I have a hypothesis:
An individual attempts to communicate with God through any one of a number of means. God then factors in hundreds of variables to form a response.
So all we have to do is figure out every single variable, how important it is, and a way to control for it, and we can predict how an intelligent being with more information than us will respond.
Not really. All you do is take a group of people and stick them in a room... Muslims, Christians, Buddhists, whatever.. get them all to pray to God so that the people in room A get better.
Now room A and room B will be populated by random patients from the hospital. You repeat this day by day and after a couple months you comapre the patients from room A and room B and check which group got better faster.
You then repeat this expierment in various hospitals around the world.
If prayer works, then on average, you would see a significant evidence that people in room A get better faster.
If prayer doesn't work, then you will just see a random distribution of data, without any clear conclusions. This result from just 1 hospital would be too inconclusive to say that prayer doesn't work, but given enough hospitals and enough trials, if the data stays random and inconslusive, then you could conclude that prayer doesn't work.. at least in hospitals.
That's what you do if you want to find a relation between 2 events. If there is a relation, simple statistics will find it.
edit: of course the patients could not be told of this experiment at all, due to the placebo effect