TRAN-STAT Statistics for Environmental Studies. Statistical Distributions for Contaminant Studies, and the Estimation of Average Concentrations

摘要

The statistical analysis of environmental contaminant data invariably involves making assumptions about the statistical distribution of the underlying phenomenon. We have discussed some of the important properties of two of the most important of these distributions, the normal and lognormal distributions. Several methods available for estimating the mean and variance of lognormal variates have been presented and illustrated. Some of these are biased, in which case expressions for the bias are given. In particular, the sample geometric mean (GM) is shown to be biased for both the mean and median of a lognormal distribution. The bias of the GM depends on the skewness of the lognormal distribution and on the number of data used to compute the GM. It is shown that a facility that emits pollutants could be declared in violation of a standard solely because only a few data were used in computing the GM, not because the true (population) GM concentration actually exceeds the standard value. The difference between two GM's can also give a distorted estimate of the difference between the two population medians if the number of data used to compute one of the GM's is very small. Also, the estimation of a concentration ratio using the GM of ratios can be biased high if n is small and the variance of the logarithmically transformed ratio (sigma exp 2 /sub y) is large. In practice, if at least n = 30 data are used to compute the GM ratio, the bias should not be of practical significance. 55 references. (ERA citation 09:014964)