Note on a Test of Monotone Association Insensitive to Outliers

Abstract

A measure of monotone association for a bivariate sample is the difference between the largest number of points that lie on a non-decreasing path through the sample and the largest number of points that lie on a nonincreasing path through the sample. If the sample is from two independent continuous random variables, exact distributions of this quantity are computed for sample sizes up to 9, and some empirical results are given for large sample sizes. A test based on this measure is shown to be more powerful in the presence of outliers than the rank correlation test. The statistic is easy to compute for moderate sample sizes, and the critical values are seen to change slowly with increasing sample size.