A new rank correlation measure

A new rank correlation measure beta (n) is proposed, so as to develop a nonparametric test of independence for two variables. beta (n) is shown to be the symmetrized version of a measure earlier proposed by Borroni and Zenga (Stat Methods Appl 16:289-308, 2007). More specifically, beta (n) is built so that it can take the opposite sign, without changing its absolute value, when the ranking of one variable is reversed. Further, the meaning of the population equivalent of beta (n) is discussed. It is pointed out that this latter association measure vanishes not only at independence but, more generally, at indifference, that is when the two variables do not show any "tendency" to positive or negative dependence. The null distribution of beta (n) needs an independent study: hence, the finite null variance and a table of critical values are determined. Moreover, the asymptotic null distribution of beta (n) is derived. Finally, the performance of the test based on beta (n) is evaluated by simulation. beta (n) is shown to be a good competitor of some classical tests for the same problem.