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$z_{\beta} \approx 0.84$

Why this formula appears here

Plugging in a fairly ordinary case — a baseline pass rate of 70 percent, a minimum shift worth caring about of 10 percentage points, a 5 percent significance level, and 80 percent power — gives $z_{\alpha/2}$ $\approx$ 1.96 and $z_{\beta}$ $\approx$ 0.84 , and the formula returns roughly 330 trials per configuration. That number is the whole argument for treating a single failed run, or even three failed runs out of five, with real suspicion rather than as proof of a regression: at ordinary sample sizes, most of what looks like a pass-rate change between two prompt versions is sampling noise, not signal. Teams that cannot afford several hundred repeated trials on every task for every change — nearly…

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z_{\beta}

Symbol z_β

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z_{\beta} \approx 0.84

Equation 7 · Model Evaluation

Building a Custom Evaluation Suite for a Production Agent

This equation gives an approximation: it relates the quantities while allowing an approximation.

Plugging in a fairly ordinary case — a baseline pass rate of 70 percent, a minimum shift worth caring about of 10 percentage points, a 5 percent significance level, and 80 percent power — gives $z_{\alpha/2}$ $\approx$ 1.96 and $z_{\beta}$ $\approx$ 0.84 , and the formula returns roughly 330 trials per configuration. That number is the whole argument for treating a single failed run, or even three failed runs out of five, with real suspicion rather than as proof of a regression: at ordinary sample sizes, most of what looks like a pass-rate change between two prompt versions is sampling noise, not signal. Teams that cannot afford several hundred repeated trials on every task for every change — nearly…

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zβ≈0.84z_{\beta} \approx 0.84zβ​≈0.84