REPLACEMENT OF CENSORED OBSERVATIONS BY A CONSTANT - AN EVALUATION

In the analysis of water quality data, samples with concentrations below the analytical detection limit are sometimes replaced by a constant between 0 and the detection limit. The performance of this replacement method has previously been examined in Monte Carlo studies by several authors. In this paper, expressions for the expectation of the sample mean and variance, obtained under the replacement method, are given for normally and lognormally distributed data. These expressions provide a simple means of calculating the bias and mean square error of the estimators used in the replacement method and thus large numbers of samples do not need to be generated by computer to evaluate the method. Thus, in a particular situation, the bias to be expected can be calculated if limits on the ranges of the mean, variance and proportion censored are available. It is shown that without knowledge of these qualities, which is the usual situation when data are being analyzed, the size and direction of bias is unknown. More objective methods of estimation are the methods of maximum likelihood and log-probability regression which are either described or made available through references. Two examples are analyzed by the latter methods and the results compared with those of the replacement method.