subscript

The passage around this formula

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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