Javier Alcaraz, Laura Anton-Sanchez, Juan Francisco Monge (Operations Research Center, University Miguel Hernández of Elche)

Abstract: The Kendall rank correlation coefficient, based on the Kendall-τ distance, is used to measure the ordinal association between two measurements. In this paper, we introduce a new coefficient also based on the Kendall-τ distance, the Concordance coefficient, and a test to measure whether different samples come from the same distribution. This work also presents a new R package, ConcordanceTest, with the implementation of the proposed coefficient. We illustrate the use of the Concordance coefficient 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 for comparing two or more samples. A comparison of the proposed Concordance coefficient and the classical Kruskal-Wallis statistic is presented through a comparison of the exact distributions of both statistics.