For square contingency tables with ordered categories, indexes that
represent the degree of departure from the marginal homogeneity (MH) model
have been proposed. There are two types of directionalities of departure from
MH. The existing indexes, however, can analyze either the degree of departure
from MH or the directionality but not both. To address this issue, this study
proposes a two-dimensional index, which combines the existing indexes, can
simultaneously analyze both the degree and directionality of departure from
MH. This study also evaluates the usefulness of the proposed index for visually
comparing degrees of departure from MH in several square contingency tables
using condence region.departmental bulletin pape
