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Mark_Eichenlaub comments on Original Research on Less Wrong - Less Wrong
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You're right. That would be true if we did n independent tests, not one test with n-times the subjects.
e.g. probability of 60 or more heads in 100 tosses = .028
probability of 120 or more heads in 200 tosses = .0028
but .028^2 = .00081
Amazing, innit? Meanwhile in the land of the sane people, the likelihood function from any given propensity to come up heads, to the observed data, is exactly squared for 120 in 200 vs. 60 in 100.