In a two-factor experiment with two levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. What result(s) would be produced by this pattern of treatment means?
A) A main effect for factor A only
B) A main effect for factor B only
C) An interaction between A and B
D) Main effects for both A and B, and an interaction

Question

Quizplus · Accepted Answer

The main effect for factor A is the difference between the average of the means for the two levels of factor A. The main effect for factor B is the difference between the average of the means for the two levels of factor B. The interaction between A and B is the difference between the difference between the means for the two levels of factor A at one level of factor B and the difference between the means for the two levels of factor A at the other level of factor B. In this case, the three treatment means that are essentially identical are all at one level of factor A and the one treatment mean that is substantially different from the others is at the other level of factor A. This means that there is a main effect for factor A. The three treatment means that are essentially identical are all at one level of factor B and the one treatment mean that is substantially different from the others is at the other level of factor B. This means that there is a main effect for factor B. The difference between the difference between the means for the two levels of factor A at one level of factor B and the difference between the means for the two levels of factor A at the other level of factor B is not zero. This means that there is an interaction between A and B.

In a Two-Factor Experiment with Two Levels of Factor a and 2