The main purpose of scattering experiments is to unveil the underlying structure of the colliding particles and their interaction. Typically one measures scattering observables (cross sections and polarizations) at discrete angles and energies and mutually consistent data may validate or falsify
proposed theories or models. However, the accumulation of data from different laboratories while
potentially improves the statistical significance it may sometimes generate mutually inconsistent
data as a side-effect. Thus, some decision has to be made on what are the maximal amount of data
which are mutually compatible. We show elastic πN and NN scattering as prominent examples
where this selection is called for. We discuss how it can be done in a self-consistent manner
invoking a principle of maximal consensus of the database and with the help of a sufficiently
flexible model involving a minimal number of theoretical assumptions. In the NN case this has
become possible with a combination of long distance field theoretical constraints at the hadronic
level such as pion exchanges and electromagnetic effects and a coarse graining of the unknown
interaction over the shortest de Broglie wavelength being probed in the scattering process.