Keyword: Consistently. It is also a "statistical anomaly" that every time I take aspirin, my headache goes away, yet in science we ascribe such strong corrolations to causality if is consistently occurs. Every time a large sample size of people take a drug, effect A occurs, then the drug is causing effect A. Likewise if a large sample size of people gets cured (Effect A) with no other influence but prayer (Drug), then the natural conclusion is the the Drug (prayer) is causing the effect (cure).

I do agree with you that as far as I know, any reports of cures have been statistically insignificant. However, in the fairness of discussion, I want to find out if anyone has other "statistics".

Since only nay-sayers are contributing to this thread, I would draw the conclusion that in fact the answer is "No" and that proving one vs. many gods is the same (if not worse) than trying to prove no vs. a god.