Purpose of the statistic

To this point we have considered only differences among groups that can be conceptualized as representing a single independent variable. There are many occasions, however, when the investigator is interested in ascertaining the joint or differential effects that two or more independent variables exert on a dependent variable.

The two most common of these scenarios involve (a) testing whether or not an intervention is differentially more effective for one group (e.g., males vs. females, severely ill vs. less severely ill patients with the same diagnosis) than another and (b) testing whether or not subjects receiving the intervention change across assessment intervals more during the course of the study than do those in the control group.

In most cases the first scenario involves a between subjects design (i.e., different people are in all of the groups) while the second is usually a mixed design (i.e., although different individuals are contained in the treatment groups everyone in these groups is measured two or more times, such as at baseline and at the end of the study). In this chapter we will present power and sample size tables for two-factor interactions involving both between subject (including ANCOVA) and mixed designs.

Regardless of the type of design employed, however, an interaction tests a completely different hypothesis than occurs when the two independent variables are considered separately.