Using Single Sample Information to Evaluate Criteria for Waterbody Health Risk

Recommendations from the U.S. Environmental Protection Agency (EPA) published in 2012 for bacteria water-quality evaluation are based on criteria using a geometric mean (GM) and a statistical threshold value (STV). If the GM calculated from water samples taken at a monitoring site exceeds the recommended GM criterion or if 10% of the samples exceed the recommended STV, then the waterbody is in violation. The recommendations indicate a minimum of four samples be used for calculations. In this report, evaluation of water quality using a single sample is statistically compared to the EPA approach for waterbodies that are in compliance and for those that are not in compliance. When the waterbody is truly in compliance with the recommended GM, the probability of a false declaration (declaring the waterbody to be in violation) for the single sample approach is below 0.5 (50%) and decreases as the true GM of the waterbody decreases. When the waterbody is truly in violation, the false declaration (saying the waterbody is in compliance), as based on a single sample, decreases from 0.5 at the GM criterion to close to zero for waterbodies with GMs that are just below the STV. When multiple samples are available, the probability of declaring a waterbody to be in violation increases as a function of sample size regardless of whether or not the waterbody is truly in violation or not. Hence there is an increase in the true declaration of a violation (when the waterbody is truly in violation) as well as in the false declaration of a violation (when the waterbody is truly in compliance). Relative to the GM approach, the single sample approach will almost always have higher error rates. The EPA approach does not involve a statistical test and error rates for GMs on or near the boundary of the decision rule. For waterbodies near the criterion, false declarations do not decline sharply as a function of sample size. When the GM is equal to the numerical criterion, the probability of declaring the waterbody as a health risk when it is not is 0.5 regardless of the sample size.