Parametric Bootstrap Tests for Unbalanced Three-factor Nested Designs under Heteroscedasticity

Abstract

In this article, we consider the three-factor unbalanced nested design model without the assumption of equal error variance. For the problem of testing “main effects” of the three factors, we propose a parametric bootstrap (PB) approach and compare it with the existing generalized F (GF) test. The Type I error rates of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the generalized F-test. The PB test performs very satisfactorily even for small samples while the GF test exhibits poor Type I error properties when the number of factorial combinations or treatments goes up. It is also noted that the same tests can be used to test the significance of the random effect variance component in a three-factor mixed effects nested model under unequal error variances.

Keywords:

• Bootstrap re-sampling
• Generalized F test
• Generalized p-values
• Unbalanced data.

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62J10.