Analysis of assumptions of recent tests of local realism

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.