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The Maximization and Minimization of Sample Overlap Problems: A Half Century of Results

Lawrence R. Ernst


Many procedures have been developed in the last half century, beginning with Keyfitz's (1951) pioneering work, to maximize or minimize the expected number of units retained in sample when a new sample is selected with selection probabilities that are different than those used to select the initial sample.. In this paper we discuss the properties of more than a dozen overlap procedures. For example, certain procedures are usable only for one sample unit per stratum designs, while other procedures can be used for designs for which there are a large number of sample units per stratum. Some procedures require identical stratifications for the designs being overlapped, while others do not. Some procedures do not work properly if used in two successive redesigns. Certain procedures use linear programming to produce a better overlap at the cost of additional computational complexity. Some recently developed overlap procedures, with mostly desirable properties, can be used only when the samples for the designs being overlapped are selected simultaneously.