  The violation of Bell, CHSH and CH inequalities indicates only that the
assumption of "conterfactual definiteness" and/or the probabilistic models used
in proofs were incorrect. In this paper we discuss in detail an intimate
relation between experimental protocols and probabilistic models. In particular
we show that local realistic and stochastic hidden variable models are
inconsistent with the experimental protocols used in spin polarization
correlation experiments. In particular these models neglect a contextual
character of quantum theory (QT) and do not describe properly quantum
measurements. We argue that the violation of various inequalities gives
arguments against the irreducible randomness of act of the measurement.
Therefore quantum probabilities are reducible what means that QT is emergent.
In this case one could expect to discover in time series of data some
unpredicted fine structures proving that QT is not predictably complete what
would be a major discovery.
