A few months ago, I cited research that tested even in double blind controlled trials, the efficacy of prayer in healing patients. The results were mixed, but more importantly, I questioned whether it was theologically sensible and halakhicly permissible to conduct such trials, and, as a consequence of a negative answer to both these questions, whether such a scientific confirmation of the efficacy of prayer was even possible, in this premessianic age.
Today I stumbled across an article discussing interesting research:
“The researchers leading the studies applied clinical scientific methodologies to the study of intercessory prayer, but Cadge found that even that approach was fraught with problems. For example, researchers asked whether the people not being prayed for by the intercessors were truly a control group, since their family members were probably praying for them. Researchers also asked what the right “dosage” of prayer would be, how prayers should be offered, and what to do about non-Christian intercessors.
With double blind clinical trials, scientists tried their best to study something that may be beyond their best tools,” said Cadge, “and reflects more about them and their assumptions than about whether prayer ‘works.'”
Reflecting a recent shift toward delegitimizing studies of intercessory prayer, recent commentators in the medical literature concluded: “We do not need science to validate our spiritual beliefs, as we would never use faith to validate our scientific data.”
That last, candid sentence is perhaps the greatest insight in the article. It is simple, but revolutionary. “BREAKING NEWS, a scientist has concluded that science can neither prove nor disprove religion in general, nor any particular religion, despite the fact that both science and religion deal with matters that are of great importance and very real.” Mathematically, science and religion are in large part in perpendicular dimensions. Thus, while they both deal with very real things, as a general rule, they do not directly interfere with each other directly.
Returning to the central thesis, that prayer may ultimately not be testable, without denying that it has a very real effect. In my earlier quoted blog post, I concluded:
Our prayers matter, and have significant impact. However, as explained above, the results do not always unfold before our eyes. That alone suffices to make studies of the effectiveness of prayer futile; we won’t know how to properly define the scope of the studies, unless the people praying all share Choni haMe’agel’s greatness. However, there are potentially actual halakhic problems with conducting such experiments, and these also involves measures that would render effective prayer ineffective. First of all, we are prohibited from trying G”d, as per the verse “Ye shall not try the HaShem your G”d-Almighty (Devarim 6:16), which, as the Talmud Ta’anit 9a teaches, prohibits making one’s observance contingent upon the fulfilment of certain wishes. All the more so that it would prohibit “measuring” G”d’s response.
Furthermore, such studies are counter productive, as the Talmud teaches (Ibid. 8b), “Rabbi Yitz’haq says: blessing is only found in that, which is hidden from the eye.” G”d does not “go on vacation,” nor does he cease to hear our prayers, however, we do live in the era of הסתר פנים – “the hiding of the Countenance” – G”d is manifest in the world, but does so in a way that leaves man the freedom to deny His existance – He leaves traces, evidence, but no proof.
Mikolot Mayim Rabbim 
The purpose of prayer is, lulei demistafina, not necessarily to obtain what you are praying for so much as to create a relationship to God, to understand His mastery over all.