There have been studies trying to prove whether or not payers work as well as studies trying to prove the existence of God.
This article flips it, and asks if there is a science to prayers? I don't think there is a concrete answer to either question.
http://www.ifcj.org/learn/holy-land-moments/daily-devotionals/jacobs-sword-and-bow-1.html
My take is exactly this from the article: "Ultimately, it’s hard to study something that can’t be seen or measured. For believers, it’s from faith and experience that we know how deeply prayer impacts our lives."
And I would say it is the same for skeptics. What would it take to convince a skeptic to believe, or a believer not to believe?