A note on the variances of the tests of Kendall, Jonckheere, and Terpstra

Abstract

Recently, some papers have been appearing that have noticed some mistakes in the calculations in the statistical software in simple and classical tests (Wilcoxon-Mann-Whitney and Log-Rank). This article examines the variance formulas for the Kendall test, the Jonckheere test, and the Terpstra test. We show in this article that these variances (in spite of what is said in the literature and in the statistical software), in the presence of ties and r3 groups, are only equal approximately and are exactly equal for two groups and ties as we prove in the Appendix.