Department of Statistics, UCLA

Spearman’s rank correlation coefficient is shown to be a deterministic transformation of the empirical polychoric correlation coefficient. The transformation is a homeomorphism under given marginal probabilities, and has a fixed point at zero. Moreover, the two measures of association for ordinal variables are asymptotically equivalent, in a certain sense. If the ordinal variables arise from discretizations, such as groupings of values into categories, Spearman’s rank correlation coefficient has some undesirable properties, and the empirical polychoric correlation coefficient is better suited for statistical inference about the association of the underlying, non-discretized variables.