A cumulative sum type of method for environmental monitoring

Abstract

We describe a graphical approach for detecting changes in the distribution of the variable over a number of monitoring sites between two or more sample times, with associated randomization tests. This method was derived from the cumulative sum (CUSUM) method that was developed initially for industrial process control, but our use differs in some fundamental ways. In particular, the standard CUSUM procedure is used to detect changes with time in the mean of a variable at one location, whereas our concern is with detecting changes with time in the distribution of a variable measured at a number of different locations. We compare our randomization test for any changes in distribution with the Mann–Kendall test and analysis of covariance in terms of the power for detecting a systematic time trend affecting all sites, with and without serial correlation in time. We also compare these different tests in the situation where trend occurs, but it is not the same at all sites, again with and without serial correlation in time. All tests were adversely affected by high serial correlation, so we repeated the comparisons with the CUSUM and analysis of covariance tests modified to take this into account. We conclude that although our randomization test sometimes has less power than the Mann–Kendall test and analysis of covariance for detecting trends, it does have reasonable power and also has the ability to detect other types of change with time. The modified randomization test is very robust to serial correlation. Copyright © 2000 John Wiley & Sons, Ltd.