Symbol z
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≈ 0.0086 , well under one percentage point. The paper’s own forty-percent threshold sits 0.40 - 0.3333 0.0667 above that null mean, which is z 7.75 standard deviations out — a one-sided tail probability, by the normal approximation to the binomial (valid here since n 667 , far above the usual rule-of-thumb minimum), of roughly 4.7 10^{-15} . At three thousand trials per dataset, in other words, a classifier with no position sensitivity of any kind would essentially never cross this threshold by chance, in either direction. Whatever explains the measured pattern, it is not noise inflated by a lenient bar. This computation does not touch the paper’s…
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Equation 8 · Language Models & Evaluation
Cognitive Bias Was the Label; Attention Sink Is the Suspect
This equation gives an approximation: it relates the quantities while allowing an approximation.
≈ 0.0086 , well under one percentage point. The paper’s own forty-percent threshold sits 0.40 - 0.3333 0.0667 above that null mean, which is z 7.75 standard deviations out — a one-sided tail probability, by the normal approximation to the binomial (valid here since n 667 , far above the usual rule-of-thumb minimum), of roughly 4.7 10^{-15} . At three thousand trials per dataset, in other words, a classifier with no position sensitivity of any kind would essentially never cross this threshold by chance, in either direction. Whatever explains the measured pattern, it is not noise inflated by a lenient bar. This computation does not touch the paper’s…
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