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The SURVEYSELECT Procedure

PPS Sampling with Replacement

If you specify the option METHOD=PPS_WR, PROC SURVEYSELECT selects units with probability proportional to size and with replacement. The procedure makes nh independent random selections from the stratum of Nh units, selecting with probability Zhi = Mhi/Mh · . Because units are selected with replacement, a unit can be selected for the sample more than once. The expected number of selections or hits for unit i in stratum h equals nh Zhi . If you request the JTPROBS option, PROC SURVEYSELECT computes the joint expected number of hits for all pairs of selected units in each stratum. The joint expected number of hits for units i and j in stratum h equals
Ph(ij) = [(nh (nh - 1))/2]   Zhi   Zhj

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