On Two Classes of Weighted Rank Correlation Measures Deriving from the Spearman's ρ

Weighted Rank Correlation indices are useful for measuring the agreement of two rankings when the top ranks are considered more important than the lower ones. This paper investigates, from a descriptive perspective, the behaviour of i) five existing indices that introduce suitable weights in the simplified formula of the Spearman’s ρ and ii) an additional five indices we derive using the same weights in the Pearson’s product-moment correlation index between ranks. For their evaluation, we consider that a good Weighted Rank Correlation index should (1) differ from ρ , if computed on the same pair of rankings and (2) assume a broad variety of values in the range [−1,+1], in order to better discriminate amongst different reorderings of the ranks. Results suggest that linear weights should be avoided and show that indices (ii) do not have equalities with ρ and are more sensitive.