A Distribution-Free Test for Related Correlation Coefficients

Let (X 1, X 2, X s ) be a continuous, trivariate random vector for which it is of interest to compare the correlation between X 1 and X 2 with that between X 3 and X 1. This problem is important, for example when both X 2 and X 3 are potential linear predictors for X 1 or, more generally, whenever the variable (X 1. X 2, X 3) represents a triplet of measurements on the same individual and correlation comparisons are desired. In this note it is shown that an exact distribution-free test for such problems can he based on a single Kendall correlation coellicient.