A MEASURE OF ASYMMETRY OF MARGINAL RIDITS FOR SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES

For square contingency tables with ordered categories, the marginal homogeneity (MH) model is equivalent to the equality of row and column marginal ridits. This paper proposes a measure to represent what degree the row marginal ridit departs from the column marginal ridit. The measure is expressed by using the Cressie-Read power-divergence or Patil-Taillie diversity index, which is applied to the marginal ridits. It is useful for comparing the degree of departure from MH in several tables. Examples are given. The proposed measure is also compared with the measure of departure from MH by Tahata, Iwashita and Tomizawa (2006), and with the goodness-of-fit test statistic of the MH model.