A Coefficient of Correlation Based on Ratios of Ranks and Anti-ranks

Rank association is a fundamental tool to express dependence for ordinal data. Measures of rank correlation have been developed in several contexts for more than a century and we were able to cite more than thirty of these coefficients, from simple ones to relatively complicated definitions involving one or more systems of weights. However, only a few of these can actually be considered reasonable measures of concordance/discordance. The main drawback with the vast majority of coefficients is their resistance-to-change which appears to be of limited value for the purposes of rank comparisons that are intrinsically robust. In this article, a new non-parametric correlation coefficient is defined that is based on ratios of two ranks. In comparing it with existing coefficients, it was found to be extremely sensitive to permutation patterns.We have illustrated the potential improvement that our index may provide in economic contexts by comparing published results with those obtained through the use of this new index. The success that we have had suggests that our index may have important applications wherever the discriminatory power of the rank correlation coefficient ought to be particularly strong.