A Measure of Departure from Average Symmetry for Square Contingency Tables with Ordered Categories
DOI:
https://doi.org/10.17713/ajs.v38i2.264Abstract
For the analysis of square contingency tables, Tomizawa (1994), Tomizawa, Seo, and Yamamoto (1998), and Tomizawa, Miyamoto, and Hatanaka (2001) considered measures to represent the degree of departure from symmetry. However, the maximum value of these measures cannot distinguish two kinds of complete asymmetry (say, complete-upper-asymmetry and complete-lower-asymmetry). The present paper proposes a measure which can distinguish two kinds of complete asymmetry for square tables with ordered categories. Especially the proposed measure is useful for representingthe degree of departure from symmetry when the conditional symmetry model holds. Examples are given.
References
Agresti, A. (2002). Categorical Data Analysis (2nd ed.). New York: JohnWiley & Sons.
Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. (1975). Discrete Multivariate Analysis: Theory and Practice. Cambridge, Massachusetts: The MIT Press.
Bowker, A. H. (1948). A test for symmetry in contingency tables. Journal of the American Statistical Association, 43, 572-574.
Caussinus, H. (1965). Contribution à l’analyse statistique des tableaux de corrélation. Annales de la Faculté des Sciences de l’Université de Toulouse, 29, 77-182.
Goodman, L. A. (1979). Multiplicative models for square contingency tables with ordered categories. Biometrika, 66, 413-418.
McCullagh, P. (1978). A class of parametric models for the analysis of square contingency tables with ordered categories. Biometrika, 65, 413-418.
Stuart, A. (1953). The estimation and comparison of strengths of association in contingency tables. Biometrika, 40, 105-110.
Stuart, A. (1955). A test for homogeneity of the marginal distributions in a two-way classification. Biometrika, 42, 412-416.
Tomizawa, S. (1984). Three kinds of decompositions for the conditional symmetry model in a square contingency table. Journal of the Japan Statistical Society, 14, 35-42.
Tomizawa, S. (1994). Two kinds of measures of departure from symmetry in square contingency tables having nominal categories. Statistica Sinica, 4, 325-334.
Tomizawa, S., Miyamoto, N., and Hatanaka, Y. (2001). Measure of asymmetry for square contingency tables having ordered categories. Australian and New Zealand Journal of Statistics, 43, 335-349.
Tomizawa, S., Seo, T., and Yamamoto, H. (1998). Power-divergence-type measure of departure from symmetry for square contingency tables that have nominal categories. Journal of Applied Statistics, 25, 387-398.
Downloads
Published
How to Cite
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.