Generalized measures of departure from marginal homogeneity for contingency tables with nominal categories
S. Tomizawa and T. Makii (2001). Generalized measures of departure from marginal homogeneity for contingency tables with nominal categories. Journal of Statistical Research, Vol. 35, No. 2, pp. 1-24.
For square contingency tables with nominal categories, Tomizawa (1995) considered two types of measures to represent the degree of departure from the marginal homogeneity (MH). This paper proposes a generalization of Tomizawa's measures. The proposed measures are expressed by using the Cressie and Read's (1984) power divergence or Patil and Taillie's (1982) diversity index. The measures are used to measure how far the marginal distributions (or the conditional marginal distributions given that an observation will fall in one of the off-diagonal cells of the table) are distant from those with an MH structure. They would be useful for comparing the degree of departure from MH in several tables. One of these measures is also extended to T-way tables $(T>3)$.
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