In a multi-factor ANOVA design, which aspect should you look at to understand interactions?

In a multi-factor ANOVA design, examining the means table is crucial for understanding interactions between factors. The means table offers a summary of the means for each combination of the levels of the factors being studied. By analyzing these means, you can identify how the effect of one factor varies across the levels of another factor.

Understanding interactions is vital because they indicate that the effect of one independent variable on the dependent variable is not consistent across the levels of another variable. For example, if you are studying the effect of dosage and time on a treatment outcome, the means table can reveal whether the effect of dosage changes depending on the time of administration.

While graphical outputs can also be very useful for visualizing interactions, they are secondary to the specific numerical values reported in the means table, which allow for precise comparisons. The overall standard deviations give an idea of variability but do not directly indicate interaction effects. Raw data may not clarify relationships without statistical analysis. Thus, the means table is essential for comprehensively understanding interactions in a multi-factor ANOVA context.