Three Ways Classical Test Theory Can Mislead About LLM Judges

Abstract

Evaluations that use a large language model (LLM) as a judge have begun to borrow reliability statistics from classical test theory and its extensions. We examine three such statistics that need one administration and no gold labels. None of them can isolate the judge, because one judge under one prompt supplies no variance component of its own. Claude Haiku 4.5 judged 210 constructed short answers against ten-element checklists. On the 180 with parsed verdicts, the Kuder-Richardson coefficient (KR-20) came out at 0.5223 on the judge's verdicts and 0.5231 on error-free gold verdicts. In simulation, bank design alone moves KR-20 from 0.01 to 0.68 at the judge's measured 4.72% error rate. The dependability index $\Phi(\lambda)$, a ratio of mean squared distances from the pass mark, sits 0.22 to 0.38 below the judge's accuracy against gold and returns 0.54 to 0.68 on error-free gold verdicts. Livingston-Lewis accuracy treats the rubric elements as a sample, and at a pass mark of five elements it credits error-free gold scores with 0.78, close to the judge's 0.81. A statement about the judge therefore needs gold labels or a varied scorer facet, and a reliability ratio needs the bank's spread beside it. One of the four closest judge-evaluation papers varies the prompt and still reads a reliability below 0.7 as a sign that a model cannot serve as a judge, although that reliability moves with the spread of the samples scored. We derive a decision table and four reporting lines from these two rules.