## 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.
The procedure 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.

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.
By default, 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
- 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 the denominator DF using
the DF= option in the MODEL 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 **L** matrix that
defines the contrast.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.