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The SURVEYSELECT Procedure

Stratified Sampling

In this section, stratification is added to the sample design for the customer satisfaction survey. The sampling frame, or list of all customers, is stratified by State and Type. This divides the sampling frame into nonoverlapping subgroups formed from the values of the State and Type variables. Samples are then selected independently within the strata.

PROC SURVEYSELECT requires that the input data set be sorted by the STRATA variables. The following PROC SORT statements sort the Customers data set by the stratification variables State and Type:

   proc sort data=Customers;
      by State Type;
   run;

The following PROC FREQ statements display the crosstabulation of the Customers data set by State and Type:

   title1 'Customer Satisfaction Survey';
   title2 'Strata of Customers';
   proc freq data=Customers;
      tables State*Type;
   run;

Figure 87.4 presents the table of State by Type for the 13,471 customers. There are four states and two levels of Type, forming a total of eight strata.

Figure 87.4 Stratification of Customers by State and Type

Customer Satisfaction Survey

Strata of Customers

The FREQ Procedure

Frequency Percent Row Pct Col Pct

Table of State by Type State Type New Old Total AL 1238 9.19 63.68 14.43 706 5.24 36.32 14.43 1944 14.43     FL 2170 16.11 61.30 25.29 1370 10.17 38.70 28.01 3540 26.28     GA 3488 25.89 64.26 40.65 1940 14.40 35.74 39.66 5428 40.29     SC 1684 12.50 65.81 19.63 875 6.50 34.19 17.89 2559 19.00     Total 8580 63.69 4891 36.31 13471 100.00

The following PROC SURVEYSELECT statements select a probability sample of customers from the Customers data set according to the stratified sample design:

   title1 'Customer Satisfaction Survey';
   title2 'Stratified Sampling';
   proc surveyselect data=Customers
         method=srs n=15
         seed=1953 out=SampleStrata;
      strata State Type;
   run;

The STRATA statement names the stratification variables State and Type. In the PROC SURVEYSELECT statement, the METHOD=SRS option specifies simple random sampling. The N=15 option specifies a sample size of 15 customers for each stratum. If you want to specify different sample sizes for different strata, you can use the N=SAS-data-set option to name a secondary data set that contains the stratum sample sizes. The SEED=1953 option specifies '1953' as the initial seed for random number generation.

Figure 87.5 displays the output from PROC SURVEYSELECT, which summarizes the sample selection. A total of 120 customers are selected.

The following PROC PRINT statements display the first 30 observations of the output data set SampleStrata:

   title1 'Customer Satisfaction Survey';
   title2 'Sample Selected by Stratified Design';
   title3 '(First 30 Observations)';
   proc print data=SampleStrata(obs=30);
   run;

Figure 87.6 displays the first 30 observations of the output data set SampleStrata, which contains the sample of 120 customers, 15 customers from each of the eight strata. The variable SelectionProb contains the selection probability for each customer in the sample. Because customers are selected with equal probability within strata in this design, the selection probability equals the stratum sample size (15) divided by the stratum population size. The selection probabilities differ from stratum to stratum because the stratum population sizes differ. The selection probability for each customer in the first stratum (State='AL' and Type='New') is 0.012116, and the selection probability for customers in the second stratum is 0.021246. The variable SamplingWeight contains the sampling weights, which are computed as inverse selection probabilities.

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