Most statistical theory is premised on an underlying infinite population. By contrast, survey sampling theory and practice are built on a foundation of sampling from a finite population. This basic difference has myriad ramifications, and it highlights why survey sampling is often regarded as a separate branch of statistical thinking. On a philosophical level, the theory brings statistical theory to a human, and thus necessarily finite, level.

Before describing the basic notion of finite population sampling, it is instructive to explore the analogies and differences with sampling from infinite populations. These analogies were first described in Jerzy Neyman's seminal articles in the 1930s and are discussed in basic sampling theory textbooks such as William Cochran's in the 1970s. In the general framework of finite population sampling, ...