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Equation 15 · Part 1 · Ten Ways an Agent Evaluation Can Mislead You Even When It's Working Correctly

Symbol hatp

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

What this part means

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

Its job in the formula

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

The passage around this formula

…widens fast 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…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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