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Say we have the following two-way ANOVA output where each of the main effects and interactions are significant,

                    Df  Sum Sq  Mean Sq   F value    Pr(>F)    
A                   2    ...      ...       ...        < 2.2e-16 
B                   2    ...      ...       ...        < 2.2e-16 
A:B                 4    ...      ...       ...          0.00013   
Residuals           100  ...      ... 

Say we then go ahead and produce a summary for our coefficients and we find that some of the coefficient estimates are insignificant. For example,

                 Estimate   Std. Error   t value   Pr(>|t|)    
(Intercept)       10.5         ...          ...     < 2e-16 
A1                6.7          ...          ...     < 2e-16 
B1               -4.0          ...          ...       0.01
A1:B2             5.7          ...          ...       0.17
A2:B2             17.3         ...          ...      < 2e-16 

Would it be alright to remove the second last interaction term A1:B2? Or is this bad idea from a statistical point of view, and if so, why?

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  • $\begingroup$ Can you clarify how many levels A has and what they are called? Similarly for B. $\endgroup$ – Isabella Ghement May 11 '18 at 2:59
  • $\begingroup$ A and B both have two levels, I've made them up and said they both have levels 1 and 2. $\endgroup$ – KuDo May 11 '18 at 6:16
  • $\begingroup$ Thanks! Next step is to clean up the second output you provided - it should only include rows for the dummy variables A2, B2 and A2:B2. If you really want your output to include multiple rows for A and multiple rows for B, you're going to have to increase the number of levels of these factors. Once this is sorted out, we can answer your question - right now, the question cannot be answered since the second output you provided is incorrect relative to the first one. $\endgroup$ – Isabella Ghement May 11 '18 at 15:25
  • $\begingroup$ I've stuck with R's set-to-zero constraint. I've removed A2 and B2. Thank you! $\endgroup$ – KuDo May 11 '18 at 23:17

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