Confidence intervals for Kendall's tau

Abstract

A simulation study was conducted to examine the performance of several confidence intervals (CIs) for Kendall's tau (txy) under a variety of population conditions. Two normal population variables (N = 10,000) were transformed to have tau correlations, τ = 0, .19, .41, or.71. Samples (n = 10, 50, 200) were drawn from the transformed populations 2000 times under each level of correlation, and accompanying CIs were computed on each sample. The results show that the CI for τ based on a consistent estimate of the variance of txy has the best coverage and power among a number of alternatives. Kendall's txy is unaffected by non-normality induced by monotonic transformations and, with its consistent variance estimated from the sample, performs well under a wide range of conditions.