Isaac Scientific Publishing

Journal of Advanced Statistics

Decompositions of Symmetry Using Odds-Symmetry for Square Contingency Tables

Download PDF (441.4 KB) PP. 23 - 30 Pub. Date: September 1, 2018

DOI: 10.22606/jas.2018.33001


  • Shuji Ando*
    Department of Information and Computer Technology, Faculty of Engineering, Tokyo University of Science, Katsushika-ku, Tokyo, 125-8585, Japan
  • Kyohei Aoba
    Department of Information and Computer Technology, Faculty of Engineering, Tokyo University of Science, Katsushika-ku, Tokyo, 125-8585, Japan


For square contingency tables, many decompositions of the symmetry model were given. If the symmetry model does not hold, the decomposition of symmetry is useful to analyze the cause that the symmetry model fits poorly. The present paper shows the decomposition of the symmetry model using odds-symmetry, and the test statistic for the symmetry model is equal to the sum of those for decomposed models. This paper also gives the decomposition of the conditional symmetry model using odds-symmetry. By comparing the existing decompositions of the symmetry model, we show that the proposed decompositions are useful.


Marginal symmetry, ordinal category, partitioning, test statistic.


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