Measure of Departure from Extended Marginal Homogeneity for Square Contingency Tables with Ordered Categories

Abstract

For the analysis of square contingency tables, Tomizawa and Makii (2001), and Tomizawa, Miyamoto and Ashihara (2003) considered the measures to represent the degree of departure from marginal homogeneity (MH). Tomizawa (1984) considered an extended marginal homogeneity (EMH) model for square tables with ordered categories. This paper proposes a measure to represent the degree of departure from EMH. The measure proposed is expressed by using the Cressie and Read’s (1984) power-divergence or Patil and Taillie’s (1982) diversity index. The measure would be useful for comparing the degree of departure from EMH in several tables. Examples are given.

Keywords

• cumulative probability
• Kullback–Leibler information
• marginal homogeneity
• measure
• ordered category
• power-divergence