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Could someone please clarify for me the difference in how interaction and main effects terms should be interpreted in ANOVA and regression? I understand that in regression, the coefficients for the various terms are qualified i.e. if an interaction term is included, the coefficients of lower order terms are conditional effects. Therefore, the interaction term has to be removed in order to interpret the 'main effects' of lower order terms.

But what about the output from ANOVA. If interaction terms are included, can the significance values associated with the lower order terms be interpreted as 'main effects' of those terms? Or, like in the case of regression, does the interaction term have to be removed to be able to observe main effects of lower order terms?

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  • $\begingroup$ If your understanding of regression is correct, then it is the same for ANOVA. Both are the same thing. Before interpreting "main effects" qualitatively, plot them to see how strong they are. If both lines do not cross, then I might interpret the main effects qualitatively, despite there being a statistically significant interaction. I would conduct a simple slopes analysis to obtain a quantitative interpretation of what is going. $\endgroup$
    – Heteroskedastic Jim
    Jul 8, 2017 at 0:02
  • $\begingroup$ Many thanks for your comments 'user162986' and 'mkt'. Could I ask why it is that the significance levels for main effects terms change when one removes an interaction term from an ANOVA? What is being reported for the F and P-values for lower-order terms when an interaction is included, and alternatively, what is being reported for the F and P-values for lower-order terms when an interaction is removed? $\endgroup$
    – RBW
    Jul 8, 2017 at 21:42

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