Many years have passed since I taught statistical analysis at university level. One very important aspect of statistical analysis that people without
professional background in the area may not know, is that confidence is a specific, measurable mathematical concept. The confidence level that the
variable for which one is testing has produced a measurable result increases with the number of subjects tested, in a way that can be computed. (To
reverse the way of putting it: a smaller subject group has a greater possibility of giving results that are atypical. E.g. if you use a small random
sample, there is greater likelihood that you have, by chance, grabbed ones who are not representative of the whole population.)
As a Christian informed by the Scripture, I would expect that generic prayer studies having to do with the human effects of prayer would not give uniform results, because of factors related to God's response. One factor that I would expect to be important: are the prayers addressed to the Biblical God of Christianity, or to some other god? The Scriptures declare that Yahweh does not like others to get credit for what He does. (I have always understood this to mean that the good He does for people bears good fruit when people recognize His love and draw closer to Him with thankful hearts.) Jesus teaches that He, Himself, is the only way to the Father. That sounds like prayers of those who reject Him will not connect to the Father. Jesus also spoke of praying to the Father in His name. And, He taught that one is to pray, believing.
And, of course, there is the fact that the Lord does not always favor healing, in this life. Sometimes, for believers, the healing comes in heaven, and their bodies may not be healed until their resurrection.
I recall one of my undergraduate professors mentioning a study in which people prayed for some plants, while the control group of plants did not have
people praying for them. The prayed-for group did better.
He remarked that, if he had set up the study, he would have liked to have set up a third group of plants, which people would curse, and observe whether the group which was cursed had any measurable differences.
Your plant study, Scholar, reminds me of something similar done some years back (I can't recall the program) as it was 20 odd years back. It was
nothing formal, on some kids program, or the like. Surprisingly enough, the stuff that was abused did not grow as well as the "control" group.
I am of the opinion that prayer does have a measurable effect, however, it would be difficult to quantise in that the various groups who are studied may well be at different understanding of God's relationship to man. i.e. some Christians do not think that God does not work "that way" any more, others, "expect" it whilst others may think "God is punishing me, so why would he heal me", yet others "God is teaching me something" and so on. That is only a small sample of the various "excuses" that I have heard in the various groups with which I have had contact over the years. Statistically, it would be difficult to quantise results, given all the variables involved. i.e. nature of the illness, faith level of those who do believe in prayer, and so on.
I thought the most interesting part was that those who did not know they were being prayed for showed greater improvement. Maybe whatever deity exists doesn't like showiness.