Tables are provided which give the minimum sample sizes per treatment (or level) for all combinations ofα= 0.5, 0.4, 0.3, 0.25, 0.2, 0.1, 0.05, 0.01 andβ= 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 levelst= 2(1)11, 13, 16, 21, 25, and 31. Relative discrimination is defined as a standardized differenceΔ/σ, whereΔis 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 rateβat a small value and allow the Type I error rate to become relatively large.