|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
Phi = nh [(Mhi)/(Mh ·)] = nh Zhi
Sampford's method first selects a unit from stratum h
with probability Zhi .
Then subsequent units are selected with probability proportional
and with replacement.
If the same unit appears more than once in the sample of size nh,
then Sampford's algorithm rejects that sample and selects a new
sample. The sample is accepted if it contains nh distinct units.
The joint selection probability for units i and j in stratum h
where S(m) denotes all possible samples
of size m, for m = 1, 2, ... , Nh .
The sum Lm(ij) is defined similarly to Lm 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
Zhi be less than 1/nh 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.