Goodman and Kruskal's λ

A new look at an old measure of association

R. W. Makuch, P. S. Rosenberg, Gwendolyn B Scott

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)619-631
Number of pages13
JournalStatistics in Medicine
Volume8
Issue number5
StatePublished - Jan 1 1989

Fingerprint

Measures of Association
Analysis of variance
Error Rate
Analysis of Variance
Prognostic Factors
Binary Response
Logistic Regression
Categorical or nominal
Predictors
Table
Acquired Immunodeficiency Syndrome
Regression
Logistic Models
Directly proportional
Regression Analysis
Prediction
Zero
Relationships
Model
Children

ASJC Scopus subject areas

  • Epidemiology

Cite this

Goodman and Kruskal's λ : A new look at an old measure of association. / Makuch, R. W.; Rosenberg, P. S.; Scott, Gwendolyn B.

In: Statistics in Medicine, Vol. 8, No. 5, 01.01.1989, p. 619-631.

Research output: Contribution to journalArticle

Makuch, R. W. ; Rosenberg, P. S. ; Scott, Gwendolyn B. / Goodman and Kruskal's λ : A new look at an old measure of association. In: Statistics in Medicine. 1989 ; Vol. 8, No. 5. pp. 619-631.
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