Optimal Statistical Analyses of Bell Experiments

We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce noise the estimation of Bell’s S or Eberhard’s J. Further improvement was obtained Wilks likelihood ratio test based on four tetranomially distributed vectors counts different outcome combinations, one 4-vector for each setting combinations. The methodology illustrated application loophole-free Bell 2015 2016 performed Delft Munich, at NIST, Vienna, respectively, also earlier (1998) Innsbruck experiment Weihs et al. recent (2022) Munich Zhang al., which investigates use a as part protocol device-independent quantum key distribution (DIQKD).