This paper introduces an approach to expanding a stratified sample design, D1, with one primary sampling unit (PSU) selected per stratum to a larger design, D2. Define a workload (WL) to be the sample size in a given stratum in D1. This three-stage approach selects the number of WLs for each stratum, the PSUs to receive the additional WLs in each stratum, and the ultimate sampling units. Procedures requiring the consideration of several cases are given for selecting PSUs in the key second stage, satisfying the following conditions when a stratum in D2 is to have s=2 or 3 WLs: (i) the expected number of WLs in a PSU is s times the probability that it was selected to get the single WL in D1; and (ii) the actual number of WLs assigned is within one of the expected number. These conditions are a generalization of probability proportional to size, without replacement sampling. A decomposition of the variance into components for the three selection stages is derived. An application of this approach to a proposed, but since cancelled, expansion of the Current Population Survey is also presented.

Revised (1993-03-15)