# Calculating statistical significance of peak over background in counting experiment

I histogrammed the invariant masses of particular events in a counting experiment. There is a specific peak which towers over the expected exponential background. How can I give the statistical significance of this peak in a similar way to how a discovery in particle physics is announced at 5-sigma? i.e. how can I say 'this peak is evidence for an x-sigma discovery'?

• Relevant arxiv article: Signal Significance in Particle Physics – lemon Apr 19 '16 at 11:04
• Do you know how to calculate the $p$ value in each bin of the histogram? This would give you the local significance. This usually involves throwing a vast amount of Monte Carlo pseudo experiments or using Asympotic Formulae (arxiv.org/abs/1007.1727) to approximate the result. – pfnuesel Apr 19 '16 at 12:01
• @pnfnusel that's not quite right. Local significances include all the data. But only consider a fixed e.g. mass and width of the resonance. A global significance considers the probability of such an extreme test-statistic for any of the mass/width hypotheses considered. – innisfree Apr 19 '16 at 12:10
• Are you doing a hypothesis test (a background model versus a signal model) or just a goodness-of-fit (testing background only)? – innisfree Apr 19 '16 at 12:13
• What sources of errors are there? Only statistical? Or appreciable systematic too? – innisfree Apr 19 '16 at 12:17