On decomposition of m × m statistical tables based on grade dependence measures

The aim of the paper is two-fold. The first is to introduce, for any given partition of ℜ², the decomposition of Spearman's rho into three terms: between, within and remainder. This decomposition, presented in the paper, is strictly connected with that of the concentration index as introduced previously by the author, and with the decomposition of Kendall's tau as introduced by Kowalczyk and Niewiadomska-Bugaj. Those earlier results are reminded in the paper, as well. The second aim of the paper is to show and exemplify how one can use the decomposition of ρ^* (Spearman's rho) and τ (Kendall's tau) to analyse, decompose and compare m × m contingency tables with the same categories for the row variable and the column variable.