maineffects

Maineffects, in statistics and experimental design, refer to the effect of a single factor on the outcome variable, averaged across the levels of other factors in a factorial design. In a study with two factors, A and B, the main effect of A is the difference in the dependent variable between the levels of A, averaged over B. This is equivalent to comparing marginal means: the mean response at each level of A after averaging over B.

Main effects are typically estimated using analysis of variance (ANOVA) or multiple regression with appropriate coding of factor levels. The size of a main effect can be described by differences in means, or by standardized measures such as partial eta-squared or Cohen’s d, depending on the design and reporting conventions. In balanced designs, estimates are straightforward, while in unbalanced designs, adjusted means may be used.

Interpreting main effects becomes more complex in the presence of interactions. A significant interaction indicates that the effect of one factor depends on the level of another factor, which can obscure or alter the interpretation of main effects. Consequently, researchers often report both main effects and interaction effects, and may conduct simple main effects analyses to explore patterns across factor levels.

Maineffects are a foundational concept in factorial experiments and ANOVA, providing a concise summary of how individual factors influence outcomes, while acknowledging that interactions can modify those influences. Limitations arise when interactions are substantial or when design balance is imperfect, affecting the stability and interpretation of estimated main effects.