Can We Hide Machines in the Crowd? Quantifying Equivalence in LLM-in-the-loop Annotation Tasks

Many evaluations of large language models (LLMs) in text annotation focus primarily on the correctness of the output, typically comparing model-generated labels to human-annotated ``ground truth'' using standard performance metrics. In contrast, our study moves beyond effectiveness alone. We aim to explore how labeling decisions -- by both humans and LLMs -- can be statistically evaluated across individuals. Rather than treating LLMs purely as annotation systems, we approach LLMs as an alternative annotation mechanism that may be capable of mimicking the subjective judgments made by humans. To assess this, we develop a statistical evaluation method based on Krippendorff's $\alpha$, paired bootstrapping, and the Two One-Sided t-Tests (TOST) equivalence test procedure. This evaluation method tests whether an LLM can blend into a group of human annotators without being distinguishable. We apply this approach to two datasets -- MovieLens 100K and PolitiFact -- and find that the LLM is statistically indistinguishable from a human annotator in the former ($p = 0.004$), but not in the latter ($p = 0.155$), highlighting task-dependent differences. It also enables early evaluation on a small sample of human data to inform whether LLMs are suitable for large-scale annotation in a given application.