I originally wrote that there is independent data showing no difference in outcomes.
This was based on a presentation at Stevens Institute of Technology where they tested clickers and found that students were more enthusiastic in class, and that attendence rose.
At the time, they said that scores did not rise. Scores after all, are the objective goal. If students don't understand any better, then the immediate goals are more ego-gratification for the professor.
Today, 10 years later, the professor says they use clickers, and find that they still achieve the immediate improvements. He cannot tell me about grades because they don't do any studies on it. It is hard to believe that grades cannot improve based on better attendance, but without objective measurement, I still believe their initial impressions which were based on comparison of year on year scores. Another way of looking at this is that as the studies by the ASU modeling curriculum found, students of physics don't believe what they are writing. When asked what happens in a "real" situation they give Aristotelian answers. In other words, the lecturer can improve lecture mechanics with clickers, but unless they change the way they teach, the fundamental scores won't change because the students don't really believe the physics. Anyway, sorry, but that's peculiar to physics.
I teach programming, and I find that multiple choice questions are of limited utility. I can sometimes ask the right question. But the best test of computer programming ability (aside from asking for an entire program) is to see whether people know what to type in a particular place without prompting. This is short answer, and complicated short answer since multiple answers can sometimes be acceptable. I will attach some sample questions I ask below.
Personally, using clickers takes time, and I have moodle and can tell them to review things at home and answer my questions there. That way, I get them to study out of class, review what we did, and it reinforces it without taking up classtime. I find that works better for me, but in any case I am teaching graduate classes, without access to uniform clickers.