A Measure of Departure from Average Symmetry for Square Contingency Tables with Ordered Categories

Abstract

For the analysis of square contingency tables, Tomizawa (1994), Tomizawa, Seo, and Yamamoto (1998), and Tomizawa, Miyamoto, and Hatanaka (2001) considered measures to represent the degree of departure from symmetry. However, the maximum value of these measures cannot distinguish two kinds of complete asymmetry (say, complete-upper-asymmetry and complete-lower-asymmetry). The present paper proposes a measure which can distinguish two kinds of complete asymmetry for square tables with ordered categories. Especially the proposed measure is useful for representing the degree of departure from symmetry when the conditional symmetry model holds. Examples are given.