JOHN - This is a sincere question—not meant to “cast doubt” etc... The church is well known for its statistical analysis of numerous issues: convert baptisms and retention, missionary efforts and baptisms, level of education and church activity rate etc... Do you know if a non-biased study has ever been done with regards to purely faith based issues such as priesthood blessings and recovery rates of certain illnesses such as cancer etc... For example—Wouldn’t a community with a large, active LDS population be expected to have a better illness recovery rate than a similar “non-LDS” community with all other things being equal (demographics, access to similar health care etc...)? This is assuming that most with a specific illness within the “active” LDS community have exercised their faith by receiving a priesthood blessing for the sick.
It’s easy for statisticians to show cause-and-effect with issues such as member missionary work and convert baptism rates, so why not with issues like prayer and priesthood blessings which are based on faith and righteousness. It would seem that there should definitely be a correlation. If there is no measurable correlation, then it appears that all blessings are just based on hard work and real faith plays little role. One could argue that it takes faith to do hard work, but many non-believing atheists work hard and haven’t the faith to move a mustard seed, much less a mountain. I realize that correlations exist between families praying together and youth retention rates, teenage pregnancy etc... , but this is not what I’m referring to. There are many more variables when looking at those types of issues. But issues purely involving faith, because all other works have been exhausted, are what I’m asking about.

JOEL - As far as I know there have been no studies performed on this subject, nor do I think there ever will be. God answers the faithful prayers of both LDS and non-LDS, so I doubt that the prevalance of such things could be identified only within LDS communities. Also often times priesthood blessings and faith-based healings are considered sacred experiences to be kept private; not something that would be shared through some sort of poll.
While on the earth Jesus often healed in private and then departed. When He healed, He often charged, "See thou tell no man; but go thy way" (Matthew 8:4; see also Luke 8:56).

Priesthood blessings allow us to call on the powers of God, as well as our faith, to change a changeable condition or situation, that would have continued had we not given the blessing; so long as that person is not appointed to experience the trial.

In regards to the outcome of priesthood blessings God tells us:

“And again, it shall come to pass that he that hath faith in me to be healed, and is not appointed unto death, shall be healed” (D&C 42:48).

All too often people overlook the qualifying phrase “and is not appointed unto death” (“or,” we might add, “unto sickness or handicap”).
Sometimes priesthood blessings are given simply to help the person survive the illness or problem rather than to cure them. What might seem as a failure of the priesthood to heal is simply an opportunity for the person to grow in character and prove his faith in the face of adversity.
The scriptures tell us that faith without works is dead (James 2: 17, 20, 26), so of course God wants us to do do all we can for ourselves to improve our situation, but I don't see how one can prove that faith or the priesthood play no part in the healing process.

God gives this great promise for those who exercize their faith by the giving and receiving of priesthood blessings:

"And the elders of the church, two or more, shall be called, and shall pray for and lay their hands upon them in my name; and if they die they shall die unto me, and if they live they shall live unto me." (D&C 42:44 )

So the way I see it priesthood blessings help regardless of the outcome. With all the different situations and outcomes that are possible with priesthood and faith-based healings, I don't see how such a thing could be quantified.
My own personal experience with this has me convinced that priesthood and faith deffinately make a difference when it comes to healing the sick, when all works have been exhausted.