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S. Tomizawa and K. Tahata, “The Analysis of Symmetry and Asymmetry: Orthogonality of Decomposition of Symmetry into Quasi-Symmetry and Marginal Symmetry for Multi-Way Tables,” Journal de la Société Francaise de Statistique, Vol. 148, No. 3, 2007, pp. 3-36.

has been cited by the following article:

• TITLE: Decompositions of Symmetry Using Generalized Linear Diagonals-Parameter Symmetry Model and Orthogonality of Test Statistic for Square Contingency Tables

  AUTHORS: Kouji Yamamoto, Motoki Ohama, Sadao Tomizawa

  KEYWORDS: umulative Probability; Global Symmetry; Linear Diagonals-Parameter Symmetry; Mean Equality; Ordinal Category; Orthogonal Test Statistic

  JOURNAL NAME: Open Journal of Statistics, Vol.3 No.6A, December 27, 2013

  ABSTRACT: For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.