A comparative analysis of Spearman's rho and Kendall's tau in normal and contaminated normal models

This paper analyzes the performances of Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and contaminated normal populations. Theoretical and simulation results suggest that, contrary to the opinion of equivalence between SR and KT in some literature, the behaviors of SR and KT are strikingly different in the aspects of bias effect, variance, mean square error (MSE), and asymptotic relative efficiency (ARE). The new findings revealed in this work provide not only deeper insights into the two most widely used rank-based correlation coefficients, but also a guidance for choosing which one to use under the circumstances where Pearson's product moment correlation coefficient (PPMCC) fails to apply.

► A computationally more tractable formula of the variance of Spearman's rho (SR) (Lemma 3) and the associated Table 1. ► Exact analytical expression of covariance between SR and Kendall's tau (KT) and the associated Table 2. ► Asymptotic relative efficiencies (AREs) concerning the three estimators of the population correlation ρρ based on SR and KT. ► Closed-form expectations of SR and KT under the contaminated normal model. ► Guidance for choosing which one to use under the circumstances where the PPMCC fails to apply.