Two-stage test of independence using Kendall's statistic

A two-stage analog of Kendall's distribution-free test for independence is presented. It is shown that the null-limiting joint distribution of the two-stage test statistics is bivariate normal. Critical values are given for alpha = .01, .05 and .10 for both one-sided and two-sided hypotheses. A Monte Carlo study indicates the usefulness of the limiting distribution for small sample sizes. A second Monte Carlo study shows that the power of the two-stage test is similar to that of the usual single-sample test with an average sample number which is smaller than the sample size of the one-stage test.