Abstract
Summary
In two-stage sampling when sampling is done with replacement at each stage, a better estimate of the population mean can be obtained by considering the distinct units only at each stage. The mean of the distinct uniss is chosen as the desired estimate and an exact expression for the variance is obtained. A sufficient condition for the variance of the estimate based on distinct units to be smaller than the variance of the usual estimate of a two-stage sample based on all units is given.
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