Decompositions of symmetry using extended palindromic symmetry models for square contingency tables. (English) Zbl 1420.62259

Summary: For square contingency tables with ordered categories, this paper gives the theorem that the symmetry model holds if and only if the following three models hold: (1) extended palindromic symmetry, (2) equality of marginal moments, and (3) subsymmetry of cumulative probabilities from the upper right and lower left corners of the table.


62H17 Contingency tables
Full Text: DOI


[1] Bhapkar, V. P.; Darroch, J. N., Marginal symmetry and quasi symmetry of general order, J. Multivariate Anal., 34, 173-184, (1990) · Zbl 0735.62057
[2] Bishop, Y. M. M., S. E. Fienberg, and P. W. Holland. 1975. Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press. · Zbl 0332.62039
[3] Bowker, A. H., A test for symmetry in contingency tables, J. Am. Stat. Assoc., 43, 572-574, (1948) · Zbl 0032.17500
[4] Caussinus, H., Contribution à l’analyse statistique des tableaux de corrélation, Ann. Faculté Sci. Univ. Toulouse, 29, 77-182, (1965) · Zbl 0168.39904
[5] Goodman, L. A., Association models and the bivariate normal for contingency tables with ordered categories, Biometrika, 68, 347-355, (1981) · Zbl 0477.62038
[6] Goodman, L. A. 1984. The analysis of cross-classified data having ordered categories. Cambridge, MA: Harvard University Press.
[7] Kullback, S., Marginal homogeneity of multidimensional contingency tables, Ann. Math. Stat., 42, 594-606, (1971) · Zbl 0215.54305
[8] McCullagh, P., A class of parametric models for the analysis of square contingency tables with ordered categories, Biometrika, 65, 413-418, (1978) · Zbl 0402.62032
[9] Mosteller, F., Association and estimation in contingency tables, J. Am. Stat. Assoc., 63, 1-28, (1968)
[10] Read, C. B., Partitioning chi-square in contingency tables: A teaching approach, Commun. Stat. Theory Methods, 6, 553-562, (1977) · Zbl 0365.62043
[11] Saigusa, Y.; Tahata, K.; Tomizawa, S., An extended asymmetry model for square contingency tables with ordered categories, Model Assisted Stat. Appl., 9, 151-157, (2014)
[12] Stuart, A., A test for homogeneity of the marginal distributions in a two-way classification, Biometrika, 42, 412-416, (1955) · Zbl 0066.12502
[13] Tahata, K.; Tomizawa, S., Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories, Adv. Data Anal. Classification, 2, 295-311, (2008) · Zbl 1284.62337
[14] Tahata, K.; Yamamoto, K.; Tomizawa, S., Decomposition of symmetry using palindromic symmetry model in a two-way classification, J. Stat. Appl. Probability, 1, 201-204, (2012)
[15] Tomizawa, S.; Miyamoto, N.; Ouchi, M., Decompositions of symmetry model into marginal homogeneity and distance subsymmetry in square contingency tables with ordered categories, Revstat Stat. J., 4, 153-161, (2006) · Zbl 1141.62329
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.