  Tests of models for new physics appearing in neutrino experiments often
involve global fits to a quantum mechanical effect called neutrino
oscillations. This paper introduces students to methods commonly used in these
global fits starting from an understanding of more conventional fitting methods
using log-likelihood and $\chi^2$ minimization. Specifically, we discuss how
the $\Delta\chi^2$, which compares the $\chi^2$ of the fit with the new physics
to the $\chi^2$ of the Standard Model prediction, is often interpreted using
Wilks's theorem. This paper uses toy models to explore the properties of
$\Delta\chi^2$ as a test statistic for oscillating functions. The statistics of
such models are shown to deviate from Wilks's theorem. Tests for new physics
also often examine data subsets for "tension" called the "parameter goodness of
fit". In this paper, we explain this approach and use toy models to examine the
validity of the probabilities from this test also. Although we have chosen a
specific scenario -- neutrino oscillations -- to illustrate important points,
students should keep in mind that these points are widely applicable when
fitting multiple data sets to complex functions.
