Simple random sampling

General observations

Simple random sampling (SRS) is the basic theoretical sampling technique. The sampling elements are selected as an independent random sample from the population. Each element of the population has the same probability of being selected. And, likewise, each combination of n sampling elements has the same probability of being eventually selected.

Every possible combination of sampling units from the population has an equal and independent chance of being in the sample.

Simple random sampling is introduced and dealt with here and in sampling textbooks mainly because it is a very instructive way to learn about sampling; many of the underlying concepts can excellently be explained with simple random sampling. However, it is hardly applied in Forest inventory because there are various other sampling techniques which are more efficient, given the same sampling effort.

Random selection (SRS)

Simple random selection requires that the sampling elements are independently randomly selected. Randomization is a design component of sampling design. The estimators for simple random sampling are unbiased if selection had been done at random. This is why we call such an estimator design-unbiased, because unbiasedness comes from the sampling design. We do not need to make assumptions with respect to the population, as the estimator is unbiased regardless of the structure of the population of interest.

It should be noted, that lack of randomization cannot be compensated by increasing sample size! Randomization is one of the most important prerequisite in the so-called class of designed-based sampling (as opposed to model based sampling, where validity comes from the model assumed and randomization is not strictly necessary). However, the spatial structure of the population does affect the precision of our estimates. Random selection is an essential component of all design based sampling. In addition, it is the basis for all statistical inference and testing. SRS is easy to implement as long as there is an explicit sampling frame (a list or a map) or known sampling units. Mistakes are frequently made because the term random (equal chance) is confused with haphazard (without any pattern) or with arbitrary (do whatever you wish …). It should be noted that randomization follows very clear rules, equal selection probabilities being the core property. It is hardly possible to simulate a random selection on a map by closing the eyes and pointing to a point in the map. Because the guarantee is not given, that, when doing that very often, really all points are being sampled with equal frequencies. Random numbers as used for randomization are generated by software called “random number generator”; this is a whole science for itself. If randomization has been applied in a study, it is a good practice to also report how it was carried out.

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