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 SURVEYREG statement. (You cannot specify both of these options in the same PROC SURVEYREG 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. See Cochran (1977) and Kish (1965) for more information.
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 SURVEYREG converts that number to a proportion. The procedure treats the value 1 as 100%, and not the percentage form 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.