DECOMPOSITION OF INDEPENDENCE USING PEARSON, KENDALL AND SPEARMAN’S CORRELATIONS AND ASSOCIATION MODEL FOR TWO-WAY CLASSIFICATIONS

Kouji Tahata (Japan), Nobuko Miyamoto (Japan) and Sadao Tomizawa (Japan)

Received March 10, 2008

Abstract

For two-way contingency tables with ordered categories, Tomizawa et al. [11] showed that the independence model holds if and only if the Pearson correlation coefficient equals zero and the linear-by-linear (LL) (or uniform (U)) association model holds, and also if and only if the Kendall’s tau-b equals zero and the LL (or U) model holds. The present paper shows that the independence model holds if and only if the Spearman’s rho based on the ridit equals zero and the LL (or U) model holds. This also shows such an example that the Spearman’s rho equals zero but the independence does not hold, and explores the reason using the decomposition of independence.

Keywords and phrases: independence, Kendall’s tau-b, linear-by-linear association, Pearson correlation coefficient, Spearman’s rho, uniform association.