ABSTRACT
When clusters have different population sizes, it is often desirable to give large clusters a higher sample selection probability than small clusters. For example, a school with 2,000 students might be assigned a higher selection probability than a school with 200 students, and then 10 students might be randomly selected from each sampled school. This chapter describes how to select samples with unequal probabilities and how to use sampling weights to calculate unbiased estimators of population quantities. Applications to telephone surveys, forestry, public health, and accounting are presented. An optional section in the chapter presents the mathematical arguments for why unequal probability sampling works and derives properties of the Horvitz-Thompson estimator.
