Example 63.1: Replicated Sampling

The SURVEYSELECT Procedure

Example 63.1: Replicated Sampling

This example uses the Customers data set from the section "Getting Started". The data set Customers contains an Internet service provider's current subscribers, and the service provider wants to select a sample from this population for a customer satisfaction survey.

This example illustrates replicated sampling, which selects multiple samples from the survey population according to the same design. You can use replicated sampling to provide a simple method of variance estimation, or to evaluate variable nonsampling errors such as interviewer differences. Refer to Kish (1965), Kish (1987), and Kalton (1983) for information on replicated sampling.

This design includes 4 replicates, each with a sample size of 50 customers. The sampling frame is stratified by State and sorted by Type and Usage within strata. Customers are selected by sequential random sampling with equal probability within strata. The following PROC SURVEYSELECT statements select a probability sample of customers from the Customers data set using this design.

   title1 'Customer Satisfaction Survey';
   title2 'Replicated Sampling';
   proc surveyselect data=Customers method=seq
         rep=4 n=(8 12 20 10)
         seed=40070 out=SampleRep;
      strata State;
      control Type Usage;
   run;

The STRATA statement names the stratification variable State. The CONTROL statement names the control variables Type and Usage. In the PROC SURVEYSELECT statement, the METHOD=SEQ option requests sequential random sampling. The REP=4 option specifies 4 replicates of this sample. The N=(8 12 20 10) option specifies the stratum sample sizes for each replicate. The N= option lists the stratum sample sizes in the same order as the strata appear in the Customers data set, which has been sorted by State. The sample size of 8 customers corresponds to the first stratum, State = `AL'. The sample size 12 corresponds to the next stratum, State = `FL', and so on. The SEED=40070 option specifies '40070' as the initial seed for random number generation.

Figure 63.1.1 displays the output from PROC SURVEYSELECT, which summarizes the sample selection. A total of 200 customers is selected in 4 replicates. PROC SURVEYSELECT selects each replicate using sequential random sampling within strata determined by State. The sampling frame Customers is sorted by control variables Type and Usage within strata, according to hierarchic serpentine sorting. The output data set SampleRep contains the sample.

Output 63.1.1: Sample Selection Summary

Customer Satisfaction Survey

Replicated Sampling

The SURVEYSELECT Procedure

Selection Method	Sequential Random Sampling
	With Equal Probability
Strata Variable	State
Control Variables	Type
	Usage
Control Sorting	Serpentine

Input Data Set	CUSTOMERS
Random Number Seed	40070
Number of Strata	4
Number of Replicates	4
Total Sample Size	200
Output Data Set	SAMPLEREP

The following PROC PRINT statements display the selected customers for the first stratum, State = `AL', from the output data set SampleRep.

   title1 'Customer Satisfaction Survey';
   title2 'Sample Selected by Replicated Design';
   title3 '(First Stratum)';
   proc print data=SampleRep;
      where State = 'AL';
   run;

Figure 63.1.2 displays the 32 sample customers of the first stratum (State = `AL') from the output data set SampleRep, which includes the entire sample of 200 customers. The variable SelectionProb contains the selection probability, and SamplingWeight contains the sampling weight. Since customers are selected with equal probability within strata in this design, all customers in the same stratum have the same selection probability. These selection probabilities and sampling weights apply to a single replicate, and the variable Replicate contains the sample replicate number.

Output 63.1.2: Customer Sample (First Stratum)

Customer Satisfaction Survey

Sample Selected by Replicated Design

(First Stratum)

Obs	State	Replicate	CustomerID	Type	Usage	SelectionProb	SamplingWeight
1	AL	1	882-37-7496	New	572	.004115226	243
2	AL	1	581-32-5534	New	863	.004115226	243
3	AL	1	980-29-2898	Old	571	.004115226	243
4	AL	1	172-56-4743	Old	128	.004115226	243
5	AL	1	998-55-5227	Old	35	.004115226	243
6	AL	1	625-44-3396	New	60	.004115226	243
7	AL	1	627-48-2509	New	114	.004115226	243
8	AL	1	257-66-6558	New	172	.004115226	243
9	AL	2	622-83-1680	New	22	.004115226	243
10	AL	2	343-57-1186	New	53	.004115226	243
11	AL	2	976-05-3796	New	110	.004115226	243
12	AL	2	859-74-0652	New	303	.004115226	243
13	AL	2	476-48-1066	New	839	.004115226	243
14	AL	2	109-27-8914	Old	2102	.004115226	243
15	AL	2	743-25-0298	Old	376	.004115226	243
16	AL	2	722-08-2215	Old	105	.004115226	243
17	AL	3	668-57-7696	New	200	.004115226	243
18	AL	3	300-72-0129	New	471	.004115226	243
19	AL	3	073-60-0765	New	656	.004115226	243
20	AL	3	526-87-0258	Old	672	.004115226	243
21	AL	3	726-61-0387	Old	150	.004115226	243
22	AL	3	632-29-9020	Old	51	.004115226	243
23	AL	3	417-17-8378	New	56	.004115226	243
24	AL	3	091-26-2366	New	93	.004115226	243
25	AL	4	336-04-1288	New	419	.004115226	243
26	AL	4	827-04-7407	New	650	.004115226	243
27	AL	4	317-70-6496	Old	452	.004115226	243
28	AL	4	002-38-4582	Old	206	.004115226	243
29	AL	4	181-83-3990	Old	33	.004115226	243
30	AL	4	675-34-7393	New	47	.004115226	243
31	AL	4	228-07-6671	New	65	.004115226	243
32	AL	4	298-46-2434	New	161	.004115226	243

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