Simultaneous inference for Kendall’s tau

Abstract

We introduce multiple contrast tests and simultaneous confidence intervals for rank correlation measures in general multivariate factorial designs. To this end, we derive the unconditional asymptotic joint sampling distribution of multiple correlation coefficients under the null and arbitrary alternatives. We neither require distributions to be discrete nor continuous and adjust for ties using a normalized version of the bivariate distribution function and scale point estimators appropriately to obtain Kendall’s τA and τB, Somers’ D, and Goodman and Kruskal’s γ. Simulation studies for a range of scenarios indicate that the proposed methods control the family wise error rate in the strong sense even when sample sizes are rather small. A case study on the iris flower data set demonstrates how to perform inference in practice.