Biometrical Letters

ISSN:1896-3811

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Volume (57) Number 1 pp. 23-35

Yusuke Saigusa 1, Tomomasa Takada 2, Aki Ishii 2, Tomoyuki Nakagawa 2, Sadao Tomizawa 2

1Department of Biostatistics, Yokohama City University School of Medicine, Japan
2Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Japan

Measure of departure from cumulative local symmetry for square contingency tables having ordered categories

Summary

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.

Keywords: comparison, confidence interval, diversity index, local symmetry, measure, ordered category, weighted harmonic mean

DOI: 10.2478/bile-2020-0003

For citation:

MLA Saigusa, Yusuke, et al. "Measure of departure from cumulative local symmetry for square contingency tables having ordered categories." Biometrical Letters 57.1 (2020): 23-35. DOI: 10.2478/bile-2020-0003
APA Saigusa, Y., Takada, T., Ishii, A., Nakagawa, T., & Tomizawa, S. (2020). Measure of departure from cumulative local symmetry for square contingency tables having ordered categories. Biometrical Letters 57(1), 23-35 DOI: 10.2478/bile-2020-0003
ISO 690 SAIGUSA, Yusuke, et al. Measure of departure from cumulative local symmetry for square contingency tables having ordered categories. Biometrical Letters, 2020, 57.1: 23-35. DOI: 10.2478/bile-2020-0003
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