Minimal sample size in balanced ANOVA models of crossed, nested, and mixed classifications

TL;DR

This paper derives the minimal sample size needed for balanced ANOVA models with various classifications, providing exact noncentrality parameters, worst-case power guarantees, and confirming a conjecture on optimal experimental design.

Contribution

It introduces a method to determine the minimal sample size for balanced ANOVA models, including a sharp lower bound and a structural result that proves a conjecture.

Findings

Derived the noncentrality parameter for exact F-tests.

Provided a sharp lower bound for minimal sample size.

Proved a conjecture on optimal experimental design.

Abstract

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.