Abstract
For square contingency tables with ordered categories, Yamamoto et al. (2007) considered a measure to represent the degree of departure from extended marginal homogeneity. It attains the maximum value when one of two symmetric cumulative probabilities is zero. The present paper proposes an improved measure so that the degree of departure from extended marginal homogeneity can attain the maximum value even when the cumulative probabilities are not zeros. An example is given.
Highlights
IntroductionTomizawa (1984, 1995) considered the extended marginal homogeneity (EMH) model which is expressed as
For the R × R square contingency table, let πi j denote the probability that an observation will fall in cell (i, j) (i = 1, . . . , R; j = 1, . . . , R)
For square contingency tables with ordered categories, Yamamoto et al (2007) considered a measure to represent the degree of departure from extended marginal homogeneity
Summary
Tomizawa (1984, 1995) considered the extended marginal homogeneity (EMH) model which is expressed as. Yamamoto et al (2007) considered a measure to represent the degree of departure from EMH, using Patil and Taillie (1982) diversity index. The measure ranges between 0 and 1, and the degree of departure from EMH is maximum when Q1(i) = 0 or Q2(i) = 0 for all i = 1, . We are interested in a measure to represent the degree of departure from EMH such that it can attain the maximum value even when each of {Q1(i)} and {Q2(i)} is not zero. For square contingency tables with ordered categories, the present paper proposes such a measure on EMH when all cumulative probabilities are positive
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