Appendix: Mann-Kendall Trend Tests

Kendall Rank Correlation Let (X1, Y1), · · · , (Xn, Yn) be a bivariate random sample of size n. The Pearson correlation coefficient provides an optimal measure of the degree of association between the X’s and the Y ’s when the sample is drawn from a bivariate normal distribution. The Pearson correlation coefficient is reasonably robust for many other distributions as well. The Kendall correlation coefficient, denoted by τ , provides a more general non-parametric measure of monotonic association. It is said to be monotonic since making a monotonic transformation on either the X’s or the Y ’s does not change the numerical value of τ . Kendall’s rank correlation coefficient (Kendall, 1970, equation 1.5) may be written, τ = S D . (2)