I find this idea absolutely fascinating. I was a psychology major in college, so I'm quite interested in hearing about your findings. I've heard a ton of anecdotal stuff, both pro-RPG and anti-RPG, and I've long wanted an empirical study of the effects of TTRPGs. I wish I could make some suggestions, but I've only played a few systems thus far. Of them, I'd suggest D&D
4e because it's relatively easy to learn, but of course it tends to be more combat-heavy. It also has a number of published adventures that might make things easier for the people actually running the experiments; which, if you can get some assistants, I would highly recommend.
How are you thinking of coding the data?