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It is not generally known, that the inequality that Bell derived using threerandom variables must be identically satisfied by any three corresponding datasets of plus and minus 1s that are writable on paper.This surprising fact isnot immediately obvious from Bell's inequality derivation based on causalrandom variables, but follows immediately if the same mathematical operationsare applied to finite data sets.For laboratory data, the inequality isidentically satisfied as a fact of pure algebra, and its satisfaction isindependent of whether the processes generating the data are local, nonlocal,deterministic, random, or nonsensical.It follows that if predicted correlationsviolate the inequality, they represent no three cross correlated data sets thatexperimentally exist or can be generated from valid probability models.Reported data that violate the inequality consist of probabilisticallyindependent data pairs and are thus inconsistent with inequality derivation.Inthe case of random variables as Bell assumed, the correlations in theinequality may be expressed in terms of the probabilities that give rise tothem.A new inequality results, the Wigner inequality that must be satisfied byquantum mechanical probabilities in the case of Bell experiments.If that werenot the case, predicted quantum probabilities and correlations would beinconsistent with basic algebra.

The Bell inequality, inviolable by data used consistently with its  derivation, leads to quantum correlations that satisfy it, and probabilities  that satisfy the Wigner inequality