What does the marginal mean represent in a factorial design in ANOVA?

The marginal mean represents the mean score for all participants at a particular level of one grouping variable in a factorial design in ANOVA. In this context, it is calculated by averaging the scores of all participants who fall into a specific category of one independent variable, regardless of the levels of any other independent variables in the study. This allows researchers to understand the effect of that particular variable on the outcome measure while controlling for the influence of other variables in the analysis.

For example, if one independent variable is treatment type (e.g., placebo vs. medication) and another is age group (e.g., young vs. old), the marginal mean for the treatment group would reflect the average score of all participants receiving the medication, not taking into account the age differences among them. Thus, marginal means provide valuable insights into the effect of each variable independently within a multifactorial framework. This is crucial for interpreting the results of factorial ANOVA comprehensively.