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Position: Don't Use the CLT in LLM Evals With Fewer Than a Few Hundred Datapoints

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arxiv 2503.01747 v3 pith:4XPFWIKY submitted 2025-03-03 cs.AI cs.LGstat.ML

classification cs.AIcs.LGstat.ML
keywords methodsuncertaintyappropriatebarsbayesianbenchmarksclt-basederror
verification ladder T0 review T1 audit T2 compute T3 formal
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Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .

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