GENERALIZED PROPORTIONAL REDUCTION IN VARIATION MEASURE FOR TWO-WAY CONTINGENCY TABLES

Abstract

For a two-way contingency table with nominal explanatory and response variables, Goodman and Kruskal (1954), and Theil (1970) proposed the measures which describe the proportional reduction in variation from the marginal distribution to the conditional distributions of the response. This paper proposes a generalization of those measures. The measure is expressed by using the Patil and Taillie's (1982) diversity index. Special cases of the proposed measure include the Goodman and Kruskal's and the Theil's measures.