PROC SURVEYFREQ: Design Effect :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The SURVEYFREQ Procedure

Design Effect

If you specify the DEFF option in the TABLES statement, PROC SURVEYFREQ computes design effects for the overall proportion estimates in the frequency and crosstabulation tables. The design effect for an estimate is the ratio of the actual variance (estimated based on the sample design) to the variance of a simple random sample with the same number of observations. See Lohr (1999) and Kish (1965) for details.

For Taylor series variance estimation, PROC SURVEYFREQ computes the design effect for the proportion in table cell $\text{[math]}$ as

	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

where $\text{[math]}$ is the estimate of the proportion in table cell $\text{[math]}$ , $\text{[math]}$ is the variance of the estimate, $\text{[math]}$ is the overall sampling fraction, and $\text{[math]}$ is the number of observations in the sample.

For Taylor series variance estimation, PROC SURVEYFREQ determines the value of $\text{[math]}$ , the overall sampling fraction, based on the RATE= or TOTAL= option. If you do not specify either of these options, then PROC SURVEYFREQ assumes the value of $\text{[math]}$ is negligible and does not use a finite population correction in the analysis, as described in the section Population Totals and Sampling Rates. If you specify RATE=value, then PROC SURVEYFREQ uses this value as the overall sampling fraction $\text{[math]}$ . If you specify TOTAL=value, then PROC SURVEYFREQ computes $\text{[math]}$ as the ratio of the number of PSUs in the sample to the specified total.

If you specify stratum sampling rates with the RATE=SAS-data-set option, then PROC SURVEYFREQ computes stratum totals based on these stratum sampling rates and the number of sample PSUs in each stratum. The procedure sums the stratum totals to form the overall total, and computes $\text{[math]}$ as the ratio of the number of sample PSUs to the overall total. Alternatively, if you specify stratum totals with the TOTAL=SAS-data-set option, then PROC SURVEYFREQ sums these totals to compute the overall total. The overall sampling fraction $\text{[math]}$ is then computed as the ratio of the number of sample PSUs to the overall total.

For BRR and jackknife variance estimation, PROC SURVEYFREQ computes the design effect for the proportion in table cell $\text{[math]}$ as

	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

where $\text{[math]}$ is the estimate of the proportion in table cell $\text{[math]}$ , $\text{[math]}$ is the variance of the estimate, and $\text{[math]}$ is the number of observations in the sample. This computation does not include the overall sampling fraction.

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