Wald-type measure of departure from symmetry for square contingency tables with nominal categories

Abstract

For square contingency tables with nominal categories, Tomizawa (1994), and Tomizawa, Seo and Yamamoto (1998) considered the power-divergence-type measures to represent the degree of departure from symmetry. The present paper proposes the Wald-type measure to represent the degree of departure from symmetry. In sample version the proposed measure is obtained by modifying the Wald test statistic by the upper limit with fixed sample size. The paper also describes the relationship between the proposed measure and asymmetry models, and the relationship between the measure and the bivariate normal distribution. Examples are given.