Technical Report, SFB 475: Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund 1999,38
The variance function of the optimal estimator of the overall mean in a heteroscedastic one-way ANOVA model is dominated by positive semi-definite quadratic functions. This makes it possible to develop closely related tests on the nullity of the overall mean parameter in one-way fixed and random effects ANOVA models, which make use of the quantiles of the t-distribution. These tests are founded on the convexity arguments similar to Hartung (1976). Simulation results indicate that the proposed tests attain type I error rates which are far more acceptable than those of the commonly used tests.
Fixed and random effects models type I error rate estimated degrees of freedom balanced and unbalanced samples homoscedastic and heteroscedastic error variances replication