6.3 Kendal’s Tau

Kendal’s tau is a second alternative to Pearson and is identical to Spearman’s rho with regard to assumptions. Kendal’s tau only differs from Spearman’s rho in how it measures the relationship. Whereas Spearman measures the correlation of the ranks, Kendal’s tau is a function of concordant (C), discordant (D) and tied (Tx and Ty) pairs of observations. Concordant means both X and Y in one observation of a pair are larger than in the other. Discordant means X is larger in one observation than the other while Y is smaller. Tied mean either both observations have the same X or both have the same Y.

\[\mathrm{Kendall's} \space \tau_b = \frac{C - D}{\sqrt{(C + D + T_x) \times (C + D + T_Y)}}\]