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Equation 10 · Part 6 · Measuring Frontier Models: Contamination, Variance, and What a Score Can Support

Numerator: p(1-p)

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

What this part means

The complete quantity above the fraction bar.

Its job in the formula

p(1-p) occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.