Accounting for Multi - stage Sample Designs in Complex Sample Variance

Nationally representative samples of large populations often have complex design features for a variety of reasons (e.g., cost efficiency). For purposes of estimating sampling variances based on complex multi-stage sample designs involving stratification and cluster sampling, the sampling error codes provided by survey organizations in public use survey data files often assume “ultimate cluster selection” of individuals from primary sampling units (PSUs). “Ultimate clusters” are the ultimate aggregate samples of individual population elements that are selected from PSUs (Wolter, 2007, p. 33), possibly based on multiple stages of sample selection (e.g., counties as PSUs, area segments within counties, households within area segments, and individuals within households). The sample selection method that is often assumed for variance estimation in practice (possibly within strata) is a single-stage, with-replacement selection of ultimate clusters from all hypothetical ultimate clusters defined by a multi-stage design, where all units within the ultimate clusters are measured (i.e., there is no subsampling within the clusters, and the ultimate clusters are what are really being sampled in a single stage of selection).