Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Generalized Measure of Departure From Global Symmetry for Square Contingency Tables with Ordered Categories

  • Tomizawa, Sadao (Department of Information Sciences, Faculty of Science and Technology, Science University of Tokyo) ;
  • Saitoh, Kayo (Department of Information Sciences, Faculty of Science and Technology, Science University of Tokyo)
  • Published : 1998.09.01
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Abstract

For square contingency tables with ordered categories, Tomizawa (1995) considered two kinds of measures to represent the degree of departure from global symmetry, which means that the probability that an observation will fall in one of cells in the upper-right triangle of square table is equal to the probability that the observation falls in one of cells in the lower-left triangle of it. This paper proposes a generalization of those measures. The proposed measure is expressed by using Cressie and Read's (1984) power divergence or Patil and Taillie's (1982) diversity index. Special cases of the proposed measure include TomiBawa's measures. The proposed measure would be useful for comparing the degree of departure from global symmetry in several tables.

Keywords

References

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