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σ=p0(1−p0)/n≈0.0086\sigma = \sqrt{p_0(1-p_0)/n} \approx 0.0086

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A skeptical reader’s first move should be to ask whether that headline number could be sampling noise dressed up by a generous threshold. It is worth actually running that check rather than asserting an answer to it. Under a null model in which a classifier’s selections are entirely independent of label position — no cognitive bias, no architectural quirk, nothing but content — the expected share of selections landing in any one third of an evenly split label list is p0p_0 = 1/3 , and with n = 3000 independent trials per dataset the standard deviation of that observed share is σ\sigma = p0(1−p0)/n\sqrt{p_0(1-p_0)/n} ≈\approx 0.0086 , well under one percentage point. The paper’s own forty-percent threshold…

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σ=p0(1−p0)/n≈0.0086\sigma = \sqrt{p_0(1-p_0)/n} \approx 0.0086

Equation 6 · 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.

A skeptical reader’s first move should be to ask whether that headline number could be sampling noise dressed up by a generous threshold. It is worth actually running that check rather than asserting an answer to it. Under a null model in which a classifier’s selections are entirely independent of label position — no cognitive bias, no architectural quirk, nothing but content — the expected share of selections landing in any one third of an evenly split label list is p0p_0 = 1/3 , and with n = 3000 independent trials per dataset the standard deviation of that observed share is σ\sigma = p0(1−p0)/n\sqrt{p_0(1-p_0)/n} ≈\approx 0.0086 , well under one percentage point. The paper’s own forty-percent threshold…

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