Experimental Analysis with Several Discrete Treatments

I am analyzing data that are originating from an randomized experiment and I am new to this. There was one control groups and three different treatment groups. The treatment groups are discrete and unordered (you can think of them as of three completely different drugs).

I want to analyze the data employing an regression.

At first I subseted the data (so that only one treatment group and the control group were left) and analyzed the following:

$$y_i=\alpha+\beta T_i + error_i$$

where $$T_i$$ is a dummy indicating whether an individual received the treatment. In this case, $$\beta$$ corresponds to the average causal effect of the treatment.

I have a question: Would, instead of subsetting, also the following expression feasible?

$$y_i=\alpha + \beta_1 T_{1,i} + \beta_2 T_{2,i} + \beta_3 T_{3,i} + error_i$$

where $$T_{1,i}$$, $$T_{2,i}$$, $$T_{3,i}$$ are dummies indicating whether an individual received the first, second or third treatment.

Best regards

• Yes, the model with 3 dummy variables is correct. – user158565 Nov 5 '18 at 14:36
• However, the dummies are correlated right? This might lead to bigger standard errors? However, due to the greater subset, the estimate might get more precise. I don't know which of these effects might be stronger :O – FeldO Nov 6 '18 at 13:08
• You have 4 groups (one control groups and three different treatment groups.), so 3 dummy variables will not correct collinearity (correlation). If you create 4 dummy variables, collinearity will appear. After you fit the model, check the 3 estimated 3 regression coefficients to see which drug is the best. – user158565 Nov 6 '18 at 18:44