Oooo! This really is a hard experiment to design. Placebo effect is real, and this xkcd cartoon posted nearby at the Curious Wavefunction hints at some of the complications. Warning: science nerds only; ordinary people may not find this funny.
Sometimes, just sometimes, it takes a philosopher to figure out why non-scientific treatments appeal to so many people. Damon Young's brief essay on homeopathy gets right to the point, although what is the solution? Have a read.