= Stuart's tau-c
{c}
{title2=$\tau_c=2m(C-D)/[n^2(m-1)]$}
= Stuart tau-c
{c}
{synonym}
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 is
$$
\tau_c=\frac{2m(C-D)}{n^2(m-1)}.
$$
It 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>.<Ordinal association measures in the DescTools documentation>[StuartTauC, Details: formula, minimum table dimension and ordinal-data requirement]{ref}
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