← Mathematical compendium

Published equation contexts

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

Why this formula appears here

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.

Read the full article-specific guide →

Read the representative guide

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.

Read this term in its guide →

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.

Research cited beside this formula

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 10 · Foundation Models

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

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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.

Equation guide → · Article →