Imagine a study where two methods are compared for treating depression. A measure of effectiveness has been developed, the higher the measure the more effective the treatment. Further assume there is reason to believe that males might respond differently to the methods compared to females. If the sample means are

and if the hypothesis of no main effects for Factor A is rejected, but the hypothesis of no interactions is not rejected, what does this suggest about which method should be used? In terms of Tukey’s three decision rule, what can be said about any interaction?

Factor B Males Females Method 1 X 50 = X2 X = 70 Factor A Method 2 X3 80 x4 = 60 =