Journal of Advanced Statistics

9

Authors: Shuji Ando, Takashi Takeuchi, Kiyotaka Iki, Sadao Tomizawa

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 a two-dimensional measure vector with above measures as elements that can simultaneously analyze the degree of departure from MH and the directionality for two types of maximum marginal inhomogeneities. Also, this paper shows the usefulness of the proposed measure vector on comparing visually degrees of departure from MH in several square contingency tables using confidence region.