Explain how the error term in a repeated measures ANOVA is actually an interaction

In a repeated measures ANOVA, the error term represents the variability that cannot be explained by the factors/variables included in the analysis. It accounts for all the random and uncontrolled factors that may influence the outcome.

To understand why the error term is considered an interaction, let's first define what an interaction is. In statistics, an interaction occurs when the effect of one variable on the outcome changes depending on the level of another variable. In other words, the relationship between two variables is not constant across all levels of another variable.

In a repeated measures ANOVA, we typically have at least two independent variables, often referred to as factors. These factors can be within-subjects factors (repeated measures) or between-subjects factors. The within-subjects factors represent variables that are measured repeatedly for the same set of subjects under different conditions.

Now, when we include these factors in the repeated measures ANOVA model, we look for main effects, which indicate the overall influence of each factor on the outcome. We also examine interactions between the factors, which reveal whether the effect of one factor depends on the level of another factor.

The error term in a repeated measures ANOVA captures the residual variation that cannot be accounted for by the main effects or the interactions. In other words, it represents the variability that remains after accounting for the systematic effects of the factors. The presence of an error term with interaction implies that the interaction effect cannot be completely explained by the model.

Therefore, considering the error term as an interaction in a repeated measures ANOVA acknowledges that there is additional variability in the outcome that is not explained by the main effects or the interactions included in the analysis.