A new rank correlation measure
A new rank correlation measure β n is proposed, so as to develop a nonparametric test of independence for two variables. β 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, β 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 β 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 β n needs an independent study: hence, the finite null variance and a table of critical values are determined. Moreover, the asymptotic null distribution of β n is derived. Finally, the performance of the test based on β n is evaluated by simulation. β n is shown to be a good competitor of some classical tests for the same problem.
KeywordsNonparametrics Rank correlation Association measures Indifference Gini’s gamma
Mathematics Subject Classification (2000)62G10 62H20
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- Cifarelli DM, Regazzini E (1977) On a distribution-free test of independence based on Gini’s rank association coefficient. In: Barra J, Brodeau F, Romier G, Van Cutsem B (eds) Recent developments in statistics. North-Holland, Amsterdam, pp 375–385Google Scholar
- Cifarelli DM, Regazzini E (1990) Some contribution to the theory of monotone dependence. Tech. Rep. 90.17. CNR-IAMI, MilanoGoogle Scholar
- Gini C (1912) Variabilità e mutabilità; contributo allo studio delle distribuzioni e relazioni statistiche. Studi economico—giuridici, R. Università di CagliariGoogle Scholar
- Gini C (1954) Corso di Statistica. Veschi, RomeGoogle Scholar
- Nelsen RB, Úbeda-Flores M (2004) The symmetric footrule is Gini’s rank association coefficient. Commun Stat Theory 33: 195–196Google Scholar