Abstract
For the analysis of square contingency tables with nominal categories, Tomizawa (1995a) and Tomizawa and Makii (2001a) considered the measures to represent the degree of departure from the marginal homogeneity (MH). This paper proposes a measure to represent the degree of departure from MH for square contingency tables with ordered categories (instead of those with nominal categories). The measure proposed is expressed by using the Cressie and Read’s (1984) power-divergence or Patil and Taillie’s (1982) diversity index, which is defined for the cumulative probablities that an observation will fall in row (column) category i or below and column (row) category i + 1 or above. The measure depends on the order of listing the categories. It would be useful for comparing the degree of departure from MH in several tables with ordered categories. The relationships between the measure and the normal distribution (also some models) are also shown. Examples are given.
