  We consider balanced one-, two- and three-way ANOVA models to test the
hypothesis that the fixed factor A has no effect. The other factors are fixed
or random. We determine the noncentrality parameter for the exact F-test,
describe its minimal value by a sharp lower bound, and thus we can guarantee
the worst case power for the F-test. These results allow us to compute the
minimal sample size. We also provide a structural result for the minimum sample
size, proving a conjecture on the optimal experimental design.
