Well, again, thanks for all the responses, but again, no one has actually given me an answer to the question I have posed.
Yes, I am aware that an actual computation of the probability is not possible. Yes, I am aware of the limitations of asking people to remember such occurrances, that they are not likely to remember misses, etc.
But I am not asking for an assessment of the probability of such an occurrance. What I am asking is at what point do you stop considering coincidence to be a justifiable explanation and start examining other possibilities. This is known as setting the significance level for a test. It is generally recommended that this level be settled on prior to beginning a study.
Generally, for most experiments and studies, 95% is used. That is, you have a 5% chance of wrongly rejecting the null hypothesis - in this case, the null would be that such events are just coincidence.
Now, I agree with the idea that extraordinary claims require extraordinary evidence. JREF requires a 99.9% level of confidence for the preliminary test, and a 99.9999% level of confidence to win the million, equivalent to a 1 in a million chance it was just coincidence.
Assuming we had the ability to gather accurate data on the phenomena (I know, a BIG assumption but just pretend it could be done), what level of significance would be appropriate for rejecting the null hypothesis?
Beth