Global testing method for clustering means in ANOVA

For the comparison of treatment means in the analysis of variance, it is reasonable to partition the treatments into disjoint groups such that treatment means in the same group are not significantly different. From the overall consideration of the coherence of the current partition with the whole data, we propose some clustering procedures based on the global pp-value for each partition. The new procedures are applied in both homogeneous and heterogeneous variances cases. We show the consistency of our procedures, and investigate their theoretical FWER behavior. Simulation studies reveal that our procedures have better overall performance than some existing methods, in terms of the number of total errors, power, and the proportion of picking out the true partition.