Simultaneous Nonparametric Prediction Limits

Prediction limits are often attractive for carrying out multiple-comparisons-with-control hypothesis tests. We present algorithms for computing simultaneous confidence levels of partially sequential nonparametric prediction limit tests used in environmental monitoring. Algorithms are given for “pof-m” (m chances to get p observations “inbounds” at each of r locations to “pass”), “California” (either the first or all of the next m−1 observations inbounds), and “modified California” (either the first or two of the next three observations inbounds) resampling strategies. The prediction limit can be any order statistic of the control or background sample. This methodology is particularly useful when a high proportion of observations are “nondetects.” We demonstrate its use in evaluating groundwater chemistry measurements at facilities monitored under U.S. Environmental Protection Agency regulations. Regulatory and practical considerations and limitations in this application area are discussed.