Which of the following is possible in a factorial design with two independent variables?

Which of the following is possible in a factorial design with two independent variables? (a) There is only one main effect present

(b) There are two main effects present

(c) There are two main effects and an interaction effect present

(d) All above are possible

✅ Correct option: (d) All above are possible

Explanation:

A factorial design with two independent variables allows researchers to examine multiple types of effects simultaneously. Each independent variable can produce its own main effect, and together they may also produce an interaction effect. Depending on the nature of the data and the relationships among variables, several outcomes are possible. It is possible that only one independent variable significantly affects the dependent variable, resulting in only one main effect. In some cases, both independent variables independently influence the dependent variable, producing two main effects. Additionally, the effect of one independent variable may depend on the level of the other independent variable, leading to an interaction effect along with the main effects. Thus, a factorial design is flexible and powerful because it can reveal all these scenarios. This efficiency is why factorial designs are commonly used in educational and psychological research. Since all listed situations can occur, the correct answer is “All above are possible.”

10 Related PPSC Facts:

Factorial designs involve two or more IVs. Main effects show independent influence. Interaction effects show combined influence. ANOVA is used in factorial designs. Factorial designs increase efficiency. Interaction effects are unique to factorial designs. Cells represent combinations of IV levels. Graphs help interpret interactions. Absence of interaction simplifies interpretation. Factorial designs improve external validity.