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

Bernhard Spangl, Norbert Kaiblinger, Peter Ruckdeschel and Dieter Rasch

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 6, 1728-1743

Abstract: We consider balanced one-way, two-way, 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, i.e. the minimal number of experiments needed. We also provide a structural result for the minimum sample size, proving a conjecture on the optimal experimental design.

Date: 2023
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DOI: 10.1080/03610926.2021.1938126

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