Firstly, I mentioned signal detection theory because on a brief read through, this paper seems to want to be a signal detection theory paper - hits, misses, correct rejection, and a number of graphs that look very like they should have a ROC curve on them. I should have guessed that you did look into it, I have only read such papers and can offer less insight than you doubtless have.

I would like to explain why I became concerned about the paper. I was never going to read it without the largely peripheral claim that it debunks ESP. This comment is somewhat disingenuous to parapsychology and several good, but heavily criticised, studies. As all good sceptics should agree, it is reasonable to class the claim of 'ESP debunked' as an extraordinary claim, one that requires extraordinary evidence.

Does this paper provide extraordinary evidence of anything? Would it pass in the scientific world inhabited by parapsychologists that is so easily dismissed by knowledgeable sceptics. (I should state here I have no formal interest in parapsychology, but I do find it fascinating).

I mentioned that I was initially concerned about Q (derivation point 5). The derivation seems sound enough reading through it (without actually checking, I trust you!), but Q is ultra-conservative. It would be much more reasonable at Q=3/9 or 4/9. After 3 seconds of inspecting a stimuli, a presumption of no knowledge is not reasonable, e.g. I imagine I could always spot a hat. I understand why your novel analysis technique does not allow this though. On the positive side, it leaves you reporting only around 4 trials out of 100 in Exp 1, a small number on which to base your interpretation of a significant result. Some would question this in a task where participants had to reliably click a 9 choice response and not make a 4% 'mechanical' response error (on the balance of probability, whilst knowing the answer), or confuse the change occasionally for a previous trial response (or the next one if demonstrating precognition?). Given the other thread, this is backed up by a control experiment tending towards significance.

Now, I understand that control experiments are good so long as they remain not significant. It would also be my understanding that in some cases requiring extraordinary evidence, the control would be very easy to debunk if it was not a very close approximation to the experiments it claimed to support. I think there are too few similarities between Exp 1 and 4 to draw any firm conclusion. Making large changes to an experiment, and then nearly getting the same result, is not a strong control and is simple to dismiss.

The problem with the control is compounded when we know that Q is ultra-conservative. Anything less conservative for Q in experiment 4, and your control becomes significant (I'm pretty sure the direction of change in significance levels on that is correct). How do we then reasonably suggest that it can rule out the other possibilities?

I am interested in what your Q was for experiment 3 though, I could probably work it out quite quickly, but it is not immediately obvious (it would be if I were a better statistician!). Experiment 3 does not seem too surprising on the face of it, it is interesting to note there was very little guessing. So when you change a large proportion of the colour of something from red to green or vice versa, people can tell. I am unsure that this relates to a subtle change in eye liner on someone’s face, and completely mystified as to how it relates to ESP.

I don't want to labour over small points, and I am happy for you to show me I am wrong on anything above (mainly the control and the conservative Q). After all, you have worked on it for months, where as I can only claim to have read it a couple of times. Following the claims for ESP debunking, I wanted to demonstrate that scepticism is easy to do, but perhaps muddies the water and is not very healthy for science. Maybe I succeeded at that, in some small way, although I doubt it!