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 The SURVEYSELECT Procedure

### Brewer's PPS Method

Brewer's method (METHOD=PPS_BREWER) selects two units from each stratum, with probability proportional to size and without replacement. The selection probability for unit i in stratum h equals 2Mhi/Mh · = 2 Zhi .

Brewer's algorithm first selects a unit with probability

[(Zhi   (1-Zhi))/(Dh   (1-2Zhi))]
where
Then a second unit is selected from the remaining units with probability
[(Zhj)/(1-Zhi)]
where unit i is the first unit selected. The joint selection probability for units i and j in stratum h equals
Ph(ij) = [(2   Zhi   Zhj)/(Dh)] ( [(1 - Zhi - Zhj)/((1-2Zhi) (1-2Zhj))] )

Brewer's method requires that the relative size Zhi be less than 0.5 for all units. Refer to Cochran (1977, pp. 261 -263) and Brewer (1963). Brewer's method yields the same selection probabilities and joint selection probabilities as Durbin's method. Refer to Cochran (1977) and Durbin (1967).

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