  When response variables are nominal and populations are cross-classified with
respect to multiple polytomies, questions often arise about the degree of
association of the responses with explanatory variables. When populations are
known, we introduce a nominal association vector and matrix to evaluate the
dependence of a response variable with an explanatory variable. These measures
provide detailed evaluations of nominal associations at both local and global
levels. We also define a general class of global association measures which
embraces the well known association measure by Goodman-Kruskal (1954). The
proposed association matrix also gives rise to the expected generalized
confusion matrix in classification. The hierarchy of equivalence relations
defined by the association vector and matrix are also shown.

Machine Learning