CONCORDANCE BETWEEN 2 LINEAR ORDERS - THE SPEARMAN AND KENDALL COEFFICIENTS REVISITED

This paper discusses the two classic measures of concordance between t wo linear orders L and L', the Kendall tau and the Spearman rho, or eq uivalently, the Kendall and Spearman distances between such orders. We give an expression for rho(L,L')-tau(L,L') as a function of the param eters of the partial order L boolean OR L', which allows the determina tion of extremal values for this difference and an investigation of wh en tau and rho are equal. This expression for rho(L,L')-tau(L,L') is d erived from a relation between the Kendall and Spearman distances betw een linear orders that is equivalent to both the Guilbaud (1980) formu la linking rho, tau, and a third coefficient sigma, and Daniels's (195 0) inequality. We also prove an apparently new monotonicity property o f rho. In the conclusion we point out possible extensions and add gene ral historical comments.