# 7.2.3 Decision Mechanism 3: Comparison of the 95% UCL on the Mean of Replicate Data from the DU to the Action Level

Project objectives may specify that the estimate of the mean concentration provided by ISM sampling must be health protective, meaning that there is low chance of underestimating the actual mean concentration within the DU. It is important to recognize that the likelihood of underestimating the mean from any sampling method (discrete, composite, or ISM) increases as the degree of heterogeneity increases. Traditionally, with discrete samples, the concern for underestimating the mean has been addressed by specifying an acceptable level of uncertainty (often 5%) and a method for calculating a conservative estimate of the mean (e.g., a 95% UCL). A similar approach can be used with ISM data as discussed below.

For those accustomed to working with 95% UCL values from discrete data sets, there are some important differences with 95% UCLs from ISM data. As discussed in Section 4, calculation of a 95% UCL for ISM data requires a minimum of three ISM samples. This is fewer than is required for discrete data sets to yield reliable 95% UCL values. Additional ISM replicates increase the performance of the mean estimate (i.e., provides a 95% UCL closer to the actual mean), and although this increases the cost, it may be worthwhile if the site is relatively heterogeneous and the result is anticipated to be close to the action level. A second difference involves what to do if the 95% UCL is higher than any of the individual values used in its calculation. With discrete data sets, the maximum concentration observed is often used as the EPC if it is less than the calculated 95% UCL. With ISM data, the calculated 95% UCL value should always be used as the EPC even if it is higher than any of the individual ISM results. This situation is not uncommon, particularly when the number of replicates is small. In fact, with three replicates, the UCL always exceeds the highest individual ISM result.

Two methods for calculating the 95% UCL from ISM data are available: Student’s-t and Chebyshev. As discussed in Section 4, the choice of method depends on the known or anticipated shape of the probability distribution of contaminant concentrations in the DU. Note that software programs for calculation of 95% UCL values for discrete sample data (e.g., ProUCL) contain algorithms optimized to perform well for discrete data only. They are generally unsuitable for calculation of 95% UCL values for ISM data. A calculator for deriving 95% UCL values for ISM data is provided in Section 4.

Comparison of the 95% UCL on the mean of replicate ISM results is most useful when the chance of underestimating the true mean must be minimized.

When replicate samples are taken over the entire DU, each is a true replicate and provides a separate estimate of the mean concentration. These estimates can be combined to derive a 95% UCL. Another approach is to divide the DU into SUs and take one ISM from each. The results from each ISM sample (i.e., each SU) can also be combined to calculate a 95% UCL for the DU. With the latter approach, the ISM samples are not true replicates of the mean throughout the DU in the sense that they provide information on different portions of the DU. Collectively, however, they can provide an unbiased estimate of the mean. The principal disadvantage to this approach is that the UCL often exceeds the true mean by a larger degree than if replicates had been collected across the entire DU. The principal advantage of subdividing the DU for this decision mechanism is that it provides some information on the spatial distribution of contamination. If the DU as a whole fails the comparison with the action level, this spatial information could be valuable if a decision is made to break the DU into smaller DUs for reevaluation. (Note: The single ISM results from each SU would not be adequate to make confident decisions regarding them. Systematic planning would be needed to establish the smaller DUs and resampling would be required.)

## Decision Mechanism 3 example

This is similar to the example for Decision Mechanism 2. The same three replicate samples are collected from the DU with reported concentrations of total PCBs of 0.12, 0.16, and 0.26 mg/kg. The 95% UCL of these results is 0.30 mg/kg with the Student’s-t method and 0.36 mg/kg with the Chebyshev method, both of which exceed the action level for residential land use of 0.22 mg/kg. Therefore, while the sample arithmetic mean is less than the action level (as we saw in the previous example), there is sufficient variability in the results that there is a relatively high likelihood that the true mean exceeds the action level. Uncertainty in the shape of the underlying distribution does not factor into this result, since both 95% UCL methods yield the same conclusion. Options in this situation include deciding that the DU fails or taking more samples to reduce uncertainty and lower the 95% UCL, perhaps to a value below the action level.