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If you consider "prayer" as a major ingredient of the over-all life of a disciple, then the answer is an overwhelming affirmation of benefits! E.g. The statistics of those in drug therapy involving Christian discipleship points to a massive benefit for success! (See the results of Teen Challenge compared to government or secular programs. I did a Master's research project on this.)
Just yesterday a research (which I missed the name of) revealed that the happiest sub-group in society were older women "of faith." The poll was a recent one.
You might check the George Barna Research Group for religious surveys. They have been around for a long time, so the Standard Deviation would be minimal.
It should be kept in mind, as previously commented above, that most prayers are private communications with Deity. So absence of institutional statistical research must not be an inference of no benefit. That would be a fallacy of logic: the argument from silence. Peace.
Note, Barna Research Group is in California, and the Teen Challenge Group is in New York. (See Google for addresses.)