Premium
Goodman and Kruskal's λ: A new look at an old measure of association
Author(s) -
Makuch Robert W.,
Rosenberg Philip S.,
Scott Gwendolyn
Publication year - 1989
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780080511
Subject(s) - measure (data warehouse) , association (psychology) , kruskal's algorithm , statistics , econometrics , computer science , psychology , mathematics , data mining , algorithm , minimum spanning tree , psychotherapist
We examine Goodman and Kruskal's λ using Efron's approach to regression and analysis of variance (ANOVA) for zero‐one outcome data. For a binary response cross‐classified by a single nominal predictor, we present a computationally simple ANOVA table in which λ is analogous to Pearson's R ‐square. We characterize the relationship between λ and the commonly used apparent error rate in logistic regression, and show that λ is based implicitly on a prediction rule for a saturated model with classification level 0.5. This relationship suggests that we can correct the apparent error rate for chance by defining a natural generalization of λ that we call PRE, the proportional reduction in error. We illustrate the use of λ and PRE in an analysis of prognostic factors for one‐year survival in children with the acquired immunodeficiency syndrome (AIDS).