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Equation 22 · Part 4 · Measuring AI Agent Reliability: What the Evidence Actually Supports

Symbol delta^2

n  ≳  (zα/2+zβ)29 δ2n \;\gtrsim\; \frac{\left(z_{\alpha/2} + z_{\beta}\right)^{2}}{9\,\delta^{2}}
δ2\delta^{2}

What this part means

delta2a^2 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

delta2a^2 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

Even when a team does report a rate rather than a single anecdote, a rate on its own understates how uncertain that number is. Evan Miller’s statistical treatment of language-model evaluation makes an argument borrowed from experimental science generally: an evaluation score is an estimate drawn from a finite, noisy sample, not a fact about the system, and it should be reported the way any other science reports a measurement — with an uncertainty attached [ 4 ] . His worked illustration is a useful gut check on how much data “enough” actually requires. To reliably detect an absolute difference of three percentage points between two systems, with conventional statistical standards for false…

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An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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