# 4.3.4.2 Effects of sampling pattern

Simple random sampling, systematic random sampling, and systematic grid sampling yield unbiased estimates of the mean. The systematic sampling patterns ensure relatively even spatial distribution of samples across the site and are generally easier to implement in the field.Just as with discrete sampling, a variety of sampling methods may be implemented with ISM sampling. One of the more common approaches in ISM is systematic random sampling (a.k.a., systematic grid sampling [Gilbert 1987]), where the DU is divided in a grid pattern, a random sampling location is identified within the first grid cell, and then samples (increments) are obtained from adjacent cells sequentially in a serpentine pattern using the same relative location within each cell (Figure 4-7). Another approach is random sampling within a grid (also called “stratified random sampling” [USEPA 1995b]), wherein samples are obtained sequentially from adjacent grid cells, but the location of the sample within each cell is random (Figure 4-8). A third approach is simple random sampling, where the samples are taken from random locations across the DU (without gridding) (Figure 4-9). Replicate ISM samples are collected with the same sampling method but not the same exact locations. Each sampling method has its strengths and weaknesses that should be considered when selecting the approach for a given site.

Figure 4-7. Systematic random sampling/systematic grid sampling with a random start (Serpentine).

Figure 4-9. Simple random sampling within the entire DU.

- If the site is relatively homogeneous, all three sampling patterns yield unbiased parameter estimates, but the magnitude of error in the mean may be higher with simple random sampling as compared with systematic random sampling. All three sampling patterns yield equivalent coverages.
- While all three sampling options are statistically defensible, collecting increments within the DU using simple random sampling is most likely to generate an unbiased estimate of the mean and variance according to statistical theory. From a practical standpoint, true random sampling is probably the most difficult to implement in the field and may leave large parts of the DU “uncovered,” meaning without any increment sample locations. It should be noted that “random” does not mean wherever the sampling team feels like taking a sample: a formal approach to determining the random sample locations must be used.
- Systematic random sampling can avoid the appearance that areas are not adequately represented in the ISM samples. This approach is relatively straightforward to implement in the field. Theoretically, it is inferior to simple random sampling for obtaining unbiased estimates of the mean, especially if the contamination is distributed systematically so that areas of high or low concentrations are oversampled with the systematic design. Random sampling within a grid is in a sense a compromise approach, with elements of both simple random and systematic sampling.