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Catanova for multidimensional contingency tables: Nominal-scale response
Authors:Robert J Anderson  J Richard Landis
Institution:1. Epidemiology-Biometry Program School of Public Health , University of Illinois at the Medical Center , 2121 W. Taylor, Chicago, Illinois, 60680;2. Department of Biostatistics School of Public Health , University of Michigan , Ann Arbor, Michigan, 48109
Abstract:This paper extends an analysis of variance for categorical data (CATANOVA) procedure to multidimensional contingency tables involving several factors and a response variable measured on a nominal scale. Using an appropriate measure of total variation for multinomial data, partial and multiple association measures are developed as R2 quantities which parallel the analogous statistics in multiple linear regression for quantitative data. In addition, test statistics are derived in terms of these R2 criteria. Finally, this CATANOVA approach is illustrated within the context of 2 three-way contingency table from a multicenter clinicaltrial.
Keywords:Goodmany-Krukal τb categorical data  partial association  multiple association
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