A complex sample design may differ from the simple procedure in one or several of three different ways: unequal probabilities, stratification, or multi-stage sampling.

Unequal probabilities may be used to over- or under-represent a specific sub-population in the sample (for example, to have a proportion of youth or of unemployed different from the corresponding proportion in the population). An indirect way of sampling can also over-represent certain individuals: for example, a simple random sample of pupils is selected in the schools of a city where their brothers and sisters will also be interviewed. In that case, a four-child family has a probability for being selected that is four times greater than that of a single-child-family. In all cases, correct estimates imply that the answers be weighted by the inverse of the probabilities the different observation units had to be in the sample.

Some multi-stage sampling uses probability-proportional-to-size selection. In this method, in order to have an equal final probability for all individuals, the same number of individuals is selected in every primary unit, so that the probability of selecting an element varies inversely with the size of the primary unit. The final probability is then the product of the probabilities at the two stages, and hence is the same throughout the sample.

Stratification selects independent samples for different sub-populations. This often allows a reduction of the sampling error. Multi-stage sampling considers two or more levels of units imbedded one in the other, such as geographic areas (primary units), factories (secondary units), employees (tertiary units). At each stage, a sample of the corresponding units is selected. A multi-stage procedure may, at any of its different stages, be combined with stratification or/and with unequal probabilities.