Groupe d’études et de recherche en analyse des décisions

G-96-29

Concordance between Two Linear Orders: Spearman and Kendall Coefficients Revisited

This paper bears on the two most classical measures of concordance between two linear orders L and L', the Kendall tau and the Spearman rho, or equivalently on the Kendall and Spearman distance between such orders. We give an expression of (L,L') - (L,L') in function of the parameters of the partial order , which allows determination of the extremal values of this difference and beginning an investigation of the case where tau and rho are equal. This expression of (L,L') - (L,L') is derived from a relation between the Kendall and Spearman distances between linear orders equivalent with the 1980 Guilbaud formula linking rho, tau and a third coefficient sigma, and with the 1950 Daniels inequality. We also prove an - apparently new - monotonicity property of rho. In the conclusion we point out some possible extensions of this work and we add some historical comments.

, 27 pages