Conditions Under Which the Kenward-Roger Approximate Test is an Exact F Test

Waseem  Alnosaier; David  Birkes

Authors

Waseem Alnosaier Statistics Department, Institute of Public Administration, Riyadh, Saudi Arabia
David Birkes Statistics Department, Oregon State University, Corvallis, Oregon, USA

Keywords:

Kenward Roger test, mixed linear model, exact F test, residual maximum likelihood estimator, fixed effects

Abstract

The Kenward-Roger (KR) test is an approximate F test, which is to say that it uses a test statistic that has approximately an F distribution under the null hypothesis. The test statistic is constructed so that in two special cases the test is an exact F test, with a test statistic that has exactly an F distribution under the null hypothesis. One of the special cases is testing for the significance of a fixed group effect in a one-factor ANOVA model. We show that this testing problem can be extended to a more general class of testing problems in which the KR test is an exact F test.

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