The advantage of the Bishop–Dudewicz ANOVA procedure is that, without assuming equal variances, the experimenter can guarantee that the Type I and Type II error probabilities areexactlyequal to α and β respectively. Because unequal variances are known to affect both Type I and Type II errors, their procedure can be important in practice. However, to use their procedure, the experimenter must determine the constant, sayd, such that Pr[Σ(Tj–T̄+(μj–μ)/√d)2≥c] = 1 – β, where theTjs areJindependent Student'strandom variables, each having ν degrees of freedom,cis the critical value used in the Bishop–Dudewicz procedure, μ = Σμj/J, and the μjs are the means ofJindependent normal random variables. Bishop&Dudewicz proposed a method of approximatingd, but for many researchers and students, the procedure is inconvenient to the point that few would apply it. This brief note proposes and examines two simple approximations tod. One of these, which is based on a new approximation of the non‐null distribution, appear