They do studies all the time in the medical field. They target a group of people with the same type symptoms... giving half a prescribed drug and the other a "placebo" (basically an empty pill). The results usually aren't what you would expect. Generally the people given the placebo show signs of improvement. Its a big mystery in the medical world why this happens... I guess your brain is more powerful than you think...
The same can be applied to different types of gas... in that you think your car is running better because you put a higher octane in your tank.