What they do when they study prayer is that they have two large groups of patients. The two groups are both told that they are being prayed for. Only one group is actually being prayed for. There's a mix of all faiths in both groups. The people praying would be genuinely praying, wanting to give positive outcomes to the patients.
At the end, the results of both groups are measured by people who aren't sure which group is which.
Then, after the results are gained by people who didn't know who to root for, the results are shared with people who did know which group was which.
What ends up happening is that both groups had equal results.
They're not testing miracles, they're testing it like they'd test Advil vs a Placebo to see if Group A reports fewer headaches than Group B, who got the placebo.
Prayer has no impact.http://www.nytimes.com/2006/03/31/health/31pray.html?pagewanted=all&_r=0
I've also been involved in prayer circles and other things in my time as a believer. There are no miracles that anyone can verify. Even improbable medical outcomes are improbable, not impossible, and play out exactly as they would normally.
If a hospital has 12 patients with a 25% chance to live, and 4 of them live, that's not a miracle, that's medical/scientific probability.
If god answered prayer, that would affect the natural world. If god affected the natural world, it could be measured.
For example, if Jesus was around today, and could heal amputees, that would be easily measurable by science. It's not that science fails to measure prayer, it's that prayer doesn't work.