2604.01209 Pearson, Spearman, and Kendall Correlations Disagree on Association Direction in Skewed Data: Exact Conditions and a Decision Flowchart
Pearson's r, Spearman's rho, and Kendall's tau are the three most widely used measures of bivariate association, yet practitioners rarely consider that these coefficients can disagree not merely in magnitude but in sign. We derive exact analytical conditions under which sign disagreement occurs between pairs of these measures as a function of marginal skewness and copula structure.