Stuart's tau-c (${\tau }_c=2m(C-D)/[n^2(m-1)]$)

For an $r\times c$ contingency table of two ordinal categorical variables, write $m=\min (r,c)>1$, $n$ for the sample size and $C,D$ for concordant pairs and discordant pairs. The coefficient isIt provides an ordinal association measure whose normalization accounts for the table dimensions. It generally differs from Kendall's tau-b and Goodman and Kruskal's gamma on a table with tied pairs. An association sign presupposes the chosen category ordering and is not a causal direction. The eponym is associated with Alan Stuart.^[ref]