Tables of Sample Sizes in the Analysis of Variance

Abstract

Tables are provided which give the minimum sample sizes per treatment (or level) for all combinations of α = 0.5, 0.4, 0.3, 0.25, 0.2, 0.1, 0.05, 0.01 and β = 0.3, 0.2, 0.1, 0.05, for relative discrimination (Δ/σ) = 1.0(0.5)3.0, and for the number of fixed-effect treatments or factor levels t = 2(1)11, 13, 16, 21, 25, and 31. Relative discrimination is defined as a standardized difference Δ/σ, where Δ is the amount by which at least two of the treatments differ. Examples are given of experiments for which it is better to fix the Type II error rate β at a small value and allow the Type I error rate to become relatively large.

• Analysis of Variance
• Fixed-Effects Model
• Relative Discrimination
• Sample Size

Additional information

Notes on contributors

T. L. Bratcher

Dr. Bratcher is an Assistant Professor in the Department of Statistics at the University of Southwestern Louisiana. Mr. Moran is a Lecturer in the Department of Statistics at the University of Reading, England. Dr. Zimmer is an Associate Professor in the Department of Mathematics and Statistics at the University of New Mexico. Mr. Moran and Dr. Zimmer were previously a Lecturer and a Visiting Professor, respectively, at the University of Dublin, Trinity College where most of the computing was performed.