ESTIMATING MEAN AND VARIANCE FOR ENVIRONMENTAL SAMPLES WITH BELOW DETECTION LIMIT OBSERVATIONS¹

Abstract

Left-censoring of data sets complicates subsequent statistical analyses. Generally, substitution or deletion methods provide poor estimates of the mean and variance of censored samples. These substitution and deletion methods include the use of values above the detection limit (DL) only, or substitution of 0, DLI2 or the DL for the below DL values during the calculation of mean and variance. A variety of statistical methods provides better estimators for different types of distributions and censoring. Maximum likelihood and order statistics methods compare favorably to the substitution or deletion methods. Selected statistical methods applicable to left-censoring of environmental data sets are reviewed with the purpose of demonstrating the use of these statistical methods for coping with Type I (and Type fl) left-censoring of normally and log-normally distributed environmental data sets. A PC program (TJNCENSOR) is presented that implements these statistical methods. Problems associated with data sets with multiple DLs are discussed relative to censoring methods for life and fatigue tests as recently applied to water quality data sets.

Evaluation of Background Mercury Concentrations in the SRS Groundwater System

“…These data, combined with the measurements above the nominal detection limit, were sorted and used to prepare a cumulative probability graph. The gee-statistical analysis was performed in Microsoft EXCEL as described in Newman et al (1989) -see method description for "order statistics." The results were checked using the PROBPLOT program (Stanley, 1987) distributed by the Association of Exploration Geochemists.…”

Nitrogen and phosphorus in cascade multi-system tropical reservoirs: water and sediment

“…Concentrations of total phosphorus and ammonium in water below the detection limit of the methods (9.0 µg dm -3 for total phosphorus and 18.0 µg dm -3 for ammonium) were changed to half of these values for use in the graphics and statistical analyses, as suggested by Newman et al (1989), Lewis et al (2007), andDDE (2012). We adopted this procedure in order to avoid unnecessary loss of information.…”

Chemistry of precipitation, streamwater, and lakewater from the Hubbard Brook Ecosystem Study: a record of sampling protocols and analytical procedures

“…However, the use of zeros "leftcensors" the database by removing values at the lowest range of the analysis; this results in lower means and increased standard deviations within each field (Newman et al 1989). For the HBES chemical dataset before 1990, a zero indicated that the value was below the minimum reportable concentration (MRC).…”