I don't think it's possible to "prove" such a thing.
I'll go even further, and say that I don't think it's really possible to study the issue of "Software Development productivity" with such a study. Which is mainly why all the evidence we ever really have to go on is what experienced people tell us (and unfortunately, each one has a different view on various methodologies).
There's a simple reason for this: people are completely different. Sit down a team of 5 people for a project of a few months (which is more, I'm guessing, than most studies ever manage; let's see anyone finance a few months of developer time), and you're bound to get completely different results. The problem is, there is no way to sepearate the many different factors here:
- Ability of the individual programmers.
- Dedication/effort put in by the programmers.
- Experience with the tools.
- The ability of whoever is acting as the team leader (just following a methodology isn't enough. If someone doesn't know how to manage a team, the methodology won't really be well represented).
And there are probably many more factors.
So what I'm trying to say is, don't believe studies that have "proven" that one methodology/tool/anything works better than others. They're almost impossible to do.