The SURVEYSELECT Procedure

Sequential Poisson sampling, which you request by specifying the METHOD=SEQ_POISSON option, is a fixed-sample-size modification of Poisson sampling. For information about Poisson sampling, see the section Poisson Sampling.

PROC SURVEYSELECT performs sequential Poisson sampling by using the method of Ohlsson (1998). A transformed random number is computed for each sampling unit as , where is the size measure of unit i in stratum h and is a uniform random number (from the procedure’s pseudorandom number stream). For more information about random number generation, see the SEED= option and the section Random Number Generation.

The transformed random numbers are ordered, and the stratum h sample consists of the sampling units that correspond to the smallest transformed random numbers.

Although this algorithm produces a sample of the fixed size that you specify, the sample selection is considered to be only approximately probability proportional to size (PPS); it is not strictly PPS. For more information, see Ohlsson (1998). The (approximate) selection probability for unit i in stratum h is computed as , where is the sample size for stratum h and is the relative size of unit i in stratum h. The relative size is computed as , which is the ratio of the size measure for unit i in stratum h () to the total of all size measures for stratum h ()

The relative size of each sampling unit cannot exceed because the selection probability ( times the relative size) cannot exceed 1. This requirement can be expressed as , or equivalently as . If your size measures do not meet this requirement, you can adjust the size measures by using the MAXSIZE= or MINSIZE= option. Or you can select the larger units with certainty by using the CERTSIZE= or CERTSIZE=P= option. Alternatively, you can use a selection method that does not have a relative size restriction, such as PPS with minimum replacement (METHOD=PPS_SEQ).