A 2 x 2 factorial design examines three variables, one dependent and two independent. For example, some people volunteered to participate in research to determine the relationship between individual and combined effects of the initial diagnosis based on the type of therapy they received. Half of them had social anxiety, while the rest had general anxiety, and some were given individual therapy while others were given group therapy.
In this study, the three main effects are examined depending on their interactions. The first one is how the two independent variables jointly relate to the dependent variable. The second one is the main effect of one independent variable and its relationship with the dependent variable without depending on the main effect and the interaction. The third one is how the other independent variable’s main effect relates to the dependent variable without relying on the other main effects and the interaction.
The main effects were those of the initial diagnosis and the type of therapy. Simultaneously, the interaction was of these two independent variables, initial diagnosis and type of treatment, and how they relate to the dependent variable, anxiety. Thus, the main effects compare marginal means while interactions compare these effects. The levels of these the first variable, the initial diagnosis, is the control, while the level of the second variable, type of therapy, is experimental.