| Abstract: | ABSTRACT: The statistical analysis of data which have trace level measurements has traditionally been a two-step process in which data are first censored using criteria based on measurement precision, and then analyzed with statistical methods for censored data. The process might be more informative if data were left uncensored. In this paper, information loss attributable to censoring and measurement noise are assessed by comparing the sample mean and median of uncensored measurements with a log regression mean and median based on censored data. Measurements are derived from lognormal parent distributions which have random variability characteristic of trace level measurement. The relative performance of estimators used with error-free samples and with samples having measurement noise can be explained by differences between the probability distributions of parents and measurements. Measurement introduces bias and dispersion and transforms lognormal parent distributions toward greater symmetry. Estimates using uncensored data are less biased and more accurate than the log regression mean and median when censoring exceeds about 50 percent, and are not much worse at any fraction censored. For data with many (80 percent) results below the limit of detection, bias may be quite severe. |
