  The Nucleon-Nucleon interaction is the starting point for ab initio Nuclear
Structure and Nuclear reactions calculations. Those are effectively carried out
via effective interactions fitting scattering data up to a maximal center of
mass momentum. However, NN interactions are subjected to statistical and
systematic uncertainties which are expected to propagate and have some impact
on the predictive power and accuracy of theoretical calculations, regardless on
the numerical accuracy of the method used to solve the many body problem. We
stress the necessary conditions required for a correct and self-consistent
statistical interpretation of the discrepancies between theory and experiment
which enable a subsequent statistical error propagation and correlation
analysis. We comprehensively discuss an stringent and recently proposed
tail-sensitive normality test and provide a simple recipe to implement it. As
an application, we analyze the deduced uncertainties and correlations of
effective interactions in terms of Moshinsky-Skyrme parameters and effective
field theory counterterms as derived from the bare NN potential containing
One-Pion-Exchange and Chiral Two-Pion-Exchange interactions inferred from
scattering data.
