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, DL/2 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 II) left‐censoring of normally and log‐normally distributed environmental data sets. A PC program (UNCENSOR) 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.