PROC SURVEYSELECT: Optimal Allocation :: SAS/STAT(R) 9.22 User's Guide

The SURVEYSELECT Procedure

Optimal Allocation

When you specify the ALLOC=OPTIMAL option, PROC SURVEYSELECT allocates the total sample size among the strata in proportion to stratum sizes, stratum costs, and stratum variances. Optimal allocation minimizes the overall variance for a specified cost, or equivalently minimizes the overall cost for a specified variance. See Lohr (2009), Cochran (1977), and Kish (1965) for details. For optimal allocation, the proportion of the total sample size for stratum $\text{[math]}$ is computed as

$\text{[math]}$

where $\text{[math]}$ is the number of sampling units in stratum $\text{[math]}$ , $\text{[math]}$ is the standard deviation within stratum $\text{[math]}$ , $\text{[math]}$ is the unit cost within stratum $\text{[math]}$ , and $\text{[math]}$ is the total number of strata. The target sample size for stratum $\text{[math]}$ is $\text{[math]}$ , where $\text{[math]}$ is the total sample size. As for proportional allocation, the values of $\text{[math]}$ are converted to integer sample sizes $\text{[math]}$ by using a rounding algorithm that requires the sum of the stratum sample sizes to equal $\text{[math]}$ . The final sample sizes $\text{[math]}$ are also required to be at least 1, or at least $\text{[math]}$ if you specify a minimum sample size with the ALLOCMIN= option. For without-replacement selection methods, the final sample sizes must not exceed the stratum sizes.

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