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Equation 18 · Part 2 · Ten Ways an Agent Evaluation Can Mislead You Even When It's Working Correctly

Symbol ρ

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

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ρ is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

ρ is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…evals [ 8 ] . The general relationship is the one long used in survey statistics: if a naive standard error assumes independence, and trials instead arrive in clusters of average size m with intraclass correlation ρ\rho within a cluster, the correctly inflated standard error is SEcluster=SEnaive×1+(m−1)ρ\mathrm{SE}_{\text{cluster}} = \mathrm{SE}_{\text{naive}} \times \sqrt{1 + (m - 1)\rho}. Agent trials add a second, harder-to-audit source of the same problem: repeated attempts by one policy on one task instance are not independent draws either, because the same weights, the same training…

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