Computerized statistical and graphical procedures were developed for use in U.S. Geological Survey (USGS) investigations of trend in stream water-quality data. These procedures, identified as EStimate TREND (ESTREND), are described in this paper to assist USGS investigators involved in multiple-station studies of water-quality trends. Additional discussion focuses on certain statistical and operational decisions required in multiple-station analysis of trends. The statistical methods used in ESTREND overcome common statistical problems encountered by conventional statistical trend techniques in the analysis of water-quality data. The problems include data that are non-normal and seasonally varying and water-quality records with missing values, 'less-than' (censored) values, and outliers, all of which adversely affect the performance of conventional statistical techniques. Parametric and nonparametric statistical trend tests are used in ESTREND. A nonparametric method, the Seasonal Kendall test, is used for data that have few less-than values or data that have been censored at only one reporting limit. A parametric test for trend involving a maximum likelihood estimation method is used for data that have been censored at multiple reporting limits. The Seasonal Kendall test for uncensored data allows for the removal of flow variability in water-quality data which improves the performance of the statistical trend tests. Menu-driven procedures in ESTREND allow the user to easily retrieve water-quality data, analyze data for trend, and view tabular and graphical results of analyses.
