A statistical approach for performing water quality impairment assessments

A statistical approach for making Total Maximum Daily Load (TMDL) impairment decisions is developed as an alternative to the simple tally of the number of measurements that happen to exceed the standard. The method ensures that no more than a small (e.g., 10 percent) percentage of water quality samples will exceed a regulatory standard with a high level of confidence (e.g., 95 percent). The method is based on the 100(1-alpha) percent lower confidence limit on an upper percentile of the concentration distribution. Advantages of the method include: (1) it provides a direct test of the hypothesis that a prespecified percentage of the true concentration distribution exceeds a regulatory standard, (2) it is applicable to a wide variety of different statistical concentration distributions. (3) it directly incorporates the magnitude of the measured concentrations unlike traditional approaches, and (4) it has explicit statistical power characteristics (i.e., what is the probability of missing an environmental impact). Detailed study of the simple tally approach reveals that it achieves high statistical power at the expense of unacceptably high false positive rates (30 to 40 percent false positive results). By contrast, the statistical approach results in similar statistical power while achieving a nominal false positive rate of 5 percent.