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Measures of Departure from Marginal Homogeneity for Contingency Tables with Nominal Categories

Sadao Tomizawa
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 44, No. 4 (1995), pp. 425-439
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2348892
Stable URL: http://www.jstor.org/stable/2348892
Page Count: 15
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Measures of Departure from Marginal Homogeneity for Contingency Tables with Nominal Categories
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Abstract

For square contingency tables with nominal categories, four kinds of measure are proposed to represent the degree of departure from marginal homogeneity (MH). The measures are expressed by using the Shannon entropy or Gini concentration. They 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. Two of these measures are also extended to $T$-way tables $(T \geqslant 3)$.

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