Distance function for ranked variables

Abstract

Rank correlation coefficients, RCC, are usually based on differences between matched pairs of modalities of two related variables in ordinal scale or on the number of inversions existing between couples of paired modalities, like \(\rho\) - Spearman and \(\tau\) - Kendall, respectively. Here a way to build a RCC based on determinants of all second order minors of a \(n \times 2\) data matrix in ordinal scale is proposed. Some possibilities of use of these determinants will be pointed out and one that seems particularly interesting will be considered showing the properties of the coefficient obtained and comparing them with the corresponding of Kendall's and Spearman's ones.