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Equation 3 · Part 1 · A Practitioner's Map of Agent Evaluation Frameworks

Symbol hat p

p^  ±  zα/2p^(1−p^)n,\hat p \; \pm \; z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}},
p^\hat p

What this part means

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

Its job in the formula

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

The passage around this formula

The second argument is about how much any one number can actually tell you, independent of harness effects, purely from how many tasks produced it. Treat a benchmark’s headline pass rate as an estimate p^\hat p of a task-set success probability, drawn from n roughly independent trials. The familiar normal approximation to a binomial confidence interval, p^  ±  zα/2p^(1−p^)n\hat p \; \pm \; z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}. gives a rough sense of how much noise sits under a given n , even granting the generous and almost certainly false assumption…

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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.

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Sources cited in the article section

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