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Classical hypothesis testing constitutes the backbone upon which scientific results are produced in most fields, but it is now under attack as a facilitator of the so-called reproducibility crisis. Although classical testing has been paramount to the discovery of the Higgs boson and the "five-sigma" threshold is considered more robust than the two-sigma threshold used in other fields, the approach has intrinsic limitations even in particle physics;
I will review the classical approach, comparing it with the Bayesian one, and delve into a few spectacular examples of "flukes" from particle physics.
Finally I will give a few perspectives in view of the latest debates on the topics of severe testing and causality in statistical inference.