Survey Summary Statistics using SAS

When conducting large-scale trials on samples of the population, it can be necessary to use a more complex sampling design than a simple random sample.

All of these designs need to be taken into account when calculating statistics, and when producing models. Only summary statistics are discussed in this document, and variances are calculated using the default Taylor series linearisation methods. For a more detailed introduction to survey statistics in SAS, see (Lohr 2022) or (SAS/STAT® 15.1 User’s Guide 2018).

For survey summary statistics in SAS, we can use the SURVEYMEANS and SURVEYFREQ procedures.

Simple Survey Designs

We will use the API dataset (“API Data Files” 2006), which contains a number of datasets based on different samples from a dataset of academic performance. Initially we will just cover the methodology with a simple random sample and a finite population correction to demonstrate functionality.

cds stype name sname snum dname dnum cname cnum flag pcttest api00 api99 target growth sch.wide comp.imp both awards meals ell yr.rnd mobility acs.k3 acs.46 acs.core pct.resp not.hsg hsg some.col col.grad grad.sch avg.ed full emer enroll api.stu pw fpc
15739081534155 H McFarland High McFarland High 1039 McFarland Unified 432 Kern 14 NA 98 462 448 18 14 No Yes No No 44 31 NA 6 NA NA 24 82 44 34 12 7 3 1.91 71 35 477 429 30.97 6194
19642126066716 E Stowers (Cecil Stowers (Cecil B.) Elementary 1124 ABC Unified 1 Los Angeles 18 NA 100 878 831 NA 47 Yes Yes Yes Yes 8 25 NA 15 19 30 NA 97 4 10 23 43 21 3.66 90 10 478 420 30.97 6194
30664493030640 H Brea-Olinda Hig Brea-Olinda High 2868 Brea-Olinda Unified 79 Orange 29 NA 98 734 742 3 -8 No No No No 10 10 NA 7 NA NA 28 95 5 9 21 41 24 3.71 83 18 1410 1287 30.97 6194
19644516012744 E Alameda Element Alameda Elementary 1273 Downey Unified 187 Los Angeles 18 NA 99 772 657 7 115 Yes Yes Yes Yes 70 25 NA 23 23 NA NA 100 37 40 14 8 1 1.96 85 18 342 291 30.97 6194
40688096043293 E Sunnyside Eleme Sunnyside Elementary 4926 San Luis Coastal Unified 640 San Luis Obispo 39 NA 99 739 719 4 20 Yes Yes Yes Yes 43 12 NA 12 20 29 NA 91 8 21 27 34 10 3.17 100 0 217 189 30.97 6194
19734456014278 E Los Molinos Ele Los Molinos Elementary 2463 Hacienda la Puente Unif 284 Los Angeles 18 NA 93 835 822 NA 13 Yes Yes Yes No 16 19 NA 13 19 29 NA 71 1 8 20 38 34 3.96 75 20 258 211 30.97 6194

Mean

If we want to calculate a mean of a variable in a dataset which has been obtained from a simple random sample such as apisrs, in SAS we can do the following (nb. here total=6194 is obtained from the constant fpc column, and provides the finite population correction):

proc surveymeans data=apisrs total=6194 mean;
    var growth;
run;
                             The SURVEYMEANS Procedure

                                    Data Summary

                        Number of Observations           200


                                    Statistics

                                                Std Error
 Variable               N            Mean         of Mean       95% CL for Mean
 ---------------------------------------------------------------------------------
 growth               200       31.900000        2.090493    27.7776382 36.0223618
 ---------------------------------------------------------------------------------

Total

To calculate population totals, we can request the sum. However SAS requires the user to specify the weights, otherwise the totals will be incorrect. These weights in this case are equivalent to the total population size divided by the sample size:

data apisrs;
    set apisrs nobs=n;
    weight = fpc / n;
run;

proc surveymeans data=apisrs total=6194 sum;
    var growth;
    weight weight;
run;
       The SURVEYMEANS Procedure

              Data Summary

  Number of Observations           200
  Sum of Weights                  6194


               Statistics

                               Std Error
Variable             Sum          of Sum
----------------------------------------
growth            197589           12949
----------------------------------------

Ratios

To perform ratio analysis for means or proportions of analysis variables in SAS, we can use the following:

proc surveymeans data=apisrs total=6194;
    ratio api00 / api99;
run;
                             The SURVEYMEANS Procedure

                                    Data Summary

                        Number of Observations           200


                                    Statistics

                                                Std Error
 Variable               N            Mean         of Mean       95% CL for Mean
 ---------------------------------------------------------------------------------
 api00                200      656.585000        9.249722    638.344950 674.825050
 api99                200      624.685000        9.500304    605.950813 643.419187
 ---------------------------------------------------------------------------------


                                   Ratio Analysis

                                                          Std
Numerator Denominator            N           Ratio           Error        95% CL for Ratio
----------------------------------------------------------------------------------------------
api00     api99                200        1.051066        0.003604    1.04395882    1.05817265
----------------------------------------------------------------------------------------------

