A coefficient of correlation based on ratios of ranks and anti-ranks

Rank correlation is a fundamental tool for expressing dependence in cases where data arearranged in order. Measures of rank correlation have been developed in several contexts formore than a century, from simple ones to relatively complicated denitions involving oneor more systems of weights. However, only a few of these can actually be considered to bereasonable measures of concordance/discordance. The main drawback with the vast majorityof coecients is their esistance-to-change", which appears to be of limited value for thepurposes of rank comparisons that are intrinsically robust. In this article, a new correlationmeasure is dened that is based on the ratios of ranks and anti-ranks. In comparing it withexisting rank correlations, we found it to be extremely sensitive to permutation patterns. Wehave illustrated the potential improvement that our index can provide in economic contextsby comparing published results with those obtained through the use of this new index. Thesuccess that we have had suggests that our index may have important applications whereverthe discriminatory power of the rank correlation coecient should be particularly strong.