How to Run Statistics over LLM Judges and Trust the Results: Calibrated Inference for Small-Sample AI Evaluation with evalstats

Abstract:Researchers across academia increasingly base significance claims on LLM judge scores and small-sample AI evaluations. Yet without well-calibrated confidence intervals (CIs), hypothesis tests, and judge-bias corrections, such claims are unreliable. We address these issues in several contributions. First, we find that running statistics over raw LLM judge scores leads to inflated false positives: counterintuitively, for many inter-rater agreement metrics, false positive risk peaks at "almost perfect" human-LLM agreement. To help researchers understand how to run statistics over LLM judges responsibly, we present guidance and tooling for the statistical analysis of mixed human-AI judge designs, and implement nine hypothesis tests via prediction-powered inference (PPI), including the first known PPI corrections for four rank-based tests (Wilcoxon signed-rank, Mann-Whitney U, and omnibus variants). To keep PPI++ stable with small human-labeled calibration sets, we introduce bootstrap-adaptive power tuning, which shrinks the estimated weight toward a target estimated from the labeled data, and accounts for that weight's own sampling variance. Second, through Monte Carlo simulations, we derive recommendations for what CI, p-value, and FWER correction methods to use for small-sample AI evaluations (N<100), and warn researchers against bootstrap CIs. We package these recommendations into evalstats, an open-source Python package that selects calibrated methods automatically, and demonstrate it in three scenarios, including one where a real LLM judge validated at "substantial agreement" would have led a researcher to publish a spurious finding. evalstats is publicly available at this https URL.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Human-Computer Interaction (cs.HC); Methodology (stat.ME)

G.3; G.4; H.5.2; I.2.7

arXiv:2609.35815 [cs.CL]

(or arXiv:2609.35815v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2609.35815 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

supplementary.pdf

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