It's the same in LHC there are two experiments that run independently, ATLAS and CMS. For exactly this reason. The Higgs was discovered by both independently w

It's the same in LHC there are two experiments that run independently, ATLAS and CMS. For exactly this reason. The Higgs was discovered by both independently with higher than 5 sigma each. The combined sigma of the 2 experiments was 7-ish if my memory serves correct. EDIT: My memory serves correct because sqrt(5^2 + 5^2) ~ 7