Advances and Applications in Statistics
Volume 8, Issue 2, Pages 209 - 218
(April 2008)
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DECOMPOSITION OF INDEPENDENCE MODEL AND SEPARABILITY OF ITS TEST STATISTIC FOR TWO-WAY CONTINGENCY TABLES WITH ORDERED CATEGORIES
Sadao Tomizawa (Japan), Nobuko Miyamoto (Japan) and Masaya Sakurai (Japan)
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Abstract: For two-way contingency tables with ordered categories, this paper shows that (i) the independence model holds if and only if the covariance of the row and column variables equals zero and the linear-by-linear (or uniform) association model holds, and (ii) the statistic for testing the independence is asymptotically equivalent to the sum of test statistics for the decomposed models. Examples are given. The relationship between the independence and the concordance (discordance) is noted. |
Keywords and phrases: concordance, correlation, covariance, decomposition, Gamma measure, independence, separability, uniform association. |
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