Equation 22 · Part 9 · Measuring AI Agent Reliability: What the Evidence Actually Supports
Numerator: (z_α/2 + z_β)^2
What this part means
The complete quantity above the fraction bar.
Its job in the formula
(z_α/2 + z_β)^2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Numerator: (z_α/2 + z_β)^2→Article meaning
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…
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.