# 2.6.1.2 Discrete sampling plans

__ Relatively Low Density__. Often only a few discrete samples are collected, and the results are used to make decisions about relatively large volumes of soil. In these situations, the number of samples collected may be determined by negotiation, budget, professional judgment, convention, or happenstance. The number of samples is often not based on statistical or other scientific rationale, and the location of the samples is often judgmental. Judgmental sampling plans can be used effectively with low numbers of discrete samples if the basis for determining the sample location and the volume of soil it applies to is appropriate. For instance, judgmental sampling plans may be useful when obvious source areas of high concentrations are present.

While low-density discrete sampling plans are tempting in terms of familiarity, relative low cost of collection and analysis, ease of implementation, and simplicity, the performance of these approaches generally is not adequately tested in terms of precision, accuracy, and decision error. However, there is a large body of work in classical statistics, Gy sampling theory, industry experience, and empirical evidence (e.g., results from duplicate samples) which suggests that (a) soil is highly heterogeneous even on extremely small scales and (b) smalls numbers of discrete samples are not likely to provide accurate or precise estimates of mean concentrations. Low-density discrete sampling plans therefore cannot be relied on to consistently produce high-quality decisions.

This is not to say that a low-density discrete sampling approach is insufficient for all cases. If, for example, the true mean in a DU is orders of magnitude above or below the action level for a contaminant of interest, it is possible that a correct decision could be made from very few (or even one) discrete samples. The key factors are the degree of heterogeneity present at the various scales, the action level, and the magnitude of the true mean. Since, as is often the case, knowledge about heterogeneity or the magnitude of the true mean is seldom available (which is why sampling is being conducted), relying on data from low-density discrete sampling plans is more likely to result in decision errors.

__ Relatively High Density__. The second type of discrete sampling plan can be called relatively high density discrete sampling plans. In this context the number of discrete samples approaches the number of increments typically collected with ISM (i.e., 30–50). The number of samples may or may not have been statistically derived based on (among other things) an estimate of the heterogeneity of the soil or the anticipated magnitude of the true mean concentration. There is a large body of guidance and reference material that describes how various discrete sampling plans of this sort can be effectively used to investigate soil contamination and make appropriate environmental decisions. However, cost limitations frequently limit the number of discrete samples employed for environmental investigation, and as discussed below, even relatively high-density discrete sampling plans may produce certain characteristics in the data set which are not ideal. The decision quality of relatively high-density discrete sampling plans, especially those derived through statistical methodology, can compare favorably with ISM sampling plans. However, the analytical costs associated with such plans will likely be considerably greater than those of a comparable ISM approach.