Goodman and Kruskal's lambda

In probability theory and statistics, Goodman & Kruskal's lambda (${\displaystyle \lambda }$) is a measure of proportional reduction in error in cross tabulation analysis. For any sample with a nominal independent variable and dependent variable (or ones that can be treated nominally), it indicates the extent to which the modal categories and frequencies for each value of the independent variable differ from the overall modal category and frequency, i.e., for all values of the independent variable together. ${\displaystyle \lambda }$ is defined by the equation

${\displaystyle \lambda ={\frac {\varepsilon _{1}-\varepsilon _{2}}{\varepsilon _{1}}}.}$

where

${\displaystyle \varepsilon _{1}}$ is the overall non-modal frequency, and

${\displaystyle \varepsilon _{2}}$ is the sum of the non-modal frequencies for each value of the independent variable.

Values for lambda range from zero (no association between independent and dependent variables) to one (perfect association).