Interaction

a. What is an interaction between two factors?

b. In general, when using two-way analysis of variance, if we find that there is an interaction effect, how does that affect the procedure?

c. Shown below is an interaction graph constructed from the data in Exercise 1. What does the graph suggest?

Data are given on the pulse rates of men and women. It is further classified according to three different age groups.

a.

An interaction effect is the effect of the two factors combined on the response variable.

.

It deals with the change in one factor caused to the effect of the other factor.

b.

In a two-way analysis of variance, a null hypothesis is set up to test the significance of the interaction effect first.

If the null hypothesis is rejected, then the effects of one factor cannot be considered without the effect of the other factor;thus, the individual effects are not tested.

This is the major change in the procedure of two-way analysis of variance compared to the one-way analysis of variance.

c.

If the two lines in the interaction graph are far from being parallel, then there is an interaction between the two factors.

In the graph shown, it can be observed that the two lines are not parallel to each other.

Thus, it can be concluded that there is an interaction effect between age and gender.