Abstract: We consider testing for main treatment effects and interaction effects in crossed two-way layouts when one or both factors have large number of levels. Random errors are allowed to be nonnormal and heteroscedastic. In the heteroscedastic case, we propose new test statistics. The asymptotic distributions of our test statistics are derived under both the null hypothesis and local alternatives. The sample size per treatment combination can either be fixed or tend to infinity. Numerical simulations indicate that the proposed procedures have good power properties and maintain approximately the nominal-level with small sample sizes. A data set from a study evaluating forty varieties of winter wheat in a large-scale agricultural trial is analyzed.
Key words and phrases: Heteroscedasticity, large number of factor levels, local alternatives, projection method, quadratic forms, unbalanced designs.