Dear Andrew,

Thanks for developing such a great toolbox!

I have a question about how to interpret and follow up a 2×2 ANOVA design in NBS. I’m running a 2(A) × 2(B) ANOVA using an F-test. The design matrix has four columns:

1. 
   

   Condition A (coded as -1, 1)

   
   
   
2. 
   

   Condition B (coded as 1, -1)

   
   
   
3. 
   

   The interaction term (column 1 × column 2)

   
   
   
4. 
   

   A column of ones (intercept)

   
   
   

The interaction contrast [0, 0, 1, 0] is not significant, but I’d like to test the main effect of A using the contrast [1, 0, 0, 0].

The main effect of A turns out to be significant; should I then perform post-hoc comparisons (e.g., to test A1 > A2 and A1 < A2)?
Or in this case, would it be more appropriate to instead run two separate t-tests using the contrasts [1, -1] and [-1, 1], since the t-tests can explicitly examine both directions (A1 > A2 and A1 < A2)?

Thanks a lot for your time and advice!

Best,
Yihe