As we saw in Interpolation, the sampling strategy that you use to collect data may have an impact on your ability to estimate the value of an attribute of an unknown location, particularly if the sample you use for the interpolation does not include locations of high variability of that attribute. Although exhaustive sampling (taking a sample at every possible location; also known as a census) ensures that you have sample points in locations with rapid change, it can be a huge waste of resources if your study area contains areas with very little change, particularly if you must actually go into the field to collect the data of interest. For this reason, we will focus on discussing strategies for non-exhaustive sampling.
We can classify sampling strategies as being either systematic or random. A systematic sample begins at some location and then places a data collection point at additional locations that are some defined distance from the starting point (e.g., every one hundred meters), resulting in a regular grid of sample locations. It is also possible to systematically define lines (transects) or areas (quadrats) for this (or any!) type of sampling strategy. Although this type of sample is one of the easiest to operationalize, and ensures an even distribution of sample points across the area of interest, there are two main disadvantages to using this method. The first is that if there is some sort of marked periodicity in the attribute you are working with (e.g., regularly spaced trees that were planted in rows), and this periodicity does not coincide with the sampling interval, it is possible that an interpolation from this sample would miss the pattern entirely and contain a substantial amount of error. The second disadvantage is that it can be very inefficient, by collecting a large number of samples in areas with little variation in the attribute in which you are interested. Given the often high cost (in terms of both time and money) of collecting data in the field, it is important to try to maximize the value of each sample point for which you are collecting data.
One way of avoiding any bias that may be introduced into the sample through systematic sampling is to use a random sampling strategy. In the simplest version of random sampling (often known as simple random sampling), a pre-determined number of points is selected from within a particular study area. These random locations are chosen by assigning numbers to all possible points within the area of interest, and then choosing random numbers using a random number generator to determine which points are used in the sample. Although this strategy generally will avoid bias, this is largely dependent upon the number of samples and the amount of variability in the study area. For example, if there is a small number of samples, bad luck may concentrate those samples in an area of low variability, leaving few points to provide information about areas of high variability. This strategy may also result in long travel times between sample locations and may not provide any information at all about small, but important features of the data.
It is possible to increase the efficiency of a sampling strategy by first stratifying the study area based on some characteristic that is relevant to the attribute you are trying to collect data about and then performing either systematic or random sampling within the different strata. One example of stratifying a study area might be when you are trying to understand the patterns of vegetation that occur in a given area. In this case, you might choose to stratify the study area based on elevation or aspect zones to make sure that you collect samples from all aspects and all elevations. Stratification can also help eliminate situations where small, yet important areas do not make it into the sample (i.e., these small areas are specifically included in the sample). Finally, if you stratify the study area based on an estimate of the amount of variability in your attribute of interest, you can also effectively create what is known as an adaptive sampling strategy - one that uses fewer samples for areas of less variability, and more samples for areas of more variability.
If you are interested in investigating this subject further, I recommend the following:
Stein, A. and C. Ettema. 2003. "An overview of spatial sampling procedures and experimental design of spatial studies for ecosystem comparisons." Agriculture, Ecosystems and Environment. 94(1): 31-47.
Duzgun, H.S.B. and N. Usul. 2002. "Sampling and determination of optimum sample size in GIS." Proceedings of the Esri User Conference.