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Bell inequality. To make this claim, the number needs to be supplemented with an
estimate of its standard error as described in Section 11.2.3. Since the experiment
was run over roughly 8 hours to collect around 34.1 million statistical samples
for each of the involved probabilities, the standard error is most likely dominated
by 1/f noise and drifts in the experiment. Thus, one would need to model these
error mechanisms in order to obtain a meaningful estimate for the standard error.
This can be avoided by breaking the dataset into sections for which the standard
error is known to be dominated by statistical sampling noise.
11.5 Analysis and Verification
11.5.1 Standard Error of the S-Value
To find the right section size, the dataset is tentatively split into n sections.
Each section is then divided into two halves that each yield an S-value S i,1 and
S i,2 . The difference between these can be used as a drift-sensitive estimate of the
internal variance for each section:
v i = (S i,2 − S i,1 ) 2 (11.5)
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