A new measure of nominal-ordinal association

A new measure for evaluating the strength of the association between a nominal variable and an ordered categorical response variable is introduced. The introduction of a new measure is justified by analysing the characteristics of a measure of the nominal-ordinal association proposed by Agresti (1981), especially with respect to the problem of the 'choice' of a predictive variable. The sample-based version of the index is studied, and its asymptotic standard error and asymptotic distribution are derived. Simulations are considered to evaluate the adequacy of the asymptotic approximation determined, following Goodman & Kruskal (1963).