Abstract
For the analysis of square contingency tables with ordered categories, Tomizawa et al. (2003) considered a measure to represent the degree of departure from marginal homogeneity (MH). Tomizawa (1993) considered an extended marginal homogeneity (EMH) model. This paper (i) proposes a measure to represent the degree of departure from EMH, (ii) proposes a measure from equality of marginal means (E), and (iii) gives a theorem that the value of measure for MH is equal to the sum of the value of measure for EMH and that for E.
Highlights
Consider an r × r square contingency table with the same row and column classifications
ΓEMH and ΓE may be useful for comparing the degree of departure from extended marginal homogeneity (EMH) and E, respectively, in several tables
In terms of {G1(i)/G2(i)}, i = 1, 2, 3, it seems natural to conclude that the degree of departure from EMH is less for Table 7a than for Table 7b
Summary
Consider an r × r square contingency table with the same row and column classifications. By considering the difference between the cumulative marginal probabilities, the MH model may be expressed as. Austrian Journal of Statistics, Vol 36 (2007), No 2, 105–114
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