# Can I use t-test for interaction in a two-way factorial ANOVA?

I have a two-way factorial design, with factors treatment (A vs. B) and time (T1 vs. T2). The same subject was measured twice, at T1 and T2, so I have repeated measurements. I am interested to see whether there is interaction between treatment and time on the response variable $x$. I am applying a t-test. $H_0$ is: $(\mu_{A,T2}-\mu_{A,T1})-(\mu_{B,T2}-\mu_{B,T1})=0$, that is, there is no differences in the average change (from T1 to T2) between the treatment A and B groups.

To conduct the t-test, I computed the differences of $x$ between T2 and T1, this gives me $\Delta x_{A}$ and $\Delta x_{B}$, and then I can apply a t-test to see whether the average of $\Delta x$ are significantly different between the A and B groups.

My question is:

1. Is this a statistically sound way to test the hypothesis?
2. What's the difference between this method and the classical ANOVA method, which computes the mean square and uses the F-test? Which one is more powerful?
• See also these other options for analysis of 2 by 2 pre-post designs May 3, 2013 at 8:14