The purpose of the BMJ piece was to ask the reader the following
question: Given a 'study' that looks methodologically correct, but tests
something that is completely out of our frame (or model) of the physical
world (e.g., retroactive intervention or badly distilled water for asthma)
would you believe in it?
There are three ways to deal with this question:
1. To answer in the affirmative. But this leads to such paradoxes (some
described by the responders to this article) that it is incompatible with
our scientific work, or even with our daily life.
2. To look for methodological or statistical faults. Here an obvious one
was that the duration of fever and the duration of hospital stay are
related. But what if the next 'study' will sport perfect methodology and
3. To deny from the beginning that empirical methods can be applied to
questions that are completely outside our scientific model of the physical
world. Or in a more formal way, if the pre-trial probability is
infinitesimally low, the results of the trial will not really change it,
and the trial should not be performed. This is what, to my mind, turns the
BMJ piece into a 'non-study' although the details provided in the
publication (randomization done only once, statement of a wish, analysis,
etc.) are correct.
The article has nothing to do with religion. I believe that prayer is a
real comfort and help to a believer. I do not believe it should be tested
in controlled trials.