Thanks to The Atheist Missionary for drawing attention to this on twitter.
This is a win-win experiment to set up for the purposes of evangelizing of course.
Reasons why you should perhaps expect some positive reports include:
(i) Atheists who agree to sign up to this fairly onerous prayer regime are more likely to think there might be something to religious belief (one positive was clearly already flip-flopping - see the letter below).
(ii) Power of suggestion: if you tell people to pray, meditate, etc. and that something unusual may be experienced, it's rather more likely to be reported. Chris French's experiment on crystals confirms that people will tend to report unusual psychological effects whether they hold a real or fake crystal - in short the effect, such as it was, was all in the mind. There's reason to expect a similar effect here.
(iii) Events (coincidences, say) can easily be interpreted as divine signs, even when they are not.
(iv) We have a natural propensity to religiosity. Some religious response is therefore to be expected whether or not there's any truth to religion.
Any positives can function as anecdotal evidence (psychologically very effective in underpinning belief, even if typically worthless as evidence) and the negatives can be quietly downplayed or forgotten.
In addition, negative results can be explained away (and were by some commentators) as being due to the atheists not praying properly, with commitment, etc. If all results are negative, the entire episode can be dismissed as a mere absence of evidence, not evidence of absence. Brierley himself suggests God cannot be "put in a test tube" (a very useful immunizing move).
Philosopher Theist Tim Mawson (who is a friend of mine) does a pretty interesting commentary, I think (which is not to say we agree about everything). The experiment actually grew out of a paper of his.
PZ Myers's thoughts on the experiment here.
A letter received by Brierley below:
I think I was hoping he would join me so I could use the experiment kind of as a way to just admit it. I then realised that I could no longer live without God. With God I feel like I have hope and positivity. I feel safe. I feel like I have direction. I found that when I was an atheist I felt lost and alone. I just couldn't deny my belief any longer.