  The evaluation of the error to be attributed to cut efficiencies is a common
question in the practice of experimental particle physics. Specifically, the
need to evaluate the efficiency of the cuts for background removal, when they
are tested in a signal-free-background-only energy window, originates a
statistical problem which finds its natural framework in the ample family of
solutions for two classical, and closely related, questions, i.e. the
determination of confidence intervals for the parameter of a binomial
proportion and for the ratio of Poisson means. In this paper the problem is
first addressed from the traditional perspective, and afterwards naturally
evolved towards the introduction of non standard confidence intervals both for
the binomial and Poisson cases; in particular, special emphasis is given to the
intervals obtained through the application of the likelihood ratio ordering to
the traditional Neyman prescription for the confidence limits determination.
Due to their attractiveness in term of reduced length and of coverage
properties, the new intervals are well suited as interesting alternative to the
standard Clopper-Pearson PDG intervals.
