← All parts of this equation

Equation 15 · Part 2 · Ten Ways an Agent Evaluation Can Mislead You Even When It's Working Correctly

Symbol n

p^±1.96p^(1−p^)n.\hat{p} \pm 1.96\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}.
nn

What this part means

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

Its job in the formula

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

The passage around this formula

…as the trial count shrinks. For a naive binomial estimate — treating each trial as an independent coin flip with unknown success probability p — the 95 percent confidence interval around an observed rate p^\hat{p} from n trials is approximately p^±1.96p^(1−p^)n\hat{p} \pm 1.96\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}. At ten trials and an observed 90 percent success rate, that formula gives an interval of roughly plus or minus nineteen percentage points — an agent genuinely succeeding anywhere from about 71 percent to essentially 100 percent of the time is…

Read this part in the article →

Learn the underlying idea

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the surrounding passage

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