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Equation 10 · Part 4 · Measuring Frontier Models: Contamination, Variance, and What a Score Can Support

fraction

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

What this part means

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

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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

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