From this it follows that the local hidden variables assumption is rejected if but the angles 0 , 1 , 2 can easily be chosen to satisfy this inequality. Thus the hypothesis of local hidden variables is false. The prototypical Bell inequality, and accompanying experiment, has in recent years spawned a multitude of variations involving more than two particles, measurements with more than two outcomes, and more than two possible measurements at each location; see for instance Zohren, et al. (2010) for a striking version of ”Bell” obtained simply by letting the number of outcomes be arbitrarily large. Popular inequalities and experiments are compared in terms of statistical efficiency by Van Dam et al. (2005). Other connections to statistics (missing data theory) and open problems are surveyed in Gill (2007). We claimed above that there were experimental results that violated Bell’s inequality and therefore ruled out local hidden variables. However, there remains several small possible loopholes. Perhaps the most important one of which is the following: in these experiments for every entangled pair that we measure we often fail to detect one of the two particles because the current experimental set-up is imperfect. The experimental results we noted above are actually the results conditional on both particles’ spins being measured. If those pairs were not representative of all pairs, that is, if the missing pairs are not missing at random, it is logically possible that the experimental results can be explained by local hidden variables where the values of Y 1 ( x 1 ) and Y 2 ( x 2 ) also determine the probability of the spin of both being Discussion E [ M (1 , 2)] − E [ M (0 , 2)] − E [ M (1 , 0)] − E [ M (0 , 0)] = sin $^{2}$(Δ 12 / 2) − sin $^{2}$(Δ 02 / 2) − sin $^{2}$(Δ 10 / 2) − 0 sin $^{2}$(Δ 12 / 2) > sin $^{2}$(Δ 02 / 2) + sin $^{2}$(Δ 10 / 2) 6