### Degrees of Freedom

PROC SURVEYREG  produces tests for the significance of model effects, regression parameters, estimable functions specified in the ESTIMATE statement, and contrasts specified in the CONTRAST statement. It computes all these tests taking into account the sample design. The degrees of freedom for these tests differ from the degrees of freedom for the ANOVA table, which does not consider the sample design.

#### Denominator Degrees of Freedom

The denominator df refers to the denominator degrees of freedom for F tests and to the degrees of freedom for t tests in the analysis.

For the Taylor series method, the denominator df equals the number of clusters minus the actual number of strata. If there are no clusters, the denominator df equals the number of observations minus the actual number of strata. The actual number of strata equals the following:

• one, if there is no STRATA statement

• the number of strata in the sample, if there is a STRATA statement but the procedure does not collapse any strata

• the number of strata in the sample after collapsing, if there is a STRATA statement and the procedure collapses strata that have only one sampling unit

Alternatively, you can specify your own denominator df by using the DF= option in the MODEL statement.

For the BRR method (including Fay’s method) without a REPWEIGHTS statement, the denominator df equals the number of strata.

For the jackknife method without a REPWEIGHTS statement, the denominator df is equal to the number of replicates minus the actual number of strata.

When there is a REPWEIGHTS statement, the denominator df equals the number of REPWEIGHTS variables, unless you specify an alternative in the DF= option in a REPWEIGHTS statement.

#### Numerator Degrees of Freedom

The numerator df refers to the numerator degrees of freedom for the Wald F statistic associated with an effect or with a contrast. The procedure computes the Wald F statistic for an effect as a Type III test; that is, the test has the following properties:

• The hypothesis for an effect does not involve parameters of other effects except for containing effects (which it must involve to be estimable).

• The hypotheses to be tested are invariant to the ordering of effects in the model.

See the section Testing Effects for more information. The numerator df for the Wald F statistic for a contrast is the rank of the matrix that defines the contrast.