Liu, W. (1997) On some sample size formulae for controlling both size and power in clinical trials. Journal of the Royal Statistical Society. Series D: The Statistician, 46 (2), 238-251. (doi:10.1111/1467-9884.00080).
Abstract
Suppose that observations are taken from a population with normal distribution N(μ, σ2) where both μ and σ2 are unknown parameters. Our goal is to design a two-sided test of H0: μ = 0 against Ha: μ ≠ 0 which has, at least approximately, size α and power β at |μ| = d > 0, where α, β and d are three preassigned constants. The classical solution is Stein's two-stage procedure, which tends to oversampling, however. Three new procedures are proposed and studied in this paper. They all have both size and power very close to the target values α and β and require only a few more observations than the necessary sample size to achieve our goal if σ2 had been completely known.
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