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December 2021 A two-dimensional index for marginal homogeneity in ordinal square contingency tables
Shuji Ando, Tomohiro Noguchi, Aki Ishii, Sadao Tomizawa
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SUT J. Math. 57(2): 211-224 (December 2021). DOI: 10.55937/sut/1641859478


For square contingency tables with ordered categories, indexes that represent the degree of departure from the marginal homogeneity (MH) model have been proposed. There are two types of directionalities of departure from MH. The existing indexes, however, can analyze either the degree of departure from MH or the directionality but not both. To address this issue, this study proposes a two-dimensional index, which combines the existing indexes, can simultaneously analyze both the degree and directionality of departure from MH. This study also evaluates the usefulness of the proposed index for visually comparing degrees of departure from MH in several square contingency tables using confidence region.


The authors would like to thank an anonymous reviewer and the editor for their comments and suggestions to improve this paper.


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Shuji Ando. Tomohiro Noguchi. Aki Ishii. Sadao Tomizawa. "A two-dimensional index for marginal homogeneity in ordinal square contingency tables." SUT J. Math. 57 (2) 211 - 224, December 2021.


Received: 28 July 2021; Published: December 2021
First available in Project Euclid: 21 April 2022

Digital Object Identifier: 10.55937/sut/1641859478

Primary: 62H17

Keywords: Comparison , confidence region , directionality , marginal inhomogeneity , visualized index

Rights: Copyright © 2021 Tokyo University of Science


Vol.57 • No. 2 • December 2021
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