The SURVEYSELECT Procedure 
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 i in
stratum h equals

P_{hi} = n_{h} [(M_{hi})/(M_{h ·})] = n_{h} Z_{hi}
Sampford's method first selects a unit from stratum h
with probability Z_{hi} .
Then subsequent units are selected with probability proportional
to

[(Z_{hi})/(1n_{h} Z_{hi})]
and with replacement.
If the same unit appears more than once in the sample of size n_{h},
then Sampford's algorithm rejects that sample and selects a new
sample. The sample is accepted if it contains n_{h} distinct units.
The joint selection probability for units i and j in stratum h
equals
where
where S(m) denotes all possible samples
of size m, for m = 1, 2, ... , N_{h} .
The sum L_{m}(ij) is defined similarly to L_{m} but
sums over all possible samples of size m that do not include
units i and j, and
Sampford's method requires that the relative size
Z_{hi} be less than 1/n_{h} for all units.
Refer to Cochran (1977, pp. 262 263)
and Sampford (1967).
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.