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Equation 18 · Part 7 · Ten Ways an Agent Evaluation Can Mislead You Even When It's Working Correctly

subtraction

SEcluster=SEnaive×1+(m−1)ρ.\mathrm{SE}_{\text{cluster}} = \mathrm{SE}_{\text{naive}} \times \sqrt{1 + (m - 1)\rho}.
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

5. Non-independence between repeated trials. The confidence-interval formula above assumes each trial is independent of the others, and that assumption is often false in ways that specifically inflate confidence. Miller’s paper measures this directly: several widely used evaluation sets draw multiple questions from a shared context — several questions about the same passage, several sub-tasks from the same underlying scenario — and properly accounting for that clustering, rather than treating every question as its own independent draw, produced clustered standard errors “over 3x larger than naive standard errors” on the affected evals [ 8 ] . The general relationship is the one long used in…

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Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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