Treatment of nondetects in multivariate analysis of groundwater geochemistry data

Principal components analysis (PCA) is used to evaluate similarities in the trace element chemistry of groundwaters. Many of the trace elements, however, occur at concentrations below the detection limits (DL), which presents problems for statistical analyses. Since the optimal methods for dealing with the ‘<DL’ values require the assumption of normality or lognormality, which is not the case for these data, simple substitution methods may be preferred. s study, a new approach was developed to determine the best substitution methods when dealing with the ‘DL’ values for a given data set. Monte Carlo simulation experiments, using a mixture multivariate model, were performed to test the effects of substitution of the ‘<DL’ values with 0, DL, and DL/2 on the results of PCA. In general, the results showed that substitution with DL/2 gave superior results compared to substitution with DL or 0. Deterioration of the performance of all substitution methods was observed when the number of ‘<DL’ values exceeded approximately 25%. <DL’ values are present within a data set, use of uncensored data (if available) may be preferred. Use of uncensored data requires statistical methodology to take into account varying uncertainties in the measurements. A new approach for the selection of variables for multivariate analysis of the trace element chemistry data was therefore developed. Selection of variables was based on the reproducibility between measurements made on duplicate samples.