# 2.3.1 All Concentrations Are Means

At the most basic level, an analytical result represents the overall mean of all the thousands of individual particles in the 1, 10, or 30 g analytical subsample. As explained earlier, different particles carry different amounts of contaminants. By means of the analytical digestion or extraction process, there is a physical averaging of the various concentrations of contaminant particles within an analytical subsample into a well-mixed liquid extract, as depicted in Figure 2-7. The laboratory result provides an estimate of the mean concentration of those particles making up the analytical subsample. Note that, as shown in Hyperlink 8, the laboratory measures contaminant mass and then derives a concentration. Laboratory results are then extrapolated to represent larger and larger volumes of soil culminating with the volume of the DU.

Figure 2-7. Process of extrapolating analytical sample results to soil concentrations.

As illustrated in Figure 2-7, the first step of the extrapolation series assumes that the result of the analytical subsample (the mean of the particles in the subsample) is representative of the mean of all the particles in the original field subsample jar. If this assumption is correct, then the results of laboratory duplicates (i.e., two samples taken from the same jar) should agree. If they do not, and commonly they do not, it is an indication that microscale heterogeneity is at work, causing within-sample data variability at the level of the sample jar.

The second step of the extrapolation series assumes that the jarred sample concentration is representative of the mean concentration of the discrete field sample taken from the DU. A prepared field sample is depicted by the pan in Figure 2-7. Note that if the field sample is small, the jarred sample may be the same as the field sample. If the assumptions of both the first and second steps are correct, then colocated samples collected from approximately the same field location (i.e., two "identical" jarred samples) should agree. When they do not, also quite common, the culprit is short-scale heterogeneity.

Finally, following the pattern above but scaled up, the assumption is that the concentration measured in the analytical subsample provides a precise and unbiased estimate of the true mean concentration for some volume of soil surrounding the location where the sample was taken. This volume of soil is seldom overtly specified but is implied by the way that data are collected and used. ISM is intended to provide an unbiased estimate of the mean contaminant concentration within a carefully defined volume of soil.

In contrast, ISM targets a volume of soil (a.k.a., the DU) that is deliberately identified up front during systematic planning. Increments of soil are collected at a high density across the entire DU and combined together. In this way there can be more confidence in the assumption that the field sample represents the DU. Steps are then taken during sample processing and subsampling to ensure that the aliquot of soil analyzed by the lab represents the field sample and thus the DU. Hyperlink 9 provides an example of how an ISM approach can better represent a DU than discrete sampling.