Marginal Asymmetry Measure Based on Entropy for Square Contingency Tables with Ordered Categories

For the analysis of square contingency tables, Tomizawa, M iyamoto and Ashihara (2003) considered a measure to represent the degree of departure fro m marginal homogeneity. The measure lies between 0 and 1, and it takes the minimu m value when the marginal ho mogeneity holds and the maximu m value when one of two symmet ric cu mulat ive probabilities for any category is zero. Th is paper proposes improvement of the measure so that the degree of departure fro m marginal homogeneity can attain the maximu m value even when the cumu lative p robabilities are not zero. The proposed measure would be useful fo r representing the degree of departure fro m marg inal ho mogeneity, especially when some asymmetry models hold as the extended marg inal ho mogeneity model or the conditional sym metry model. Examp les are given.