The Concordance coefficient: An alternative to the Kruskal-Wallis test

Abstract: Kendall rank correlation coefficient is used to measure the ordinal association between two measurements. In this paper, we introduce the Concordance coefficient as a generalization of the Kendall rank correlation, and illustrate its use to measure the ordinal association between quantity and quality measures when two or more samples are considered. In this sense, the Concordance coefficient can be seen as a generalization of the Kendall rank correlation coefficient and an alternative to the non-parametric mean rank-based methods to compare two or more samples. A comparison of the proposed Concordance coefficient and the classical Kruskal-Wallis statistic is presented through a comparison of exact distributions of both statistics.