined so that they should resemble the situation in classical testing and the resultant p-values are analysed in conjunction with the lower bounds on the posterior probabilities. The situation of decision making under quadratic loss is also considered. |
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