Department of Statistics, UCLA

The polychoric correlation coefficient is a measure of association for ordinal variables which rests upon an assumption of an underlying joint continuous distribution. More specifically, in Karl Pearson’s original definition an underlying joint normal distribution is assumed. In this article, the definition of the polychoric correlation coefficient is generalized so that it allows for other distributional assumptions than the joint normal distribution. The generalized definition is analogous to Pearson’s definition, and the two definitions agree under bivariate normal distributions. Moreover, the polychoric correlation coefficient is put into a framework of copulas which is both mathematically and practically convenient. The theory is illustrated with examples which, among other things, show that the measure of association suffers from lack of statistical robustness.