Problem
The scientists at Initech have been developing a new medicine called "Joyzepam" for treating depression. Now that that they are ready for human trials, they set up an experiment. The participants first filled out a questionnaire that asked them about their general mood, then they were randomly assigned to take the new Joyzepam, a placebo, or an existing medication called "Anxifree." In addition, the scientists were concerned about how whether talk therapy (specifically, cognitive behavioral therapy or "CBT") might also be beneficial. Therefore, half of the participants were randomly assigned to go to talk therapy as well, while the others were not. At the end of two months, the participants once again rated their general mood, so the scientists could see any gain.
What type of analysis would be appropriate for this study?