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Equation 9 · Part 4 · Cognitive Bias Was the Label; Attention Sink Is the Suspect

subscript

np0(1−p0)≈667np_0(1-p_0) \approx 667
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

​ ≈ 0.0086 , well under one percentage point. The paper’s own forty-percent threshold sits 0.40 - 0.3333 ≈\approx 0.0667 above that null mean, which is z ≈\approx 7.75 standard deviations out — a one-sided tail probability, by the normal approximation to the binomial (valid here since np0(1−p0)p_0(1-p_0) ≈\approx 667 , far above the usual rule-of-thumb minimum), of roughly 4.7 ×\times 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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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