In a standard least squares fit, only as many parameters are estimable as there are model degrees of freedom. In conducting the tests in the Effect Tests report, each effect is considered to be the last effect entered into the model.
• If all the Model degrees of freedom are used by the other effects, an effect shows DF equal to 0. When DF equals 0, no sum of squares can be computed. Therefore, the effect cannot be tested.
• If not all Model degrees of freedom are used by the other effects, then that effect has nonzero DF. However, its DF might be less than its number of parameters (Nparm), indicating that only some of its associated parameters are testable.
An F test is conducted if the degrees of freedom for an effect are nonzero, assuming that there are degrees of freedom for error. Whenever DF is less than Nparm, the description LostDFs is displayed to the far right in the row corresponding to the effect (Figure 3.50). These effects have the opportunity to explain only model sums of squares that have not been attributed to the aliased effects that have absorbed their lost degrees of freedom. It follows that the sum of squares given in the Effect Tests report most likely under represents the “true” sum of squares associated with the effect. If the test is significant, its significance is meaningful. But lack of significance should be interpreted with caution.
For statistical details, see the section “Statistical Background” in the “Introduction to Statistical Modeling with SAS/STAT Software” chapter in SAS Institute Inc. (2024c).