RESUMO
The units at the early stages of multi-stage area samples are generally sampled with probabilities proportional to their estimated sizes (PPES). With such a design, an overall equal probability (EP) sample design would yield a constant number of final stage units from each final stage cluster if the measures of size used in the PPES selection at each sampling stage were directly proportional to the number of final stage units. However, there are often sizable relative differences between the measures of size used in the PPES selections and the number of final stage units. Two common approaches for dealing with these differences are: (1) to retain a self-weighting sample design, allowing the sample sizes to vary across the sampled primary sampling units (PSUs) and (2) to retain the fixed sample size in each PSU and to compensate for the unequal selection probabilities by weighting adjustments in the analyses. This article examines these alternative designs in the context of two-stage sampling in which PSUs are sampled with PPES at the first stage, and an equal probability sample of final stage units is selected from each sampled PSU at the second stage. Two-stage sample designs of this type are used for household surveys in many countries. The discussion is illustrated with data from the Population-based HIV Impact Assessment surveys that were conducted using this design in several African countries.