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Published equation contexts

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

Why this formula appears here

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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nn

Symbol n

n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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zα/2z_{\alpha/2}

Symbol z_α/2

z_α/2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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zβz_{\beta}

Symbol z_β

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

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δ2\delta^{2}

Symbol delta^2

delta2a^2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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(zα/2+zβ)2\left(z_{\alpha/2} + z_{\beta}\right)^{2}

Numerator: (z_α/2 + z_β)^2

The complete quantity above the fraction bar.

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9 δ29\,\delta^{2}

Denominator: 9delta^2

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction.

Research cited beside this formula

Published contexts (1)

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

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

Equation 22 · AI Agents & Systems

Measuring AI Agent Reliability: What the Evidence Actually Supports

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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