Theoretical comparison of the Satterthwaite and Kenward-Roger approximate tests for fixed effects in linear mixed models

Abstract

The Satterthwaite and Kenward-Roger tests are approximate F tests, where both tests approximate Wald-type statistics as F distributions under the null hypothesis, and the denominator degrees of freedom of the F distribution are estimated. For the Kenward-Roger test, a scale factor is also estimated. The estimated values for the two tests are typically different because each uses a different approach to compute them. We show that under certain conditions, both tests yield the same estimates of the denominator degrees of freedom, and the scale factor for the Kenward-Roger test equals one. We also present an additional condition where the two tests become identical.