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Equation 10 · Measuring Frontier Models: Contamination, Variance, and What a Score Can Support

What does this equation mean?

SE=p(1−p)n,\mathrm{SE} = \sqrt{\frac{p(1-p)}{n}} ,

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Start withp(1-p)
Divide byn
This relates toSE
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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pp

Symbol p

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

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nn

Symbol n

n occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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fraction

fraction

Divide the expression above the line by the one below it.

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√

√

Take a square root.

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p(1−p)p(1-p)

Numerator: p(1-p)

The complete quantity above the fraction bar.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

For a suite of n independent items with true rate p , the standard error of the estimate is SE=p(1−p)n\mathrm{SE} = \sqrt{\frac{p(1-p)}{n}} . which for p ≈\approx 0.5 and n = 200 is about 3.5 percentage points — before adding any run-to-run generation variance, and before accounting for the fact that benchmark items are not independent. A reported two-point difference between two systems on such a suite is not evidence of anything.

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Sources cited in the article section

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