coincidences in each category (N++, N−−, N+− and N−+) are recorded. The experimental estimate for E(a, b) is then calculated as: Once all four E’s have been estimated, an experimental estimate of the test statistic can be found. If S is numerically greater than 2 it has infringed the CHSH inequality. The experiment is declared to have supported the QM prediction and ruled out all local hidden-variable theories. A strong assumption has had to be made, however, to justify use of expression (2). It has been assumed that the sample of detected pairs is representative of the pairs emitted by the source. That this assumption may not be true comprises the fair sampling loophole. The derivation of the inequality is given in the CHSH Bell test page. A typical CH74 (single-channel) experiment Prior to 1982 all actual Bell tests used "single-channel" polarisers and variations on an inequality designed for this setup. The latter is described in Clauser, Horne, Shimony and Holt's much-cited 1969 article as being the one suitable for practical use. As with the CHSH test, there are four subexperiments in which each polariser takes one of two possible settings, but in addition there are other subexperiments in which one or other polariser or both are absent. Counts are taken as before and used to estimate the test statistic. where the symbol ∞ indicates absence of a polariser. If S exceeds 0 then the experiment is declared to have infringed Bell's inequality and hence to have "refuted local realism". In order to derive (3), CHSH in their 1969 paper had to make an extra assumption, the so-called "fair sampling" assumption. This means that the probability of detection of a given photon, once it has passed the polarizer, is independent of the polarizer setting (including the 'absence' setting). If this assumption were violated, then in principle a local hidden-variable (LHV) model could violate the CHSH inequality. In a later 1974 article, Clauser and Horne replaced this assumption by a much weaker, "no enhancement" assumption, deriving a modified inequality, see the page on Clauser and Horne's 1974 Bell test. Experimental assumptions In addition to the theoretical assumptions made, there are practical ones. There may, for example, be a number of "accidental coincidences" in addition to those of interest. It is assumed that no bias is introduced by subtracting their estimated number before calculating S, but that this is true is not