# Is it possible to add the standard errors of 2 groups together to obtain the standard error of the 2 groups combined

I am trying to recreate the results in this table. The results have been obtained by difference in difference estimation. I can obtain values from all columns except for column 5 and 6.

Column 5 says that it is obtained by subtracting column 1 from column 2, and this is simple to do for the means, however I don't know of a way to add OLS regression standard errors of 2 groups together to give a combined standard error, and I don't know of any other way to estimate the combined standard errors.

Does anyone know if/how this can be done. Or does anyone have any advice on alternative methods for obtaining these values.

Thank you for any help.

Chris

Let $$X_1$$ be column 1, $$X_2$$ be column 2, $$X_5$$ be column 5.
$$X_5 = X_2 - X_1$$ $$Var(X_5) = Var(X_1) + Var(X_2) -2Cov(X_1,X_2) =[SE(X_1)]^2 + [SE(X_2)]^2 -2Cov(X_1,X_2)$$
And $$SE(X_5)=\sqrt{Var(X_5)}$$.
So you need to get $$Cov(X_1,X_2)$$ in order to get $$SE(X_5)$$. Or you can prove that $$X_1$$ and $$X_2$$ are independent such that $$Cov(X_1,X_2) =0$$.