Bell's inequality violation experiments are becoming increasingly popular in the practical teaching of undergraduate and master's degree students. Bell's parameter S is obtained from 16 polarization correlation measurements performed on entangled photons pairs. We first report here a detailed analysis of the uncertainty u(S) of Bell's parameter taking into account coincidence count statistics and errors in polarizers' orientation. We show using both computational modeling and experimental measurement that the actual sequence of the polarizer settings has an unexpected and strong influence on the error budget. This result may also be relevant to measurements in other settings in which errors in parameters may have non-random effects in the measurement.

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As usual when measuring coincidence rates, the non-perfect quantum efficiency of the detection system is irrelevant as long as it is random and independent of the photon polarization which is the case here. We can, therefore, assume that all pairs transmitted by both polarizers are detected, or alternatively that undetected photon pairs were not even generated.
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