Multistage and Cluster (Sub)Sampling

This chapter focuses on multistage sampling designs. Unlike in stratified sampling, in multistage sampling not all clusters (or strata) are sampled; only a subset of n clusters is sampled. In the second stage (sub)samples are drawn from those clusters drawn in the first stage in order to estimate the corresponding cluster totals. This is called two-stage sampling. When the clusters are divided into subclusters and the subcluster totals are estimated first, one calls this three-stage sampling, and so on; see also Sections 3.4 and 3.9. Some of the results mentioned already in Chapter 3 are also given in this chapter where we bring together the various results on multistage sampling. This chapter also discusses the problem when clusters are not disjoint or when some elements of the population are observed more than once. The last section of this chapter deals with the postclustification estimator, which can be used when poststratification is inappropriate because some strata are missing in the sample.