#### Abstract

The test of a variance component in random and mixed normal linear models can be done using the F statistic from the analysis of variance or the Wald statistic which is the ratio of the variance component estimate to its estimated standard error. These are the methods used in the GLM and MIXED procedures of SAS®. We show that these two tests can give different results on the same data. For the one-way random model, the one-sided Wald test on the among group variance component can never be significant at the 0.05 probability level when the number of levels of the random factor is six or less. This is in contrast to the F test which, under the null model, will achieve the nominal level, even when using Satterthwaite's approximation for the distribution of the test statistic. The Wald test is conservative for even relatively large numbers of levels of the among group factor. Increasing the number of observations per level increases, rather than decreases, the difference between the actual and nominal significance levels. The reason that the Wald test is so conservative is that it uses the estimated standard error, which is a function of the variance component estimate. These results help explain why the F test and the Wald test can be so different.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

McNew, Ron and Mauromoustakos, Andy
(1997).
"TESTING VARIANCE COMPONENTS USING THE GLM AND MIXED PROCEDURES OF SAS®,"
*Annual Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/1997/proceedings/20

TESTING VARIANCE COMPONENTS USING THE GLM AND MIXED PROCEDURES OF SAS®

The test of a variance component in random and mixed normal linear models can be done using the F statistic from the analysis of variance or the Wald statistic which is the ratio of the variance component estimate to its estimated standard error. These are the methods used in the GLM and MIXED procedures of SAS®. We show that these two tests can give different results on the same data. For the one-way random model, the one-sided Wald test on the among group variance component can never be significant at the 0.05 probability level when the number of levels of the random factor is six or less. This is in contrast to the F test which, under the null model, will achieve the nominal level, even when using Satterthwaite's approximation for the distribution of the test statistic. The Wald test is conservative for even relatively large numbers of levels of the among group factor. Increasing the number of observations per level increases, rather than decreases, the difference between the actual and nominal significance levels. The reason that the Wald test is so conservative is that it uses the estimated standard error, which is a function of the variance component estimate. These results help explain why the F test and the Wald test can be so different.