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Maximizing and Minimizing Overlap of Ultimate Sampling Units

Lawrence R. Ernst


Several general procedures have been developed for maximizing the expected number of primary sampling units in common to the new and initial samples, without altering unconditional selection probabilities, when redesigning a survey with a stratified, multi-stage design. Previous procedures for the analogous problem for ultimate sampling units (USUs) have been limited to simple cases, such as Poisson sampling. A procedure was developed several years ago at the Bureau of Labor Statistics, and currently used in the sample selection for the Occupational Compensation Surveys Program (OCSP), for increasing overlap of USUs when both the initial and new samples are selected with equal probability within a stratum. In this paper we present a modification of that procedure, which further increases the overlap in certain situations. We then generalize this procedure to the unequal probability case. Finally, we demonstrate how this approach can also be used when it is desired to minimize, rather than maximize, the overlap of USUs. These procedures are all computationally quite simple.