  Likelihood ratio tests are a widely used method in global analyses in
particle physics. The computation of the statistical significance (p-value) of
these tests is usually done with a simple formula that relies on Wilks'
theorem. There are, however, many realistic situations where Wilks' theorem
does not apply. In particular, no simple formula exists for the comparison of
models that are not nested, in the sense that one model can be obtained from
the other by fixing some of its parameters. In this paper I present methods for
efficient numerical computations of p-values, which work for both nested and
non-nested models and do not rely on additional approximations. These methods
have been implemented in a publicly available C++ framework for maximum
likelihood fits called myFitter and have recently been applied in a global
analysis of the Standard Model with a fourth generation of fermions.
