| Abstract: | ABSTRACT: A common problem arises in testing for trends in water quality when observations are reported as “less than detection limit.” If a single detection limit is used for the entire study, existing non-parametric statistical methods, modified for ties, are applicable. If, however, the detection limit varies during the course of the study, resulting in multiple detection limits, then the commonly used trend detection methods are not appropriate. A statistic similar to Kendall's tau, but based on expected ranks, is proposed. Monte Carlo simulations show that the normal approximation to the distribution of this statistic is quite good, even for small samples and a large proportion of censored observations. The statistic is also shown to have greater power than the ad-hoc method of treating all observations less than the target censored observation as tied. |
