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

Abstract

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.

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“…The Chi-square test, often denoted as Χ², is a powerful statistical tool used to assess associations between categorical variables. Specifically, it helps determine whether the observed frequency distribution of a categorical variable significantly deviates from the expected distribution (Zhang, 2019;Aslam & Smarandache, 2023). Researchers employ Chisquare tests to test hypotheses related to the distribution of categorical variables, such as assessing whether two variables are associated or independent (Gaboardi et al, 2016;Cardona et al, 2020).…”