I should point out that many fields have commonly used p ≤ .05 as a "significance line". The significance line in particle physics is generally 5-sigma, or p ≤

I should point out that many fields have commonly used p ≤ .05 as a "significance line". The significance line in particle physics is generally 5-sigma, or p ≤ 3x10⁻⁷. The Higgs is now at p ≤ 1x10⁻⁹. I think that meets GP's criteria of obviousness, at least in spirit. Also -- you can look at the plots in the Higgs discovery papers and go "oh yeah, there's definitely a bump there".