Model without interaction between the factors

The simplest model for the effect of two factors on a response is an additive one of the form:

(mean response)   =   (base value)   +   (effect of factor A)   +   (effect of factor B )

One implication of this model is that the effect on the response of changing the level of factor A is the same, whatever the level of factor B. In a similar way, the model assumes that the effect of changing factor B is the same whatever the level of factor A.

If this model holds, the effects of the two factors can be separately described in a table of means.

  Factor B
    Level B1     Level B2  
Mean response   87.25 70.25
  Factor A
     Level A1       Level A2       Level A3       Level A4   
Mean response  
66.5
120.0
79.0
49.4

It should be noted that this model does not always hold. Interaction between the effects of A and B occurs if the effect of changing B is different for different levels of A (and vice versa).