Suppose I find that being Mormon raises income, makes your children nicer, and does all sorts of wonderful things. In fact, suppose God blessed every person who converted instantly and spectacularly with beautiful hair and perfect teeth. Well then that would seem to really put a damper on the whole “veil” thing. The same would be true if archaeological digging revealed a big old fat stone with the genealogy from Lehi back to Joseph of Egypt and down to Moroni. At that point, really, He might as well have left the plates for us too, because he’s given away a rather chunky part of the faith needed to join the Church. Not that we couldn’t still mess up, but clearly that would be a wildly different world than the one in which we find ourselves. Whatever objective evidence we have of the gospel, God, and the truthfulness of the Church, it appears to be sufficiently ambiguous that one canchoose to believe or not, without requiring that every knee shall bow. That part, we’re told, comes later.
This can wreak havok with statistical studies of Church members. The data I see is the result of a set of decisions made both by God and by the individual. Social scientists spend a lot of time thinking about the way people behave and how that messes with statistical methods, but another real problem is how is God behaving. Is God, who reveals himself only at His pleasure and after long and careful spiritual preparation by us, likely to be uncovered by my shabby little matrix inversion? I don’t think so. God is too smart for that. So to hide Himself from me and my intrusive math, I can think of a couple clear options (outside of destroying me and so forth) He can make it so that on average, there is no observable effect of righteousnesses on whatever outcome I am looking at, or He can make sure that there are other plausible explanations.
And so, yes, Mormons do live longer. But they live about as long as you’d expect somebody with a Word of Wisdom lifestyle to live. Many Mormons are prosperous, but plenty aren’t. And anyway they work hard so it’s not miraculous– just obvious.
Here’s the fun part: To make the averages work out, of course, requires that for every inexplicable blessing God hands a member, owing to their being a member, He turns around and imposes an inexplicable trial (or curse or whatever) on that member or some other member. Of course, this is only a problem as data collection is good enough to make it an issue. If blessings are publicly unobserved, no such averaging is needed. Does that play a role in why miracles are to be kept quiet? Do my public, but inexplicable, trials* allow God to bless others publicly but inexplicably, since the balance is restored? I have no idea, but the questions are interesting.
* hypothetically, or course. All my actual trials are perfectly explicable.