A variance stabilizing transformation for coefficients of concordance and for Spearman's rho and Kendall's tau

Abstract

SUMMARY Kendall & Babington Smith (1939) and Ehrenberg (1952) have suggested measures of the concordance of a set of m rankings, but little is known about the distribution of these statistics in the nonnull case, i.e. the case when some association exists. Expressions are given for the variances of these statistics for a class of underlying distributions, and a simple transformation which stabilizes the variances considerably is described.