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For square contingency tables with ordered categories, Tahata et al. (2006) and Tahata et al. (2012) considered measures which represent the degree of departure from the marginal homogeneity (MH) model using the cumulative marginal probabilities. The former measure can judge whether or not the MH model holds, but the latter cannot. Also, the latter measure can distinguish the directionality for two types of maximum marginal inhomogeneities, but the former cannot. The present paper proposes adoi:10.22606/jas.2019.43001 fatcat:qnuzam6msffcte6nko36tobtbq