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Measure of departure from symmetry for the analysis of collapsed square contingency tables with ordered categories |
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| Authors: | Kouji Yamamoto Fumika Shimada Sadao Tomizawa |
| Institution: | 1. Department of Clinical Epidemiology and Biostatistics, Graduate School of Medicine, Osaka University, 2-2, Yamadaoka, Suita, Osaka, 565-0871, Japan;2. Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan |
| Abstract: | For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper considers the symmetry model for collapsed square contingency tables and proposes a measure to represent the degree of departure from symmetry. The proposed measure is defined as the arithmetic mean of submeasures each of which represents the degree of departure from symmetry for each collapsed 3×3 table. Each submeasure also represents the mean of power-divergence or diversity index for each collapsed table. Examples are given. |
| Keywords: | collapsed table diversity index Kullback–Leibler information measure power-divergence Shannon entropy symmetry |