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Equation 14 · Part 1 · How to Actually Compare Frontier AI Models Without Building a Misleading Leaderboard

Symbol hat p

SE(p^)≈p^(1−p^)n,\mathrm{SE}(\hat p) \approx \sqrt{\frac{\hat p (1-\hat p)}{n}},
p^\hat p

What this part means

hat p occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

hat p occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Reported variance, not a bare point estimate. A score computed from n independent trials with an underlying success probability p^\hat p carries a standard error of roughly SE(p^)≈p^(1−p^)n\mathrm{SE}(\hat p) \approx \sqrt{\frac{\hat p (1-\hat p)}{n}}. and two point estimates whose intervals overlap should not be reported as a ranking. Evan Miller’s statistical treatment of language-model evaluation makes this argument in more general form, framing individual evaluation questions as…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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