Concordance coefficients to measure the agreement among several sets of ranks

In this paper, two measures of agreement among several sets of ranks, Kendall's concordance coefficient and top-down concordance coefficient, are reviewed. In order to illustrate the utility of these measures, two examples, in the fields of health and sports, are presented. A Monte Carlo simulation study was carried out to compare the performance of Kendall's and top-down concordance coefficients in detecting several types and magnitudes of agreements. The data generation scheme was developed in order to induce an agreement with different intensities among m ( m >2) sets of ranks in non-directional and directional rank agreement scenarios. The performance of each coefficient was estimated by the proportion of rejected null hypotheses, assessed at 5% significance level, when testing whether the underlying population concordance coefficient is sufficiently greater than zero. For the directional rank agreement scenario, the top-down concordance coefficient allowed to achieve a percentage of significant concordances that was higher than the one achieved by Kendall's concordance coefficient. Mainly, when the degree of agreement was small, the results of the simulation study pointed to the advantage of using a weighted rank concordance, namely the top-down concordance coefficient, simultaneously with Kendall's concordance coefficient, enabling the detection of agreement (in a top-down sense) in situations not detected by Kendall's concordance coefficient.