# Hyperlink 15. Making Decisions Under Different Concentration Scenarios

Consider a theoretical spatial distribution where a heavily contaminated volume of soil (DU 1) is surrounded by two successively less-contaminated volumes (DU 2 and DU 3) as shown in Figure H15-1.

Figure H15-1. Implications of lognormal distribution at varying levels of contaminant concentrations in soil.

**DU 1—Heavy Contamination.** DU 1 in this figure represents heavy contamination, where the true mean exceeds the action level and where further action is warranted according to the risk assessment results. In this DU, the concentration of the contaminant at any given point is well above the action level. Therefore, even a small number of discrete samples are likely to indicate the correct decision (“mean > action level”). Note how far both the mode (the most frequently observed sample result) and the mean are from the action level in histogram 1 on the figure. Of course, a much larger number of discrete samples would be required for this DU if the decision required a mean estimate with a higher degree of precision than that needed by a simple “clean-dirty” decision.

**DU 2—Moderate Contamination. **The reliability of a decision using a small number of discrete samples changes drastically when the true mean concentration is closer to the action level, as shown in DUs 2 and 3 of the figure. In this situation, the precision with which the mean concentration is estimated, as well as the effects of the right-tail of the distribution, are more important. In histogram 2 of the figure, the mode is below the action level, but the mean is above the action level. Because the mean concentration is greater than the action level, a correct decision for this DU would result in remedial action. However, note that because the mode is lower than the action level, the majority of discrete samples will likely contain concentrations *below* the mean. Therefore a low-density discrete sampling approach in this DU would usually be expected to mislead the investigator into thinking that the DU is “clean” when it is not. The more samples collected, the more likely it is that one or more will exceed an action level (and even exceed the true mean). So, the more discrete samples collected, the closer the estimate of the mean is to the true mean.

**DU 3—Light Contamination. **DU 3 contains low concentrations. Note that in histogram 3 of the figure, both the mean and the mode fall below the action level. No action would be required in this DU from a risk-based perspective, as this DU would be considered “clean.” However, this does not mean that the concentration for every discrete soil sample potentially collected in DU 3 will be below the action level. It is quite possible that, due to the right-tailed lognormal distribution of histogram 3, some discrete samples collected in DU 3 will contain concentrations above the action level. If enough discrete samples are collected, such an outcome is even expected. In this situation, discrete data sets may be characterized by isolated, sample-size hot spots that do not represent meaningfully sized volumes of soil and do not pose a significant risk to human health or the environment.

As is apparent from the histograms in the figure, with enough samples, the pattern of contamination in DU 3 will be very different from that in DU 1, where most sample points will be above the action level, or DU 2, where a distinct clustering of elevated sample points is likely. However, because insufficient numbers of discrete samples are generally relied on, investigators are frequently unable to distinguish which situation is actually present. In the face of this uncertainty, they make the conservative assumption that the mean concentration in a DU will be represented by the maximum encountered concentration. As shown by this example, however, the maximum concentration from a small set of discrete samples can underestimate or overestimate the true mean, sometimes by a large magnitude.