I need to do a study of what apps are actually used among a group of test users taking part of an experiment. I would like to know the time each of the random 3rd party apps
I would use an analytics tool like Flurry Analytics to get the data concerning usage statistics, which you could then download into your app using their API. They can get you very details stats on how your users are using your app, how frequently, etc. It's a great tool, plus it's free!