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Maximizing and Minimizing Overlap When Selecting a Large Number of Units per Stratum Simultaneously for Two Designs

Lawrence R. Ernst


A number of procedures have been developed, beginning with the work of Keyfitz, for maximizing or minimizing the overlap of sampling units for two stratified designs. Most of these procedures are not applicable at all, or are not feasible to implement, unless the number of units per stratum is very small. The previous procedures that the author is aware of for increasing or decreasing overlap when a large number of units per stratum are selected either do not generally yield an optimal overlap or do not guarantee fixed sample sizes. Furthermore, these overlap procedures have typically been developed for use when the two designs must be selected sequentially, as is the case when the second design is a redesign of the first design. In the current article a very different, large sample per stratum procedure is presented for maximizing or minimizing overlap when the units can be selected for the two designs simultaneously, as may be the case for two different surveys. The procedure guarantees fixed sample sizes and also an optimal overlap if the two designs have identical stratifications, but can still be used, with loss of optimality, if the stratifications differ. An application of this procedure to the joint selection of samples for two U.S. Bureau of Labor Statistics compensation surveys is discussed.