Is it possible to test significance of difference between main effect and the (total) interaction effect? In a model with dummies A and B, and an interaction term, AB, if AB has a negative sign (and A and B are positive), is it possible to test whether A and AB are equal?
I have a model Y = A + B + AB.
If A = 101.5, B = 25.8, and AB = -25, is it possible to test if AB (101.5 + 25.8 - 25 = 102.3) equal to A?
Edit: as an option, I consider an ordinary t-test of whether A=102.3. Is this an acceptable approach?
 A: I take your A, B and AB values to be the estimates of the regression coefficients for the corresponding variables and their interaction.
You can performs tests on differences between 0 and any linear combination of regression coefficients that you want, provided that you take the covariances among the coefficient estimates into account. So you can't do it the way that you propose in your last paragraph, as that doesn't take into account the variability in the estimate of the sum of the three coefficients that provided the point estimate of 102.3.
Statistical programs can provide the covariance matrix among the regression coefficient estimates, although not usually by default. In R, for example, you usually can get that with the vcov() function applied to the model.
The t-test values for individual coefficients that are usually reported simply use the diagonal elements of that matrix as estimates of the variance of each coefficient, to use in the t-test formula. The off-diagonal values of the matrix are the covariances of the corresponding pair of predictors. So you simply use the formula for the variance of a sum of correlated variables to estimate the variance of your particular linear combination of coefficients and use that estimate as the basis of your significance test.
