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This study evaluates statistical reasoning in large language models (LLMs) using a multidimensional framework that incorporates response accuracy, response behavior, structural topic modeling, and lexical similarity analysis. By analyzing explanations generated by 15 LLMs across 90 statistics questions from various educational levels, the research reveals that accuracy alone is insufficient to assess model performance, with scores ranging from 55% to 78%. Additionally, the analysis uncovers a shared conceptual organization of statistical reasoning among models, alongside notable vendor-specific differences in explanatory styles, emphasizing the complexity of evaluating LLMs beyond mere accuracy metrics.
Accuracy is just the tip of the iceberg; a deeper look reveals shared reasoning patterns and distinct explanatory styles among LLMs from different vendors.
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.
