A Parametric Bootstrap Test for Two-Way ANOVA Model Without Interaction Under Heteroscedasticity

Abstract

In this article we consider the two-way ANOVA model without interaction under heteroscedasticity. For the problem of testing equal effects of factors, we propose a parametric bootstrap (PB) approach and compare it with existing the generalized F (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the GF 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 random effect variance component in a two-way mixed-effects model under unequal error variances.

Keywords:

• Bootstrap re-sampling
• Generalized F-test
• Generalized p-values
• Mixed effects

Mathematics Subject Classification:

• Primary 62F03; Secondary 62J10

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (11171002), Beijing Natural Science Foundation (The Theory of Mixed Effects Models of Multivariate Complex Data and Its Applications; 1112008), and National Social Science Foundation of China (12BTJ014).