# 4.3.3 Objectives of the Simulation Studies

The objective of the simulation studies was to address several issues of practical importance in obtaining and using ISM data. As noted above, simulation studies have the unique advantage of evaluating the performance of ISM in estimating the mean under a variety of conditions where the right answer (i.e., the true mean) is known. Thus, they are the best, and in fact the only, way that the accuracy of ISM estimates of the mean concentration can be assessed.

Some of the simulation studies were directed to the basic design of an ISM sampling event (the number of replicates), and the pattern in which the samples are taken within a DU. The accuracy of ISM estimates and 95% UCL coverage based on differing numbers of increments, replicates, and sampling patterns were evaluated with attention to bias and magnitude of error (i.e., RPD). Simulation studies evaluated different approaches for computing a 95% UCL using ISM data. Performance of sampling methods was evaluated in terms of coverage provided by a UCL95, as well as the extent of overestimation of the mean (RPD_{A}). Ideally, a calculation method yields a 95% UCL with adequate coverage without excessive overestimation of the mean.

Simulations conducted with hypothesized distributions (e.g., lognormal) did not attempt to distinguish between different sources of error (see Section 2.5) or real-site complexities associated with spatial patterns such as mixtures (i.e., multiple sources of contamination at a site) or hot spots (i.e., sources with elevated concentrations that occur in relatively small subareas across the DU). By sampling from a single lognormal distribution, the simulations do not explicitly address inherent heterogeneities (e.g., CH and both small- and large-scale DH). However, these simulations are particularly applicable for scenarios in which the contamination is expected to be homogeneous through the DU (meaning that the mean and variance are the same in all subareas) and simple random sampling is applied. These simulations provide a convenient framework to begin to evaluate the performance of different UCL calculation methods with different sampling designs (i.e., numbers of increments and replicates) under a range of skewness and variance in the distribution. The simulations with maps extend the evaluation by exploring the effect of sampling methods (e.g., systematic or simple random) on bias in parameter estimates as well as the effect of DU heterogeneity on the performance of the 95% UCL.