PROC SURVEYSELECT: Sampford’s PPS Method :: SAS/STAT(R) 9.22 User's Guide

The SURVEYSELECT Procedure

Sampford’s PPS Method

Sampford’s method (METHOD=PPS_SAMPFORD) is an extension of Brewer’s method that selects more than two units from each stratum, with probability proportional to size and without replacement. The selection probability for unit $\text{[math]}$ in stratum $\text{[math]}$ equals $\text{[math]}$ . (Because selection probabilities cannot exceed 1, the relative size for each unit, $\text{[math]}$ , must not exceed $\text{[math]}$ .)

Sampford’s method first selects a unit from stratum $\text{[math]}$ with probability $\text{[math]}$ . Then subsequent units are selected with probability proportional to

$\text{[math]}$

and with replacement. If the same unit appears more than once in the sample of size $\text{[math]}$ , then Sampford’s algorithm rejects that sample and selects a new sample. The sample is accepted if it contains $\text{[math]}$ distinct units.

If you specify the JTPROBS option, PROC SURVEYSELECT computes the joint selection probabilities for all pairs of selected units in each stratum. The joint selection probability for units $\text{[math]}$ and $\text{[math]}$ in stratum $\text{[math]}$ equals

$\text{[math]}$

where

$\text{[math]}$

and $\text{[math]}$ denotes all possible samples of size $\text{[math]}$ , for $\text{[math]}$ . The sum $\text{[math]}$ is defined similarly to $\text{[math]}$ but sums over all possible samples of size $\text{[math]}$ that do not include units $\text{[math]}$ and $\text{[math]}$ . See Cochran (1977, pp. 262–263) and Sampford (1967) for details.

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