A Simple Method of Multiple Comparisons of Means

Abstract A simple procedure for multiple comparisons of means is proposed for unequally sized samples. The procedure is attractive for its simplicity and for a graphical display which allows the experimenter to evaluate all comparisons of interest at a glance. The critical points used are those of the Studentized Maximum Modulus and two inequalities are involved: a conservative probability inequality and a radical algebraic inequality. Apparently, the joint effect of the two inequalities is conservative unless the imbalance in sample sizes is very large. For equally sized samples one can use critical points of the Studentized Range and the procedure becomes equivalent to Tukey's well-known T-method.