 Kendall rank correlation coefficient

A family of ordinal association measures based on concordant pairs and discordant pairs. Without a tie adjustment, the coefficient is ${\tau }_a=(C-D)/\left(\genfrac{}{}{0ex}{}{n}{2}\right)$: the arithmetic mean, over unordered pairs, of the product of the two coordinate comparison signs. Reversing one ordering reverses the sign, and strictly increasing relabellings preserve it. Kendall's tau-b makes an explicit adjustment for tied pairs. The name commemorates Maurice Kendall.