A new test against an umbrella alternative and the associated simultaneous confidence intervals

For the usual balanced one-way fixed effects analysis of variance (ANOVA) model, a new test of the null hypothesis H₀: μ₁==μ_k against the umbrella alternative H_h:μ₁≤≤μ_h≥≥μ_k with at least one strict inequality is proposed. More usefully, this new test can be easily inverted to produce a set of one-sided simultaneous confidence intervals (SCIs) for all the ordered pairwise differences μ_j−μ_i for 1≤i<j≤h and h≤j<i≤k, and therefore enables the experimenter to infer which μ_i's are different when H₀ is rejected. A table of critical values is provided to allow immediate and simple implementation of this new inference procedure.