A MEASURE OF ASYMMETRY FOR MULTI-WAY CONTINGENCY TABLES WITH ORDERED CATEGORIES

Abstract

For square contingency tables with ordered categories, Tomizawa, Miyamoto and Hatanaka (2001) considered a measure that represents the degree of departure from symmetry. This paper extends the measure to multi-way tables with ordered categories. The measure proposed is expressed by using the Cressie-Read power-divergence or the Patil-Taillie diversity index. The measure could be useful for comparing the degrees of departure from symmetry in several multi-way tables with ordered categories. Examples are given.