Nonparametric Tests for Trend in Water Quality

TLDR

Nonparametric trend tests for water quality were developed to address violations of normality, linearity, independence, and to handle missing, censored, and seasonal data, yet their relative power has not been reported. This study examines intrablock and aligned rank procedures in detail and offers recommendations for handling missing values and multiple observations per season. The authors analyze intrablock and aligned rank methods, and extend them to multistation designs and trend–season or trend–site interaction models using Kendall’s tau. Aligned rank methods are asymptotically more powerful, while intrablock methods are more adaptable, and the authors provide guidance for datasets with missing values and multiple seasonal observations.

Abstract

Recently, several nonparametric tests for trends in water quality have been proposed. These tests have been developed because the assumptions of classical parametric methods (i.e., normality, linearity, independence) are usually not met by typical water quality data. Additional idiosyncrasies of the data, such as missing values, censored data, and seasonality, compound the analysis problem. The nonparametric methods are more flexible and can handle these problems more easily. However, information on relative power of the various nonparametric procedures has not been reported in the hydrologic literature. For this reason, two classes of procedures, intrablock methods (procedures that compute a statistic, such as Kendall's tau, for each block or season and then sum these to produce a single overall statistic), and aligned rank methods (procedures that remove the block effect from each datum, sum the data over blocks, and then create a statistic from these sums) are examined in detail. Results from the statistical literature show that aligned rank methods are asymptotically more powerful than intrablock methods. In contrast, intrablock methods are more adaptable. Procedures to analyze more general models, including multistation designs and models, which include a trend‐season or trend‐site interaction, are developed by using Kendall's tau and intrablock methods. Finally, some recommendations on the analysis of data sets with missing values and multiple values per season values are presented.