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Equation 22 · Part 2 · Measuring AI Agent Reliability: What the Evidence Actually Supports

Symbol z_α/2

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

What this part means

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

Its job in the formula

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

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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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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