What does a significant main effect indicate in a factorial design?

A significant main effect in a factorial design indicates the average differences across levels of the independent variable. In such a design, researchers analyze how different factors influence an outcome. When one observes a significant main effect, it means that the levels of the independent variable lead to statistically significant differences in the dependent variable, indicating that the independent variable has a measurable impact irrespective of other factors in the design.

For example, if a study is examining the effects of different study methods (independent variable) on test scores (dependent variable), and a significant main effect is found for study method, this suggests that the different methods produce differing average test scores, thereby showing the influence of the independent variable.

Understanding this helps in interpreting the results of factorial designs, as it is critical for determining how different levels of independent variables contribute to the overall results of the study.