Biometrical Letters Vol. 57(1), 2020, pp. 23-35
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MEASURE OF DEPARTURE FROM CUMULATIVE LOCAL SYMMETRY FOR SQUARE CONTINGENCY TABLES HAVING ORDERED CATEGORIES Yusuke Saigusa1, Tomomasa Takada2, Aki Ishii2, Tomoyuki Nakagawa2, Sadao Tomizawa2 1Department of Biostatistics, Yokohama City University School of Medicine, Yokohama City, Kanagawa 236–0004, Japan, e-mail: saigusay@yokohama-cu.ac.jp 2Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba 278–8510, Japan e-mail: t_takad@yahoo.co.jp, a.ishii@rs.tus.ac.jp, t_nakagawa@rs.tus.ac.jp, tomizawa@is.noda.tus.ac.jp |
For square contingency tables with nominal categories, a local symmetry model which indicates the symmetric structure of probabilities for only one pair of symmetric cells is proposed. For ordinal square tables, the present paper proposes (1) another local symmetry model for cumulative probabilities from the upper-right and lower-left corners of the table, and (2) a measure to represent the degree of departure from the proposed model. The measure has the form of a weighted harmonic mean of the diversity index, which includes the Shannon entropy as a special case. Examples are given in which the proposed method is applied to square table data on decayed teeth in Japanese women patients.
comparison, confidence interval, diversity index, local symmetry, measure, ordered category, weighted harmonic mean
