Rethinking Poisson-based statistics for ground water quality monitoring

Both the U.S. Environmental Protection Agency (EPA) and the American Society for Testing and Materials (ASTM) provide guidance for selecting statistical procedures for ground water detection monitoring at Resource Conservation and Recovery Act (RCRA) solid and hazardous waste facilities. The procedures recommended for dealing with large numbers of nondetects, as may often be found in data for volatile organic compounds (VOCs), include, but are not limited to, Poisson prediction limits (in both the EPA guidance and ASTM standard) and Poisson tolerance limits(EPA guidance only). However, many of the proposed applications of the Poisson model are inappropriate. The development and application of the Poisson-based methods are explored for two types of data, counts of analytical hits and actual concentration measurements. Each of these two applications is explored along two lines of reasoning, a first-principles argument and a simple empirical fit.The application of Poisson-based methods to counts of analytical hits, including simultaneous consideration of multiple VOCs, appears to have merit from both a first principles and an empirical standpoint. On the other hand, the Poisson distribution is not appropriate for modeling concentration data, primarily because the variance of the distribution does not scale appropriately with changing units of measurement. Tolerance and prediction limits based on the Poisson distribution are not scale invariant. By changing the units of observation in example problems drawn from EPA guidance, use of the Poisson-based tolerance and prediction limits can result in significant errors. In short, neither the Poisson distribution nor associated tolerance or prediction limits should be used with concentration data. EPA guidance does present, however, other, more appropriate, methods for dealing with concentration data in which the number of nondetects is large. These include nonparametric tolerance and prediction limits and a test of proportions based on the binomial distribution.