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Local realism in recent experiments is excluded on condition of freedom orrandomness of choice combined with no signaling between observers byimplementations of simple quantum models. Both no-signaling and the underlyingquantum model can be directly checked by analysis of experimental data. Forparticular tests performed on the data, it is shown that two of theseexperiments give the probability of the data under no-signaling (or choiceindependence in one of them) hypothesis at the level of 5%, accounting for thelook-elsewhere-effect, moderately suggesting that no-signaling is violated with95% confidence. On the other hand the data from the two other experimentsviolate the assumption of the simple quantum model. Further experiments arenecessary to clarify these issues and freedom and randomness of choice.

Analysis of assumptions of recent tests of local realism