It's very difficult to perform a fair test.

If I test random programmers by getting them to do the same project either with TDD or without, TDD proponents might (justifiably) complain that the programmers didn't do TDD properly, since they didn't know how.

If I use TDD proponents to do the TDD side of the test, and TDD skeptics the non-TDD side, then one might claim that there is a bias in the quality of programmer (either people who like TDD make better programmers, or TDD skeptics make better programmers, depending on the results).

For every test you come up with, there's a potential bias that you cannot eliminate, since there will be some hypothetical correlation somewhere that doesn't correspond to TDD itself.