Canonical Association between Nominal Measurements

Abstract

The problem of the measurement of association between two attributes is of importance in social sciences [5]. Following Hotelling [6, 7], Lancaster [9], and Kendall [8], the canonical structure of a two-way classification is obtained. Based on the canonical correlations, three measures of association are suggested. Their metric properties are summarized. One of the measures is shown to reduce to the measure suggested by Cramér [1]. Their large sample distributions are approximated on the null hypothesis of independence between the two attributes.