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

Abstract

For the analysis of square contingency tables, Tomizawa, Miyamoto and Ashihara (2003) considered a measure to represent the degree of departure from marginal homogeneity. However, the maximum value of this measure cannot distinguish two kinds of marginal inhomogeneity. This paper proposes a measure which can distinguish two kinds of marginal inhomogeneity for square tables with ordered categories. The measure is constructed using the arc-cosine function of symmetric cumulative probabilities. Especially the proposed measure is useful for representing the degree of departure from marginal homogeneity when the extended marginal homogeneity model holds. Examples are given.