Perhaps one should also beware of the study by one man. I have a vague recollection of hearing that, at the time Turing was expressing his opinion of telepathy, there seemed to be experimental evidence for it, but it turned out that all the evidence came from one person, using unsound methods (including, IIRC, counting "one before" or "one after" guesses as successes if the results had higher than the expected frequency of one of those outcomes.)

Tentatively, that person may be Joseph Banks Rhine.