Measuring Association for Nominal Data: Alternative Derivation and Interpretation of Lambda

Abstract

Using the deviation-from-the-mode index of variation for categorical data, a measure of association for nominal variables is derived. This measure (R²) gives exactly the same numerical results as the popular lambda (λ) measure, but their derivations and operational interpretations differ. While λ is based on a proportional-reduction-in-error logic, R² is based on a proportional-reduction-in-variation logic analogous to the coefficient of determination for quantitative variables. Both asymmetric and symmetric R² are considered.