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Obviously the tests have to be rigorous enough to rule out simple probability. Since they would publish the methodology before the test, one would have nothing to lose by agreeing to the challenge.
If the test is too rigorous, other people will point that out. It would be easy to get a statistician or mathematician to determine how rigorous the test has to be in order to be accurate. Any advanced stats class would take it as a five-minute assignment. It would be easy to spark enough debate that a truly accurate test could be determined.
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