What is the primary purpose of an interaction effect in a two-way ANOVA?

The primary purpose of an interaction effect in a two-way ANOVA is to determine the effect of the combination of two independent variables. In a two-way ANOVA, researchers are often interested not only in the main effects of each independent variable but also in how these variables interact with one another. An interaction effect explores how the effect of one independent variable on the dependent variable varies at different levels of another independent variable. This is crucial because it reveals whether the impact of one factor depends on the level of another factor, providing deeper insights into the data.

In contrast, while assessing the individual effect of each independent variable is important, that aspect pertains more to the main effects, not interaction effects. Comparing dependent variables across different groups focuses on the broad outcomes but does not specifically examine the interplay between independent variables. Controlling for Type I errors is a statistical consideration that applies more broadly across tests and does not specifically pertain to the understanding of interaction effects in two-way ANOVA. Therefore, understanding the combined influence of two independent variables is essential and highlights the major role of interaction effects in this analytical method.