<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

Yokohama City University School of Medicine

Department of Information Sciences, Faculty of Science and Technology

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

For square contingency tables with nominal categories, a local symmetry model which indicates the symmetric structure of probabilities for only one pair of...

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

Published Online: Jun 12, 2020

Page range: 23 - 35

DOI: https://doi.org/10.2478/bile-2020-0003

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

© 2020 Yusuke Saigusa et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Jun 12, 2020

Page range: 23 - 35

DOI: https://doi.org/10.2478/bile-2020-0003

Keywordscomparison, confidence interval, diversity index, local symmetry, measure, ordered category, weighted harmonic mean

© 2020 Yusuke Saigusa et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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