Uncertainty and Trend Analysis -- Radium in Groundwater and Drinking Water.

Soderberg, K., and R. J.-C. Hennet. 2007. Groundwater Monitoring and Remediation: 27, no. 4, 122-129.

Abstract

Radium activity measurements in water samples are encumbered by relatively large error bars, including for activity values near the regulatory drinking water maximum contaminant level of 5 pCi/L. The large error bars create uncertainty in the evaluation of temporal trends. This uncertainty is often the object of debate and disagreement in regulatory determinations, the design of remedial actions, and/or in litigation. The Mann-Kendall nonparametric test is perhaps the most commonly used test for trend evaluation in environmental sciences. The test is simple and easy to apply by nonstatisticians and is recommended in several regulations and guidance documents. As typically applied, the Mann-Kendall test does not consider the uncertainty related to error bars for individual data values. Ignoring this uncertainty can result in misleading conclusions on the presence or absence of trends. In this article, a procedure for trend analysis that accounts for error bars is described. For each data series analyzed, the procedure creates 1000 new data series by randomly assigning values that fall within the error bar around each data point. Trend analysis is then performed on the randomly created data series. The approach is applied to the evaluation of a radium data base containing analytical results from 137 locations (407 water samples) in Escambia County, Florida.

The evaluation of the radium data base using the Mann-Kendall test without accounting for the uncertainty reveals 10 significant trends at the 90% confidence level. Only two of these trends are supported by the data when the uncertainty from analytical error is accounted for.
 
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