AN ASSOCIATION INDEX FOR RECTANGULAR CONTINGENCY TABLES WITH ORDERED/UNORDERED VARIABLES

Abstract

In a previous work, Mineo and Ruggieri (2005) introduce a new index to measure the association in square contingency tables; in this paper such an index is extended to rectangular tables, preserving the same properties. The considered domain includes all the contingency tables with equal n (the total number of observations), since the tables of maximum dependence, useful for computing the denominator of the proposed index, belong to it. The main findings, which prove the effectiveness of the proposed measure, are presented. In particular, the new measure assumes values in the range [-1,+1], taking value zero in tables with distributive independence and positive/negative values if association/dissociation occurs. The importance of the sign for an association index computed on rectangular contingency tables and the need to recognize association from dissociation is explained. It is also shown as the absolute value of the new measure is invariant to permutation of rows and/or columns of the observed table. Finally, some relevant examples and case studies are reported.