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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, which is the 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 89.4 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 89.4 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 61.3 25.29
 1370 10.17 38.7 28.01
 3540 26.28
GA
 3488 25.89 64.26 40.65
 1940 14.4 35.74 39.66
 5428 40.29
SC
 1684 12.5 65.81 19.63
 875 6.5 34.19 17.89
 2559 19.00
Total
 8580 63.69
 4891 36.31
 13471 100

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

Figure 89.5 Sample Selection Summary
 Customer Satisfaction Survey Stratified Sampling

The SURVEYSELECT Procedure

Selection Method Simple Random Sampling State Type

Input Data Set CUSTOMERS 1953 15 8 120 SAMPLESTRATA

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 89.6 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.

Figure 89.6 Customer Sample (First 30 Observations)
 Customer Satisfaction Survey Sample Selected by Stratified Design (First 30 Observations)

Obs State Type CustomerID Usage SelectionProb SamplingWeight
1 AL New 002-26-1498 1189 0.012116 82.5333
2 AL New 070-86-8494 106 0.012116 82.5333
3 AL New 121-28-6895 76 0.012116 82.5333
4 AL New 131-79-7630 265 0.012116 82.5333
5 AL New 211-88-4991 108 0.012116 82.5333
6 AL New 222-81-3742 83 0.012116 82.5333
7 AL New 238-46-3776 278 0.012116 82.5333
8 AL New 370-01-0671 123 0.012116 82.5333
9 AL New 407-07-5479 1580 0.012116 82.5333
10 AL New 550-90-3188 177 0.012116 82.5333
11 AL New 582-40-9610 46 0.012116 82.5333
12 AL New 672-59-9114 66 0.012116 82.5333
13 AL New 848-60-3119 28 0.012116 82.5333
14 AL New 886-83-4909 170 0.012116 82.5333
15 AL New 993-31-7677 64 0.012116 82.5333
16 AL Old 124-60-0495 80 0.021246 47.0667
17 AL Old 128-54-9590 56 0.021246 47.0667
18 AL Old 204-05-4017 17 0.021246 47.0667
19 AL Old 210-68-8704 4363 0.021246 47.0667
20 AL Old 239-75-4343 430 0.021246 47.0667
21 AL Old 317-70-6496 452 0.021246 47.0667
22 AL Old 365-37-1340 21 0.021246 47.0667
23 AL Old 399-78-7900 108 0.021246 47.0667
24 AL Old 404-90-6273 824 0.021246 47.0667
25 AL Old 421-04-8548 1332 0.021246 47.0667
26 AL Old 604-48-0587 16 0.021246 47.0667
27 AL Old 774-04-0162 318 0.021246 47.0667
28 AL Old 849-66-4156 79 0.021246 47.0667
29 AL Old 937-69-9106 182 0.021246 47.0667
30 AL Old 985-09-8691 24 0.021246 47.0667

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