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Pearson's is the most common correlation statistic, used mainly in parametricsettings. Most common among nonparametric correlation statistics are Spearman'sand Kendall's. We show that for bivariate normal i.i.d. samples the pairwiseasymptotic relative efficiency between these three statistics dependsmonotonically on the population correlation coefficient. This monotonicity is acorollary to a stronger result. The proofs rely on the use of l'Hospital-typerules for monotonicity patterns.

Monotonicity properties of the asymptotic relative efficiency between common correlation statistics in the bivariate normal model