Okay, this proves that they just don't get it! How can they measure and study prayer when they don't even understand it??! God is not some genie in a bottle that you rub the right way and get your wish! There is no "formula" or "equation". It is a relationship. A conversation. A meeting of the minds and the wills.
And they think they can set up a test that will measure God's effectiveness? Remember the temptation of Christ? When Satan wanted him to throw himself off the temple top and let the angels run and catch him, Christ said you don't put the Lord God to foolish tests.
Yes, prayer could be proven. But I don't believe God will allow it. If He did then there would be no faith required. The Bible tells us that Salvation comes by faith. And the salvation of mankind is God's most important mission. He would not jeopardize it.
As for their doubt and "explanations" of the miracles God performs I feel like the little boy in the joke: He's on the park bench reading where Moses led the Israelites thru the parted Red Sea. And he starts praising God and His greatness. A man on the bench asks him what he's so excited about. When the boy tells him, the man tells him that science has proven that the water level was probably much lower then, just a few inches and was no real feat for them to walk across. The boy, quiet, returns to Exodus. In a few minutes he goes to jumping and hollering and praising God all the more. The startled man asked, "Why, didn't I just explain to you this was foolishness?" But the boy said, "Mister, God drowned the whole Egyptian army in just a few inches of water!"
Thank God there are scientists out there that are also Christians. That can see and accept the hand of God, and admit wedon't know it all and never will in this world.
As for the others, that's okay. Let 'em do their thing. One day their knee will bow and their tongue confess.