In HEP, it’s more that the bar is so damned high, and your n equals something in the billions or trillions, and oversight from the community is extreme. The confidence required for example, to make people feel generally positive about the discovery of the Higgs boson, was in the realm of billions to one. Generally there is a model, and dats needs to fit that model to what would be an insane degree of confidence in most other fields.
There is a bit more to it than just pure sigma values; it is also a matter of how closely the data fits the model overall, a lack of competing hypotheses to explain said data, and to what degree other evidence exists to support the model. Of course, if the theory being confirmed is complementary to existing physics, that also helps a lot. Having said that, 3 sigma is about when people started to get excited about the Higgs, and 5 sigma was confirmation.
There is a bit more to it than just pure sigma values; it is also a matter of how closely the data fits the model overall, a lack of competing hypotheses to explain said data, and to what degree other evidence exists to support the model. Of course, if the theory being confirmed is complementary to existing physics, that also helps a lot. Having said that, 3 sigma is about when people started to get excited about the Higgs, and 5 sigma was confirmation.