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The SURVEYSELECT Procedure |

In equal probability sampling, each unit in the sampling frame,
or in a stratum, has the same probability of being selected for
the sample.
PROC SURVEYSELECT provides the following methods that select
units with equal probability: simple random sampling, unrestricted
random sampling, systematic random sampling, and sequential random
sampling.
In simple random sampling, units are selected *without
replacement*, which means that a unit cannot be selected more than once.
Both systematic and sequential equal probability sampling are also
without replacement.
In unrestricted random sampling, units are selected *with replacement*,
which means that a unit can be selected more than once. In with-replacement
sampling, the *number of hits* refers to the number of times a unit
is selected.

In probability proportional to size (PPS) sampling, a unit's selection probability is proportional to its size measure. PROC SURVEYSELECT provides the following methods that select units with probability proportional to size (PPS): PPS sampling without replacement, PPS sampling with replacement, PPS systematic sampling, PPS sequential sampling, Brewer's method, Murthy's method, and Sampford's method. PPS sampling is often used in cluster sampling, where you select clusters (or groups of sampling units) of varying size in the first stage of selection. For example, clusters may be schools, hospitals, or geographical areas, and the final sampling units may be students, patients, or citizens. Cluster sampling can provide efficiencies in frame construction and other survey operations. Refer to Kalton (1983), Kish (1965), and the other references cited in the following sections for more information.

The following sections give detailed descriptions of the
sample selection methods available in PROC SURVEYSELECT.
In these sections, *n*_{h} denotes the sample size (the number of units
in the sample) for stratum *h*, and *N*_{h} denotes the population
size (number of units in the population) for stratum *h*, for
*h* = 1, 2, ... , *H*. When the sample design is not stratified,
*n* denotes the sample size, and *N* denotes the population size.
For PPS sampling, *M*_{hi} represents the size measure for unit *i*
in stratum *h*, *M*_{h ·} is the total of all size measures for
the population of stratum *h*, and *Z*_{hi} = *M*_{hi} / *M*_{h} is
the relative size of unit *i* in stratum *h*.

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