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A number of papers have suggested that it is inappropriate to combine datafrom different experiments when undertaking experimental tests of Bell'sinequalities. It has been suggested that a correct analysis, using a singleprobability space, leads to inequalities which are not violated by experiment.If correct, this would be contrary to the normal interpretation of suchexperimental data.  However, in this note, a generalised Clauser-Horne-Shimony-Holt (CHSH)inequality is derived for a system of four experiments constructed on a singleprobability space which combines the data from the four experiments. It isshown that this leads to the standard CHSH inequality which is normally used tointerpret experimental data. Thus the commonly accepted conclusion thatexperimental violations of Bell's inequality imply that local realistic modelsare inconsistent with the predictions of quantum mechanics has not beenchallenged.

CHSH Inequality on a single probability space