On some common practices of systematic sampling

Systematic sampling is a widely used technique in survey sampling. It is easy to execute, whether the units are to be selected with equal probability or with probabilities proportional to auxiliary sizes. It can be very efficient if one manages to achieve favourable stratification effects through the listing of units. The main disadvantages are that there is no unbiased method for estimating the sampling variance, and that systematic sampling may be poor when the ordering of the population is based on inaccurate knowledge. In this paper we examine an aspect of the systematic sampling that previously has not received much attention. It is shown that in a number of common situations, where the systematic sampling has on average the same efficiency as the corresponding random sampling alternatives under an assumed model for the population, the sampling variance fluctuates much more with the systematic sampling. The use of systematic sampling is associated with a risk that in general increases with the sampling fraction. This can be highly damaging for large samples from small populations in the case of single-stage sampling, or large sub-samples from small sub-populations as in the case of multi-stage sampling.