The interaction concept

The interaction A*B is the fact that the degree of A has an influence on the effect of B and vice versa.

In the preceding example we observe in the figure on the left:

Whatever the level of the factor B, the effect of A on Y is the same and A has an effect of 1 on the result. There is thus no interaction between A and B.

We observe on the figure on the right: When the level of factor B is at its minimum, the effect of A on Y is 2. When the level of factor B is at its maximum, the effect of A on Y is 1. The effect of A varies according to the level of B and, therefore, there is an interaction between A and B.

When an interaction occurs the interaction effect is modelled by a multiplier in the Y prediction equation, A*B in this example. The prediction equation would be in this form:

The term α₃ corresponds to the interaction A*B