  Application of a Goodness--of--fit (GOF) statistic is an essential element of
parameter estimation. We discuss the computation of GOF when estimating
parameters from anisotropy measurements of the cosmic microwave background
(CMB), and we propose two GOF statistics to be used when employing approximate
band--power likelihood functions. They are based on an approximate form for the
distribution of band--power estimators that requires only minimal experimental
information to construct. Monte Carlo simulations of CMB experiments show that
the proposed form describes the true distributions quite well. We apply these
GOF statistics to current CMB anisotropy data and discuss the results.
