The Significance of an Excess in a Counting Experiment: Assessing the Impact of Systematic Uncertainties and the Case with a Gaussian Background

Several experiments in high-energy physics and astrophysics can be treated as on/off measurements, where an observation potentially containing a new source or effect (“on” measurement) is contrasted with a background-only observation free of the effect (“off” measurement). In counting experiments, the significance of the new source or effect can be estimated with a widely used formula from Li & Ma, which assumes that both measurements are...