= Goodman and Kruskal's lambda
{c}
{title2=$\lambda_{Y\mid X}=(E_0-E_1)/E_0$}
{wiki}
Predict categorical response $Y$ by a most frequent category. Without knowing $X$, the number of mistakes in a <contingency table> is $E_0=n-\max_j n_{+j}$. Allowing a separate most frequent response for each predictor row gives $E_1=n-\sum_i\max_j n_{ij}$. <Goodman and Kruskal's lambda> is the fractional reduction in those mistakes when $E_0>0$. Its direction matters, and it can vanish despite <statistical association>: if every row has the same most frequent response category, knowledge of $X$ changes no modal predictions even when the row distributions differ.
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