An Exact Test on the Goodman–Kruskal λ for Prediction on a Dichotomy

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1983 · Volume 45 · Issue 3

DOI: 10.1111/j.2517-6161.1983.tb01264.x

Abstract

Goodman and Kruskal (1954) introduced a measure λ of predictive association when predicting the category of a variableBfrom a category of a variableA. The measure λ is such that 0 ≤ λ ≤ 1 with a zero value meaning no predictive gain while λ = 1 indicates a perfect predictive association betweenAandB.Thus, the test ofH0: λ = 0 versusH1: λ > 0 is of prime importance, since it is entirely analogous to a test for significance of regression or correlation. We present an exact test, developed through a reparameterization scheme, of the above hypothesis whenBis dichotomous. The testing procedure is quite simple, requiring few calculations. In addition, this paper presents the method of calculation of power for any point in the resulting parameter space and relates the power to the original parameter λ.

Keywords

contingency table measure, goodman-kruskal λ, hypothesis test, prediction on a dichotomous variable, power

Enable JavaScript for citation tools and additional paper interactions.