  We present a new inequality constraining correlations obtained when
performing Einstein-Podolsky-Rosen-Bohm experiments. The proof does not rely on
mathematical models that are imagined to have produced the data and is
therefore ``model-free''. The new inequality contains the model-free version of
the well-known Bell-CHSH inequality as a special case. A violation of the
latter implies that not all the data pairs in four data sets can be reshuffled
to create quadruples. This conclusion provides a new perspective on the
implications of the violation of Bell-type inequalities by experimental data.
