Journal of Advanced Statistics

8

Authors: Shuji Ando, Kyohei Aoba

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.