Criteria for the validity of Fisher's condition for balanced block designs |
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| Institution: | 1. Department of Epidemiology and Health Statistics, School of Public Health, Anhui Medical University, No. 81 Meishan Road, Hefei 230032, Anhui, China;2. School of Medicine, The University of Adelaide, Adelaide, SA 5005, Australia;3. Changfeng Centers for Disease Control and Prevention, Hefei, China;4. The Second Affiliated Hospital of Anhui Medical University, Hefei, China;1. Rehabilitation Hospital of Indiana, Indianapolis, IN;2. Indiana University School of Medicine, Indianapolis, IN;1. Physics and Earth Sciences Department, Messina University, Viale F. StagnoD’Alcontres 31, 98166 Messina, Italy;2. Institute of Petroleum Geology and Geophysics, SB RAS, Prospekt Akademika Koptyuga 3, Novosibirsk 630090, Russia;1. Institute on Community Integration (INICO), University of Salamanca, Avda. de la Merced, 109–131, 37005 Salamanca, Spain;2. Department of Psychology, University of Valladolid, Campus Miguel Delibes, Paseo de Belen 1, 47011 Valladolid, Spain;1. The Pennsylvania State University, Department of Mechanical and Nuclear Engineering, United States;2. Nuclear Engineering Program, Materials Science and Engineering, University of Florida, United States |
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| Abstract: | A block design is said to satisfy Fisher's condition if the rows of its incidence matrix are linearly independent. In this note, the results of Kageyama and Tsuji (1980, 1984), concerning the validity of Fisher's condition for variance- and combinatorially-balanced block designs, are strengthened by replacing sufficient conditions involved in them by necessary and sufficient conditions. |
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