What does "interaction effect" refer to in a factorial design?

An interaction effect in a factorial design refers to the situation where the influence of one independent variable on the dependent variable changes depending on the level of another independent variable. This means that the effect of one variable cannot be interpreted in isolation from the other; instead, the combined effects of these variables yield unique outcomes. Understanding interaction effects is crucial, as they can reveal complexities in data relationships that single-variable effects might miss.

In a factorial design, researchers often examine how different combinations of independent variables interact with each other, leading to varying results. For example, if you were studying the impact of study method and test anxiety on test scores, the interaction effect would help you understand how different levels of anxiety affect scores based on the type of study method used. This captures the nuance that a simpler analysis might overlook, ensuring a more comprehensive understanding of the factors influencing the outcome.