Standard Article

Goodman–Kruskal Measures of Association

  1. G. Upton

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a10023

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Upton, G. 2005. Goodman–Kruskal Measures of Association. Encyclopedia of Biostatistics. 3.

Author Information

  1. University of Essex, Colchester, UK

Publication History

  1. Published Online: 15 JUL 2005


The measures of association proposed by Goodman and Kruskal between 1954 and 1972 can all be described as proportional reduction in error (PRE) measures. They describe the association between two categorical variables in terms of the increase in the probability of correctly predicting the category of one variable when information is supplied about the category of the other variable. The measures λ and τ are for use with any categorical variables, whereas the measure γ is for use when both variables are ordinal.


  • association;
  • categorical variable;
  • contingency table;
  • γ;
  • Goodman–Kruskal;
  • λ;
  • measure of association;
  • ordinal variable;
  • proportional reduction in error;
  • PRE;
  • τ