  Nucleon-Nucleon potentials are commonplace in nuclear physics and are
determined from a finite number of experimental data with limited precision
sampling the scattering process. We study the statistical assumptions implicit
in the standard least squares fitting procedure and apply, along with more
conventional tests, a tail sensitive quantile-quantile test as a simple and
confident tool to verify the normality of residuals. We show that the
fulfilment of normality tests is linked to a judicious and consistent selection
of a nucleon-nucleon database. These considerations prove crucial to a proper
statistical error analysis and uncertainty propagation. We illustrate these
issues by analyzing about 8000 proton-proton and neutron-proton scattering
published data. This enables the construction of potentials meeting all
statistical requirements necessary for statistical uncertainty estimates in
nuclear structure calculations.
