Evaluation of Statistical Treatments of Left-Censored Environmental Data Using Coincident Uncensored Data Sets. II. Group Comparisons

The main classes of statistical treatments that have been used to determine if two groups of censored environmental data arise from the same distribution are substitution methods, maximum likelihood (MLE) techniques, and nonparametric methods. These treatments along with using all instrument-generated data (IN), even those less than the detection limit, were evaluated by examining 550 data sets in which the true values of the censored data were known, and therefore "true" probabilities could be calculated and used as a yardstick for comparison. It was found that technique "quality" was strongly dependent on the degree of censoring present in the groups. For low degrees of censoring (<25% in each group), the Generalized Wilcoxon (GW) technique and substitution of root 2/2 times the detection limit gave overall the best results. For moderate degrees of censoring, MLE worked best, but only if the distribution could be estimated to be normal or log-normal prior to its application; otherwise, GW was a suitable alternative. For higher degrees of censoring (each group >40% censoring), no technique provided reliable estimates of the true probability. Group size did not appear to influence the quality of the result, and no technique appeared to become better or worse than other techniques relative to group size. Finally, IN appeared to do very well relative to the other techniques regardless of censoring or group size.