Measure of departure from marginal point-symmetry for two-way contingency tables

Abstract

For two-way contingency tables, Tomizawa (1985) considered the point-symmetry and marginal point-symmetry models, and Tomizawa, Yamamoto and Tahata (2007) proposed a measure to represent the degree of departure from point-symmetry. The present paper proposes a measure to represent the degree of departure from marginal pointsymmetry for two-way tables. The proposed measure is expressed by using Cressie-Read power-divergence or Patil-Taillie diversity index. This measure would be useful for comparing the degrees of departure from marginal point-symmetry in several tables. The relationship between the degree of departure from marginal point-symmetry and the measure is shown when it is reasonable to assume underlying bivariate normal distribution. Examples are shown.