Regional Sampling Methods

By Heidi Christopher and Dottie Schmitt

Random Sampling
Stratified Sampling
Systematic Sampling

It is often impractical to study each unit in a population, therefore it is necessary to accurately estimate the parameters of the population. Random, stratified, and systematic sampling are three main types of sampling designs used to compute specific regional statistics, usually sample means. Each sampling method has different strengths and weaknesses allowing one to choose an optimum sampling design dependent on the site and the presence of trends or cycles.

Random Sampling

In its most basic form, random sampling allows each unit of the sampled population an equal probability of being selected. Typically a table of random numbers (i.e. x and y coordinates) is used to identify the sampling points. Equations are available to calculate the number of samples necessary to ensure that the magnitude of the difference between sample mean and population mean are within a pre specified margin of error. (Gilbert, Cangelosi )

Animation illustrating random sampling within a stabilized chemical spill.

Stratified Sampling

Stratified sampling is often used when the sampling population can be split into non-overlapping strata that individually are more homogeneous than the population as a whole. If there are no obvious "dividing lines", grid lines can be used to divide the population. Random samples are taken from each stratum and the results are combined to estimate a population mean. Stratified sampling is most successful when the variance within each stratum is less than the overall variance of the population.
See Gilbert and Cangelosi for appropriate equations.

The following animation illustrates stratified sampling based on concentration gradients in a stabilized chemical spill. Due to the greater variance in the high concentration areas, more samples are taken there. The estimated regional mean is based on a weighted average of the strata mean, otherwise the greater number of samples would bias the sample mean on the high side.

Stratified sampling animation

Three simple guidelines for stratified sampling are to take more samples if:

A stratum is larger
A stratum is more variable internally
Sampling is cheaper in the stratum

Systematic Sampling

Systematic sampling is commonly used to guarantee complete coverage of an area or time. It always has a random start with subsequent sample units located at a set interval. It is difficult to estimate the statistical precision or margin of error for the population mean because it is sensitive to underlying population characteristics (i.e. cycles). Systematic sampling yields a smaller variance than regular random sampling when linear trends are present, and is often recommended over random sampling for detecting long-term trends such as seasonal cycles.

Animation illustrating systematic sampling.

One dimensional systematic sampling involves choosing an interval (temporally or spatially). The interval (k) depends on the sample size and is determined by the equation i = N/n where N = population size and n = sample size. For example, one would first pick an interval (k) of every three days (temporally) or every fifty yards (spatially) along a stream. Then a random value between one and k would be chosen. This value would be the starting value that is used throughout the sampling.
If periodicities or cycles are present and the interval chosen is a near multiple of the period, the average can be very biased. The following image displays the worst and best cases when an underlying cycle is present.

Two dimensional sampling is also common. Different types include: aligned grid, central aligned grid, or unaligned grid square. An aligned grid picks a random x -, y - coordinate in the first grid and uses this same coordinate in all of the other grids. An example follows:

A central aligned grid uses the middle of each grid as the sampling point as seen below:

An unaligned grid picks a random point in the first grid. The remaining grids in column A will have random x - coordinates and the same y - coordinate as the first grid. The remaining grids in row 1 will pick random y - coordinates and have the same x - coordinate as the first grid. The remaining grids will have a corresponding x - coordinate along a row and a corresponding y - coordinate down a column. This design is superior to aligned grid and stratified random sampling. An example is shown below:

It should be noted that purely random locations in each grid is classified as stratified sampling.

When no trends or natural strata occur in the population, systematic and random sampling result in approximately the same variance. However, when linear trends are present, systematic sampling yields a smaller variance than random sampling and stratified sampling is even better yet. The following image shows how systematic and stratified sampling do with a linear trend. If the systematic sampling starts above the mean of the stratum, then all the other samples will fall above the strata means. On the other hand, stratified sampling would get a better overall mean measurement because it picks a random point in each strata. This allows for some low mean values and some high mean values for each stratum.
See Gilbert and Cangelosi for appropriate equations.