NONPARAMETRIC TEST PERFORMANCE FOR TRENDS IN WATER QUALITY WITH SAMPLING DESIGN APPLICATIONS1

Abstract

ABSTRACT: In this paper four nonparametric tests for monotonic trend detection are compared with respect to their power and accuracy. The importance of comparing powers at equal empirical significance levels rather than nominal levels is stressed. Therefore, an appropriate graphical method is presented. The effect of the sampling frequency is also assessed using Monte Carlo simulations and a trajectory representation that visualizes the dynamics of the trade‐off between the type I and type II errors. These methods are applied to compare four nonparametrical tests (seasonal Mann. Kendall, modified seasonal Mann‐Kendall, covariance eigenvalue and covariance inversion) under several conditions. It is concluded with respect to the power that it is not worthwhile for the modified seasonal Mann‐Kendall test applied to the AR(1) process considered in this paper to increase the sampling frequency from monthly to biweekly for detecting a monotonic trend of 5 percent, 10 percent, or 15 percent of the process variance. Under these conditions the seasonal Mann‐Kendall test is highly liberal, while the covariance inversion and the covariance eigenvalue test are conservative. This research is situated in the development of an efficient sampling design for the Flemish water quality monitoring network.