Proportions

To calculate a proportion in SAS, we use the PROC SURVEYFREQ, in the simplest case below:

proc surveyfreq data=apisrs total=6194;
table 'sch.wide'n / cl;
run;
                          The SURVEYFREQ Procedure

                                Data Summary

                    Number of Observations           200


                             Table of sch.wide

                                       Std Err of    95% Confidence Limits
 sch.wide     Frequency     Percent       Percent         for Percent
 -------------------------------------------------------------------------
 No                  37     18.5000        2.7078     13.1604      23.8396
 Yes                163     81.5000        2.7078     76.1604      86.8396

 Total              200    100.0000                                       

Quantiles

To calculate quantiles in SAS, we can use the quantile option to request specific quantiles, or can use keywords to request common quantiles (e.g. quartiles or the median). This will use Woodruff’s method for confidence intervals, and a custom quantile method (SAS/STAT® 15.1 User’s Guide 2018, 9834).

proc surveymeans data=apisrs total=6194 quantile=(0.025 0.5 0.975);
    var growth;
run;
                             The SURVEYMEANS Procedure

                                    Data Summary

                        Number of Observations           200




                                     Quantiles

                                                      Std
 Variable       Percentile       Estimate           Error    95% Confidence Limits
 ---------------------------------------------------------------------------------
 growth           2.5          -16.500000        1.755916    -19.962591 -13.037409
                   50 Median    26.500000        1.924351     22.705263  30.294737
                 97.5           99.000000       16.133827     67.184794 130.815206
 ---------------------------------------------------------------------------------

Summary Statistics on Complex Survey Designs

Much of the previous examples and notes still stand for more complex survey designs, here we will demonstrate using a dataset from NHANES (“National Health and Nutrition Examination Survey Data” 2010), which uses both stratification and clustering:

SDMVPSU SDMVSTRA WTMEC2YR HI_CHOL race agecat RIAGENDR
1 83 81528.77 0 2 (19,39] 1
1 84 14509.28 0 3 (0,19] 1
2 86 12041.64 0 3 (0,19] 1
2 75 21000.34 0 3 (59,Inf] 2
1 88 22633.58 0 1 (19,39] 1
2 85 74112.49 1 2 (39,59] 2

To produce means and standard quartiles for this sample, taking account of sample design, we can use the following:

proc surveymeans data=nhanes mean quartiles;
    cluster SDMVPSU;
    strata SDMVSTRA;
    weight WTMEC2YR;
    var HI_CHOL;
run;
                             The SURVEYMEANS Procedure

                                    Data Summary

                        Number of Strata                  15
                        Number of Clusters                31
                        Number of Observations          8591
                        Sum of Weights             276536446


                                     Statistics

                                                     Std Error
                      Variable            Mean         of Mean
                      ----------------------------------------
                      HI_CHOL         0.112143        0.005446
                      ----------------------------------------


                                     Quantiles

                                                      Std
 Variable       Percentile       Estimate           Error    95% Confidence Limits
 ---------------------------------------------------------------------------------
 HI_CHOL           25 Q1                0        0.024281    -0.0514730 0.05147298
                   50 Median            0        0.024281    -0.0514730 0.05147298
                   75 Q3                0        0.024281    -0.0514730 0.05147298
 ---------------------------------------------------------------------------------

To produce an analysis of separate subpopulations in SAS we can use the DOMAIN statement (note: do not use the BY statement as it will not give statistically valid analysis), here we also request the design effect:

proc surveymeans data=nhanes mean deff;
    cluster SDMVPSU;
    strata SDMVSTRA;
    weight WTMEC2YR;
    var HI_CHOL;
    domain race;
run;

               The SURVEYMEANS Procedure

                      Data Summary

          Number of Strata                  15
          Number of Clusters                31
          Number of Observations          8591
          Sum of Weights             276536446


                       Statistics

                               Std Error          Design
Variable            Mean         of Mean          Effect
--------------------------------------------------------
HI_CHOL         0.112143        0.005446        2.336725
--------------------------------------------------------

               Statistics for race Domains

                                       Std Error          Design
race    Variable            Mean         of Mean          Effect
------------------------------------------------------------------------
   1    HI_CHOL         0.101492        0.006246        1.082734
   2    HI_CHOL         0.121649        0.006604        1.407822
   3    HI_CHOL         0.078640        0.010385        2.091156
   4    HI_CHOL         0.099679        0.024666        3.098290
------------------------------------------------------------------------
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─ External software ──────────────────────────────────────────────────────────
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References

“API Data Files.” 2006. California Department of Education. https://web.archive.org/web/20060813165101/http://api.cde.ca.gov/datafiles.asp.
Lohr, Sharon L. 2022. Sampling: Design and Analysis. 3rd ed. CRC Press, Taylor & Francis Group.
“National Health and Nutrition Examination Survey Data.” 2010. Centers for Disease Control; Prevention (CDC). https://wwwn.cdc.gov/nchs/nhanes/search/datapage.aspx?Component=laboratory&CycleBeginYear=2009.
SAS/STAT® 15.1 User’s Guide. 2018. SAS Institute Inc.