On the size of the F-test for the one-way random model with heterogeneous error variances

Abstract

Traditional analysis of variance tests are based on the assumption of homogeneous error variances, which often fails in real experimental situations. Violation of this assumption affects not only the power of the standard F-test, but also its size. When a design is unbalanced, the effect of unequal error variances is even more complex. In this paper, we study the effect of heterogeneous error variances on the size of the F-test concerning the among-group variance component in an unbalanced random one-way model. We also provide a method for computing the true critical value of the F-test for a given level of significance.

Keywords:

• Among-group variance component
• Davies' algorithm
• Level of significance
• Measure of imbalance
• Unbalanced design

Acknowledgements

J. Lee was supported by grant A06-0171-B51004-06N1-00050B from the Korea health 21 R&D Project, Ministry of Health & Welfare, Republic of Korea; S. Lee was supported by a grant no. R05-2003-000-10690-0 from the Basic Research Program of the Korea Science and Engineering Foundation.