Chapter 9 Correlation and Tests of Independence 457 9.3.11 Spearman's rho Assign ranks to the X values, ignoring Y , and assign ranks to the Y values ignoring X . Then Spearman's rho, r s , is just Pearson's correlation based on the resulting ranks. Like all of the correlations in this section it provides protection against outliers among the X values, ignoring Y , as well as outliers among the Y values, ignoring X , but outliers properly placed can alter its value substantially. Letting s be the population value of Spearman's rho, the influence function of s is I F(x, y) = -3 s - 9 + 12{F(x)G(y) + E[F(X )I (Y y)] + E[G(Y )I (X x)]}, where F and G are the marginal distributions of X and Y , respectively, and I is the indicator function (Croux & Dehon, 2010). In terms of asymptotic efficiency and other robustness considerations, results in Croux and Dehon (2010) indicate that Kendall's tau is preferable to Spearman's rho. When X and Y are independent, s = 0. The usual test of H 0 : s = 0 is to reject if |T | t, where t is the 1 - /2 quantile of Student's t-distribution with = n - 2 degrees of freedom, and