Association Between Nominal Categorical Variables: New Measure Formulation Based on Metric Distances and Value Validity

Abstract When dealing with nominal categorical data, it is often desirable to know the degree of association or dependence between variables. While there literally no limit number alternative measures that have been proposed over years, they all yield greatly varying, contradictory, and unreliable results due their lack an important property: value validity. After discussing value-validity property, this paper introduces a new measure (dependence) based on mean Euclidean distance probability distributions, one being distribution under independence. Both asymmetric form, when variable can be considered as explanatory (independent) response (dependent) variable, symmetric form are introduced. Particular emphasis given 2 × case each has two categories, but general any categories also covered. Besides having prerequisites good measure. Comparisons made well-known Goodman–Kruskal lambda tau measures. Statistical inference procedure for derived numerical examples provided.