Equation 5 · Part 9 · Building a Custom Evaluation Suite for a Production Agent

subscript

n \approx \frac{2\,p(1-p)\,(z_{\alpha/2} + z_{\beta})^2}{\delta^2} .

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

Because a “pass” verdict is itself often a noisy measurement, not a fact, it is worth being explicit about how much noise a single run’s outcome carries before treating a change in the pass rate as real. If a task’s true pass rate is p under a baseline configuration and a candidate change is worth detecting only once it shifts that rate by at least $\delta$ , the number of repeated trials needed per configuration to detect the shift reliably — at significance level $\alpha$ and statistical power 1- $\beta$ — is approximately $n \approx \frac{2\,p(1-p)\,(z_{\alpha/2} + z_{\beta})^2}{\delta^2}$ . 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…

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Learn the underlying idea

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

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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