Estimating statistical significance and sensitivity

In particle physics a search for a new signal process often takes the
form of a frequentist statistical test based on observed numbers of
events.  An approximate expression is derived for the expected
discovery significance for a Poisson counting experiment in which the
background rate is constrained by a Poisson control measurement.  The
validity of the new expression is compared with Monte Carlo results
and to other formulae for expected significance often used in particle
physics.

In general the statistical tests make reference to the numbers of
events expected under different hypotheses, and in some cases these
numbers are estimated using weighted Monte Carlo events.  Methods for
incorporating such events into a statistical tests are examined and
the properties of several approaches are investigated with numerical
examples.