# Independent-samples t-test on the “Gain Scores” from two groups

I have a simple Pre-Test Post-Test Control design like this:

where, $R$ = Random Assignment to groups; $O$ = Observation; $T$ = Treatment; $C$ = Control.

A colleague suggested that by doing and independent-samples t-test between the Gain Scores (i.e., $Posttest - Pretest$) of the two groups, I am actually looking at the interaction effect in a two-way design.

# Question:

I am wondering how there could exist an interaction effect in such a design?

My colleague says: "You start with two groups, one of which will receive treatment. This is the first factor with means $\mu_1$ and $\mu_2$. Then you measure them again, with one group receiving treatment, the second factor with means $\mu_3$ and $\mu_4$. No interaction is $\mu_1-\mu_3=\mu_2-\mu_4$.

You can plot this by putting: x-axis first two groups, y-axis means, the two lines corresponding to the second factor."

• what is the logic given by him for interaction effect ? and what is the reason you do not agree with his opinion ? – Subhash C. Davar Nov 15 '17 at 14:26
• @subhashc.davar, I updated my question. I basically can't understand my colleagues comment regarding how to think of this design as an interaction effect and even how to plot this as an interaction plot? – Reza Nov 15 '17 at 21:35
• @subhashc.davar, could you now better understand OP's question? – rnorouzian Nov 17 '17 at 15:23
• It is difficult to contemplate what is beng considered as interaction ? interaction between groups or relatedness of subjects in the treatment and control group etc. And how do you estimate interactions either mathematically or statistically. – Subhash C. Davar Nov 17 '17 at 16:12