A Class of Association Measures for Categorical Variables Based on Weighted Minkowski Distance

Measuring and testing association between categorical variables is one of the long-standing problems in multivariate statistics. In this paper, I define a broad class of association measures for categorical variables based on weighted Minkowski distance. The proposed framework subsumes some important measures including Cramér’s V, distance covariance, total variation distance and a slightly modified mean variance index. In addition, I establish the strong consistency of the defined measures for testing independence in two-way contingency tables, and derive the scaled forms of unweighted measures.