On decomposition of m x 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 [R^2], the decomposition of Spearman's rho into three terms: bet~cveen, within and remainder. This decomposition, presented in Section 4, is strictly connected with that of the concentration index ar as introduced in Kowalczyk (1998), and with the decomposition of Kendall's tau as introduced in Kowalczyk and Niewiadomska-Bugaj (2000). Those earlier results are reminded in Sections 2 and 3. The second aim of the paper is to show and exemplify how one can use the decompositions of p* (Spearman's rho) and r (Kendall's tau) to analyse, decompose and compare m x m contingency tables with the same categories for the row variable and the column varable. The examples given in Section 5 concern social mobility tables with data from Britain and Poland. An important observation from the analysis of these data is that p* and r lead there to practically equivalent decompositions.