Goodman and Kruskal’s lambda coefficient measures the proportional reduction in error in crosstab analysis. The statistic can be symmetric, where you do not have to specify which variable is dependent, and asymmetric where the dependent variable is specified.
ε1 is the overall non-modal frequency and ε2 is the sum of the non-modal frequencies for each value of the independent variable.
Use of the Lambda Coefficient
The lambda coefficient isn’t used very often, perhaps because the underlying calculations are “…not generally understood by behavioral scientists” (Hartwig, 1973). Despite some “major weaknesses” (source), it is useful as a way to understand how variables relate to each other. Specifically, λ shows how one variable’s values can help to reduce prediction errors in a second variable.
Hartwig, F.: Statistical significance of the lambda coefficients. Behavioral Science 18 (1973), 307-310