A More Powerful Post Hoc Multiple Comparison Procedure in Analysis of Variance

Scheffé’s test ( Scheffé, 1953 ), which is commonly used to conduct post hoc contrasts among k group means, is unnecessarily conservative because it guards against an infinite number of potential post hoc contrasts when only a small set would ever be of interest to a researcher. This paper identifies a set of post hoc contrasts based on subsets of the treatment groups and simulates critical values from the appropriate multivariate F-distribution to be used in place of those associated with Scheffé’s test. The proposed method and its critical values provide a uniformly more powerful post hoc procedure.