It's possible to combine the data and get a higer significance. AFAIK, Officially, CERN doesn't do these combinations, but independent people do. See here:
This paper combines different channels from CMS, but not CMS and ATLAS.
"In this Letter, we report on the combination of Higgs boson searches carried out in proton-proton collisions at
Sqrt[s] = 7 TeV using the Compact Muon Solenoid (CMS) detector at the LHC.
...
Combined results are reported from searches for the SM Higgs boson in proton-proton collisions at Sqrt[s] = 7TeV in five Higgs boson decay modes: gg, bb, tt, WW, and ZZ."
Those two detectors are attached to the same accelerator, right? My guess is they don't because they cannot guarantee the results to be independent from each other?
Clarification:
http://public.web.cern.ch/public/en/lhc/LHCExperiments-en.ht...