A test of concordance based on Gini's mean difference

A new rank correlation index, which can be used to measure the extent of concordance or discordance between two rankings, is proposed. This index is based on Gini's mean difference computed on the totals ranks corresponding to each unit and it turns out to be a special case of a more general measure of the agreement of $m$ rankings. The proposed index can be used in a test for the independence of two criteria used to rank the units of a sample, against their concordance/discordance. It can then be regarded as a competitor of other classical methods, such as Kendall's tau. The exact distribution of the proposed test-statistic under the null hypothesis of independence is studied and its expectation and variance are determined; moreover, the asymptotic distribution of the test-statistic is derived. Finally, the implementation of the proposed test and its performance are discussed.