A martingale approach is used to establish the asymptotic normality of a simple new measure of rank correlation.

Given a fixed line L (in Rn) and a uniform distribution of points (c) on the unit sphere, L(tc), the point of intersection of L and the hyperplane P · c = 0, leads to a mapping Xn : Rn --> R, which is shown to have a Cauchy distribution.

A martingale approach is used to establish the asymptotic normality of a class of weighted correlation statistics, including the statistic proposed by Salama and Quade (1982).

An equivalent representation of the Spearman footrule is considered and a characterization in terms of a Markov chain is established. A martingale approach is thereby incorporated in the study of the asymptotic normality of the statistics.