Beyond Accuracy: A Multidimensional Evaluation of Statistical Reasoning in Large Language Models
Monnie McGee, Mateo Langston Smith, Julian Cabrera
cs.CL, stat.AP
Submitted: 2026-08-04
Comments: 15 pages, 5 tables, 2 figures, presented at JSM 2026 and submitted for publication
Project page: https://www.almabetter.com/bytes/articles/chat-gpt-4-vs-gpt-3-5
License: http://creativecommons.org/licenses/by/4.0/
The gist: Statistical reasoning is multidimensional, yet evaluations of large language models (LLMs) typically emphasize response accuracy while overlooking how models construct and communicate statistical
Terminology
Abstract
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.
Sources
- Can we trust LLMs as a tutor for our students? Evaluating the Quality of LLM-generated Feedback in Statistics Exams
- LLM4DS: Evaluating Large Language Models for Data Science Code Generation
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