For the analysis of square contingency
tables with the same row and column ordinal classifications, this article
proposes new models which indicate the structures of symmetry with respect to
the anti-diagonal of the table. Also, this article gives a simple decomposition
in 3 ′ 3 contingency table using the proposed models. The proposed models
are applied to grip strength data.
References
[1]
Bowker, A.H. (1948) A Test for Symmetry in Contingency Tables. Journal of the American Statistical Association, 43, 572-574. http://dx.doi.org/10.1080/01621459.1948.10483284
[2]
Martin, N. and Pardo, L. (2010) A New Measure of Leverage Cells in Multinomial Loglinear Models. Communications in Statistics - Theory and Methods, 39, 517-530. http://dx.doi.org/10.1080/03610920903139991
[3]
Kolassa, J.E. and Bhagavatula, H.G. (2012) Accurate Approximations to the Distribution of a Statistic Testing Symmetry in Contingency Tables. Institute of Mathematical Statistics, 8, 181-189. http://dx.doi.org/10.1214/11-imscoll812
[4]
Tahata, K. and Tomizawa, S. (2014) Symmetry and Asymmetry Models and Decompositions of Models for Contingency Tables. SUT Journal of Mathematics, 50, 131-165.
[5]
Stuart, A. (1955) A Test for Homogeneity of the Marginal Distributions in a Two-Way Classification. Biometrika, 42, 412-416. http://dx.doi.org/10.1093/biomet/42.3-4.412
[6]
Read, C.B. (1977) Partitioning Chi-Square in Contingency Table: A Teaching Approach. Communications in Statistics-Theory and Methods, 6, 553-562. http://dx.doi.org/10.1080/03610927708827513
[7]
Tomizawa, S. (1986) Four Kinds of Symmetry Models and Their Decompositions in a Square Contingency Table with Ordered Categories. Biometrical Journal, 28, 387-393. http://dx.doi.org/10.1002/bimj.4710280402
