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 Introduction to Survey Sampling and Analysis Procedures

## Survey Data Analysis

The SURVEYMEANS and SURVEYREG procedures perform statistical analysis for survey data. These analytical procedures take into account the design used to select the sample. The sample design can be a complex sample design with stratification, clustering, and unequal weighting.

You can use the SURVEYMEANS procedure to compute the following statistics:

• population total estimate and its standard deviation and corresponding t test
• population mean estimate and its standard error and corresponding t test
• proportion estimate for a categorical variable and corresponding t test
• confidence limits for the population total estimates, the population mean estimates, and the proportion estimates
• data summary information

PROC SURVEYREG fits linear models for survey data and computes regression coefficients and their variance-covariance matrix. The procedure also provides significance tests for the model effects and for any specified estimable linear functions of the model parameters.

PROC SURVEYMEANS presently does not perform domain analysis (subgroup analysis). However, note that you can produce a domain analysis with PROC SURVEYREG (see Example 62.7). This capability will be available in a future release of the SURVEYMEANS procedure.

#### Variance Estimation

The SURVEYMEANS and SURVEYREG procedures use the Taylor expansion method to estimate sampling errors of estimators based on complex sample designs. This method obtains a linear approximation for the estimator and then uses the variance estimate for this approximation to estimate the variance of the estimate itself (Woodruff 1971, Fuller 1975). When there are clusters, or primary sampling units (PSUs), in the sample design, the procedures estimate the variance from the variation among the PSUs. When the design is stratified, the procedures pool stratum variance estimates to compute the overall variance estimate.

For a multistage sample design, the variance estimation method depends only on the first stage of the sample design. Thus, the required input includes only first-stage cluster (PSU) and first-stage stratum identification. You do not need to input design information about any additional stages of sampling. This variance estimation method assumes that the first-stage sampling fraction is small or that the first-stage sample is drawn with replacement, as it often is in practice.

For more information on variance estimation for sample survey data, refer to Lee, Forthoffer, and Lorimor (1989), Cochran (1977), Kish (1965), Srndal, Swenson, and Wretman (1992), Wolter (1985), and Hansen, Hurwitz, and Madow (1953).

In addition to the traditional Taylor expansion method, other methods for variance estimation for survey data include balanced repeated replication and jackknife repeated replication. These methods usually give similar, satisfactory results (Wolter 1985, Srndal, Swenson, and Wretman 1992); the SURVEYMEANS and SURVEYREG procedures currently provide only the Taylor expansion method.

See Chapter 61, "The SURVEYMEANS Procedure," and Chapter 62, "The SURVEYREG Procedure," for complete details.

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