What is indicated by differing cell means across rows in a factorial design?

In a factorial design, differing cell means across rows suggest that the interaction between the factors may be influencing the outcome. An interaction effect occurs when the effect of one independent variable on the dependent variable changes depending on the level of another independent variable. Therefore, when you observe different cell means, it indicates that the impact of the levels of one factor varies at different levels of another factor, which is a hallmark of interaction effects.

This phenomenon is crucial to understand, as it means that simply looking at main effects (the independent effects of each factor on the outcome) might be insufficient. The variations in the cell means signal that there may be more complex relationships at play, necessitating a deeper analysis to fully understand how the factors work together. This exploration often leads to more meaningful insights into the data and the underlying psychological phenomena being studied.