A nonparametric test for the ordered alternative based on Kendall's correlation coefficient

Several methods have been developed for testing the ordered alternative. These include the Jonckheere-Terpstra (JT) test (Jonckheere, 1954; Terpstra, 1952), a modified JT test (MJT) (Tryon and Hettmansperger, 1987), and a test proposed by Terpstra and Magel (TM) (Terpstra and Magel, 2003), among others. This article proposes a new method for testing the ordered alternative. The proposed test is based on Kendall's tau statistic. The asymptotic distribution of the test statistic is given. A Monte Carlo simulation study is conducted comparing the estimated powers of the proposed test with existing tests under a variety of sample sizes and distributions.