Subsections:

To include a finite population correction (fpc) in Taylor series variance estimation, you can input either the sampling rate or the population total by using the RATE= or TOTAL= option in the PROC SURVEYMEANS statement. (You cannot specify both of these options in the same PROC SURVEYMEANS statement.) The RATE= and TOTAL= options apply only to Taylor series variance estimation. The procedure does not use a finite population correction for BRR or jackknife variance estimation.

If you do not specify the RATE= or TOTAL= option, the Taylor series variance estimation does not include a finite population correction. For fairly small sampling fractions, it is appropriate to ignore this correction. For more information, see Cochran (1977); Kish (1965).

If your design has multiple stages of selection and you are specifying the RATE= option, you should input the first-stage sampling rate, which is the ratio of the number of PSUs in the sample to the total number of PSUs in the study population. If you are specifying the TOTAL= option for a multistage design, you should input the total number of PSUs in the study population. See the section Primary Sampling Units (PSUs) for more details.

For a nonstratified sample design, or for a stratified sample design with the same sampling rate or the same population total
in all strata, you can use the RATE=value or TOTAL=value option. If your sample design is stratified with different sampling rates or population totals in different strata, use the
RATE=SAS-data-set or TOTAL=SAS-data-set option to name a SAS data set that contains the stratum sampling rates or totals. This data set is called a *secondary data set*, as opposed to the *primary data set* that you specify with the DATA= option.

The secondary data set must contain all the stratification variables listed in the STRATA statement and all the variables
in the BY statement. If there are formats associated with the STRATA variables and the BY variables, then the formats must
be consistent in the primary and the secondary data sets. If you specify the TOTAL=SAS-data-set option, the secondary data set must have a variable named `_TOTAL_`

that contains the stratum population totals. Or if you specify the RATE=SAS-data-set option, the secondary data set must have a variable named `_RATE_`

that contains the stratum sampling rates. If the secondary data set contains more than one observation for any one stratum,
then the procedure uses the first value of `_TOTAL_`

or `_RATE_`

for that stratum and ignores the rest.

The value in the RATE= option or the values of `_RATE_`

in the secondary data set must be nonnegative numbers. You can specify value as a number between 0 and 1. Or you can specify value in percentage form as a number between 1 and 100, and PROC SURVEYMEANS converts that number to a proportion. The procedure
treats the value 1 as 100% instead of 1%.

If you specify the TOTAL=value option, value must not be less than the sample size. If you provide stratum population totals in a secondary data set, these values must not be less than the corresponding stratum sample sizes.

When you have clusters, or primary sampling units (PSUs), in your sample design, the procedure estimates variance from the variation among PSUs when the Taylor series variance method is used. See the section Variance and Standard Error of the Mean and the section Variance and Standard Deviation of the Total for more information.

BRR or jackknife variance estimation methods draw multiple replicates (or subsamples) from the full sample by following a specific resampling scheme. These subsamples are constructed by deleting PSUs from the full sample.

If you use a REPWEIGHTS statement to provide replicate weights for BRR or jackknife variance estimation, you do not need to specify a CLUSTER statement. Otherwise, you should specify a CLUSTER statement whenever your design includes clustering at the first stage of sampling. If you do not specify a CLUSTER statement, then PROC SURVEYMEANS treats each observation as a PSU.

It is common practice to compute statistics for domains (subpopulations), in addition to computing statistics for the entire
study population. Analysis for domains that uses the entire sample is called *domain analysis* (also called subgroup analysis, subpopulation analysis, or subdomain analysis). The formation of these subpopulations of
interest might be unrelated to the sample design. Therefore, the sample sizes for the subpopulations might actually be random
variables.

Use a DOMAIN statement to incorporate this variability into the variance estimation. Note that using a BY statement provides completely separate analyses of the BY groups. It does not provide a statistically valid subpopulation or domain analysis, where the total number of units in the subpopulation is not known with certainty.

For more detailed information about domain analysis, see Kish (1965).