When considering the relationship among three or more variables, an interaction may arise. Interactions describe a situation in which the simultaneous influence of two variables on a third is not additive. Most commonly, interactions are considered in the context of regression analyses, but they may also be evaluated using two-way ANOVA.
A simple setting in which interactions can arise is a two-factor experiment analyzed using Analysis of Variance (ANOVA). Suppose we are interested in studying the effects of cocaine on sleep. We might design an experiment to simultaneously test whether both the use of cocaine and the duration of usage affect the number of hours a squirrel will sleep in a night. We might give half of the squirrels we test cocaine, and the other half a placebo (control) substance (the substance variable). And we might vary the duration of usage by administering cocaine or placebo for one of two possible durations before test, 4 weeks or 12 weeks (the usage duration variable).
4-Week Control |
4-Week Cocaine |
12-Week Control |
12-Week Cocaine |
7.5 |
5.5 |
8.0 |
5.0 |
8.0 |
3.5 |
10.0 |
4.5 |
6.0 |
4.5 |
13.0 |
4.0 |
7.0 |
6.0 |
9.0 |
6.0 |
6.5 |
5.0 |
8.5 |
4.0 |
have two binary factors A and B. For example, these factors might indicate whether a treatment was administered to a patient, and for how long the treatment was used. We can then consider the average treatment response (e.g. the symptom levels following treatment) for each patient, as a function of the treatment combination that was administered. The following table shows one possible situation: