### 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 language | English |
---|---|

Pages (from-to) | 619-631 |

Number of pages | 13 |

Journal | Statistics in Medicine |

Volume | 8 |

Issue number | 5 |

State | Published - Jan 1 1989 |

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### ASJC Scopus subject areas

- Epidemiology

### Cite this

*Statistics in Medicine*,

*8*(5), 619-631.

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

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 8, no. 5, pp. 619-631.

}

TY - JOUR

T1 - Goodman and Kruskal's λ

T2 - A new look at an old measure of association

AU - Makuch, R. W.

AU - Rosenberg, P. S.

AU - Scott, Gwendolyn B

PY - 1989/1/1

Y1 - 1989/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0024556423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024556423&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 619

EP - 631

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 5

ER -