  Local realism in recent experiments is excluded on condition of freedom or
randomness of choice combined with no signaling between observers by
implementations of simple quantum models. Both no-signaling and the underlying
quantum model can be directly checked by analysis of experimental data. For
particular tests performed on the data, it is shown that two of these
experiments give the probability of the data under no-signaling (or choice
independence in one of them) hypothesis at the level of 5%, accounting for the
look-elsewhere-effect, moderately suggesting that no-signaling is violated with
95% confidence. On the other hand the data from the two other experiments
violate the assumption of the simple quantum model. Further experiments are
necessary to clarify these issues and freedom and randomness of choice.
