On Comparing Treatment Effects to a Standard when the Variances are Unknown and Unequal

Abstract

Let δ = μ _e – μ _c be the difference between the means of an experimental and control group, and suppose it is desired to determine whether δ ≥ δ₀, where δ₀ is a known constant specified by the experimenter. In this paper, I describe how to determine whether enough observations have been sampled to be reasonably certain that a correct decision will be made about how δ compares to δ₀. The solution is exact regardless of what the variances might be. In particular, equal variances are not assumed.