Some developments about a new nonparametric test based on Gini’s mean difference

In this paper the performance of a new nonparametric test proposed by Borroni and Zenga (2003) for the independence of two criteria is discussed. The test-statistic is based on Gini’s mean difference computed on the total ranks assigned to each sampled unit according to the chosen criteria of sorting. The performance of the test is measured by simulating its power function via Monte Carlo methods when it is applied as a one-sided test of independence against concordance. At this aim, after assuming that the two criteria of ranking are based on the values taken by two quantitative variables, a wide range of bivariate models is set for the two populations. The choice of the simulated models reflects the common situation of sampling from non-Normal populations, usually faced in economic applications. The reported results show that the new proposed test has often good performances and can be considered as a natural competitor of other common nonparametric tests.

Keywords: nonparametric tests, rank correlation indexes, Gini’s mean difference, Monte Carlo simulations.