Question

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?

Short answer

a. The interaction effect among two factors is the effect upon the combination of both the factors. It is the effect of one factor over the other factor.

b. If two-way analysis of variance is applied, the hypothesis is set up to test the interaction effect first. If the interactioneffectcomes out to be significant,the individual effects of the factors cannot be considered separately.

c. Since the two lines are not parallel;there is an interaction effect between the factors age and gender.

Step-by-step solution

Given information

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

Interaction effect

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.

Two-way analysis of variance

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.

Interpret the graph

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.