The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction?
A)10
B)20
C)30
D)40

Question

The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction? 
A)10​ 
B)​20 
C)​30 
D)​40

Quizplus · Accepted Answer

If the missing mean was 20, then the means for each level of factor A would be 20, 40, and 60. Likewise, the means for each level of factor B would be 20, 30, and 40. If there is no interaction between factors A and B, then the difference between the means of factor A at each level of factor B should be the same. In this case, the differences are 20-20=0, 40-30=10, and 60-40=20. These differences are all different, indicating an interaction between factors A and B. Therefore, the missing mean must be adjusted until the differences between the means of factor A at each level of factor B are approximately equal, which occurs when the missing mean is 20.

The Following Data Represent the Means for Each Treatment Condition