  Observables in particle physics and specifically in lattice QCD calculations
are often extracted from fits. Standard $\chi^2$ tests require a reliable
determination of the covariance matrix and its inverse from correlated and
auto-correlated data, a challenging task often leading to close-to-singular
estimates. These motivate modifications of the definition of $\chi^2$ such as
uncorrelated fits. We show how the goodness-of-fit measured by their p-value
can still be estimated robustly for a broad class of such fits.
