On the measurement of binomial data with background

This paper analyzes in detail how to estimate, from the fraction of events that pass a cut, the fraction of signal events present in the sample. We examine various methods which give the confidence interval of the amount of signal, taking into account the cut efficiencies (with their uncertainties) for the signal and background detection. The coverage properties of these confidence intervals are studied in detail from the frequentist point of view. The problem to find a reliable significance to test for the presence of the signal in the sample is also solved in the framework of the profile likelihood method.