Critical point computations for one-sided and two-sided pairwise comparisons of three treatment means

This paper addresses the problem of critical point calculations for pairwise comparisons of three normal means. One-sided and two-sided pairwise comparisons are standard multiple comparisons procedures, and while tables of critical points exist for balanced situations with equal sample sizes, only limited tables of critical points exist for unbalanced cases. A new algorithm is developed in this paper using elementary methods which allows the critical points to be found in all situations using only a one-dimensional numerical integration. Programs have been developed to implement the algorithm which will allow experimenters to easily find the required critical points and p-values.