Skewed Score: A statistical framework to assess autograders

TL;DR

This paper introduces a Bayesian statistical framework to evaluate autograders for large language models, addressing reliability, bias, and interpretability issues in automated LLM output assessment.

Contribution

It presents a novel Bayesian GLM-based method for assessing autograders, enabling bias detection, uncertainty quantification, and improved interpretability in LLM evaluation.

Findings

Effective bias detection in autograders

Quantification of scoring uncertainties

Enhanced interpretability of evaluation results

Abstract

The evaluation of large language model (LLM) outputs is increasingly performed by other LLMs, a setup commonly known as "LLM-as-a-judge", or autograders. While autograders offer a scalable alternative to human evaluation, they have shown mixed reliability and may exhibit systematic biases, depending on response type, scoring methodology, domain specificity, or other factors. Here we propose a statistical framework based on Bayesian generalised linear models (GLMs) that enables researchers to simultaneously assess their autograders while addressing their primary research questions (e.g., LLM evaluation). Our approach models evaluation outcomes (e.g., scores or pairwise preferences) as a function of properties of the grader (e.g., human vs. autograder) and the evaluated item (e.g., response length or the LLM that generated it), allowing for explicit quantification of scoring differences and potential biases within a unified framework. In addition, our method can be used to augment traditional metrics such as inter-rater agreement, by providing uncertainty estimates and clarifying sources of disagreement. Overall, this approach contributes to more robust and interpretable use of autograders in LLM evaluation, enabling both performance analysis and bias detection.