A note on multiple comparison procedures for detecting differences in simply ordered means

In the one-way ANOVA, we consider procedures that determine whether [mu]i=[mu]j or [mu]i<[mu]j when the means are known a priori to be nondecreasing. It is known that the one-sided Studentized range test (OSRT) controls the familywise error rate, but the one-sided least significant difference test has larger powers. We show that for balanced designs, the familywise error rate of the latter is largest when all of the means are equal but one. This leads to a modification of the one-sided least significant difference procedure that controls familywise error rate and has larger powers than the OSRT. Some recommendations for unbalanced designs are also given.