Benchmarking Language Models for Statistical Problem Formulation

Despite rapid advances in large language models (LLMs), statistical reasoning remains underrepresented in existing LLM benchmarks, which often do not reflect the layered, proof-driven nature of real statistical practice. To address this gap, we introduce \textbf{StatEval}, the first large-scale benchmark for statistical reasoning across curricular and research-level settings. StatEval includes over 100,000 curated problems, with 20,000+ foundational questions spanning undergraduate and graduate curricula and 80,000+ research-level proof tasks extracted from leading statistical journals. To construct StatEval, we develop \textbf{TRACE} (Topology and Reasoning-Aware Context Extractor), a multi-agent pipeline with human-in-the-loop validation that converts unstructured academic texts into self-contained theorem-level reasoning tasks. We also propose an Adaptive Process-Based Scoring Pipeline for complex statistical proofs, enabling fine-grained evaluation beyond final-answer matching. Experiments show that while LLMs perform reasonably on foundational tasks, they struggle with rigorous research-level reasoning. Beyond evaluation, StatEval serves as a resource for improving reasoning, as retrieval-augmented generation and domain-specific alignment consistently enhance performance. Together, these results establish StatEval as both a benchmark and an infrastructure for advancing statistical reasoning in LLMs.

Statistical analysis is a broad, complex field requiring both domain knowledge and tool proficiency. While prior work has evaluated large language models (LLMs) in this domain, existing benchmarks remain limited in scope and format. To bridge this gap, we introduce StatABench (Statistical AnalysisBenchmark), a benchmark designed to systematically assess LLMs' statistical analysis capabilities. StatABench comprises two complementary components: Stat-Closed, containing 404 questions across 18 statistical topics in multiple formats (multiple-choice, fill-in-the-blank, decision-making, and practical application), and Stat-Open, featuring 30 complex open-ended modeling tasks adapted from professional competitions. We evaluate diverse LLMs using the LangChain MCP framework and multiple data science agents, and assess Stat-Open solutions via a validated LLM-as-Judge protocol. Experiments show that even GPT-5.1 achieves only 68.6% on Stat-Closed, while the best open-source model reaches 60.6%. On Stat-Open, the top agent framework scores 61.86 on average. These results reveal the gap between current LLMs and reliable statistical analysis, highlighting persistent challenges in tool-grounded reasoning, methodological decision-making, and end-to-end statistical modeling.

Statistical reasoning is multidimensional, yet evaluations of large language models (LLMs) typically emphasize response accuracy while overlooking how models construct and communicate statistical explanations. This study demonstrates the value of a multidimensional evaluation by combining response accuracy, response behavior, structural topic modeling, and lexical similarity analysis. The framework is applied to explanations generated by 15 current-generation LLMs responding to 90 questions drawn from four statistics examinations spanning high school, undergraduate, and graduate levels. Accuracy varied substantially across models, ranging from 55% to 78%. In contrast, structural topic modeling revealed a common conceptual organization of statistical reasoning across all models, while lexical similarity analysis identified modest but consistent vendor-specific differences in explanatory style. Models developed by the same vendor (e.g. Anthropic, OpenAI) produced explanations that were slightly more similar than models from different vendors. These findings demonstrate that statistical reasoning in contemporary LLMs cannot be characterized by accuracy alone and illustrate how complementary analyses of response behavior and model-generated explanations provide a more comprehensive evaluation of statistical reasoning in generative AI.