In a probability sample, each subset of the population has a known probability of being selected as the sample. This allows the survey sampler to draw conclusions about the population even though most of it is not sampled. Simple random sampling, in which each possible sample of size n is equally likely to be selected from the population, is the foundation of all probability sampling methods. Each sampled observation has the same sampling weight—it represents the same number of units in the population. This chapter discusses the bias and variance of estimators from simple random samples and tells how to choose the sample size so that survey objectives will be met.

Probability concepts needed to understand probability sampling are presented in an Appendix to the book. Optional sections present the theory of randomization-based and model-based inference for survey samples.