The SURVEYSELECT Procedure |
Proportional Allocation
When you specify the ALLOC=PROP option, PROC SURVEYSELECT allocates the total sample size among the strata in proportion to the stratum sizes, where the stratum size is the number of sampling units in the stratum. The allocation proportion of the total sample size for stratum
equals
where
is the number of sampling units in stratum
and
is the total number of sampling units for all strata. Based on this allocation proportion, the target sample size for stratum
is
where
is the total sample size that you specify in the SAMPSIZE= option.
The target sample size values,
, might not be integers, but the stratum sample sizes must be integers. PROC SURVEYSELECT uses a rounding algorithm to convert the
to integer values
and maintain the requested total sample size
. The rounding algorithm includes the restriction that all values of
must be at least 1, so that at least one unit will be selected from each stratum. If you specify a minimum stratum sample size with the ALLOCMIN= option, then all values of
must be at least
, where ALLOCMIN=
. For without-replacement selection methods, PROC SURVEYSELECT also requires that each stratum sample size must not exceed the total number of sampling units in the stratum,
. If a target stratum sample size exceeds the number of units in the stratum, PROC SURVEYSELECT allocates the maximum number of units,
, to the stratum, and then allocates the remaining total sample size proportionally among the remaining strata.
PROC SURVEYSELECT provides the target allocation proportions
in the output data set variable AllocProportion. The variable ActualProportion contains the actual proportions for the allocated sample sizes
. For stratum
, the actual proportion is computed as
where
is the allocated sample size for stratum
and
is the total sample size. The actual proportions
can differ from the target allocation proportions
due to rounding and the restrictions that
(or
) and
.
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