Brewer's PPS Method

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 2M_hi/M_{h ·} = 2 Z_hi .

Brewer's algorithm first selects a unit with probability

[(Z_hi (1-Z_hi))/(D_h (1-2Z_hi))]

where

$D_h = \sum_{i=1}^{N_h} \frac{Z_{hi} (1-Z_{hi})} {1-2Z_{hi}}$

Then a second unit is selected from the remaining units with probability

[(Z_hj)/(1-Z_hi)]

where unit i is the first unit selected. The joint selection probability for units i and j in stratum h equals

P_h(ij) = [(2 Z_hi Z_hj)/(D_h)] ( [(1 - Z_hi - Z_hj)/((1-2Z_hi) (1-2Z_hj))] )

Brewer's method requires that the relative size Z_hi 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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