Summary The paper introduces two novel randomized response models specifically designed to investigate higher order interactions between three sensitive attributes, going beyond the typical binary analysis of single sensitive questions. The study develops estimators for all seven parameters involved in the new models, allowing for comprehensive analysis of the interactions between the sensitive attributes. We also derive variance expressions for the proposed estimators and compare them to Fisher's information matrix to assess the efficiency of the estimation process. The models are applied to primary data collected from a real‐world study, demonstrating their practical utility in analyzing sensitive behaviors. We discuss potential issues that may arise during the estimation process and provide strategies to mitigate them. A novel test statistic is developed to test the independence of three sensitive attributes, allowing researchers to investigate potential relationships between them. The study concludes with insights regarding the prevalence of the three sensitive attributes (regular cigarette smoking, chewing tobacco and vaping) based on the analyzed data.
As large language models (LLMs) become increasingly integrated into analytical workflows, an urgent question arises: Can these models replace the trained statistician? This paper presents a controlled experiment to directly test the statistical reasoning ability of LLMs. We employ Monte Carlo simulations to generate datasets with known ground-truth parameters and pose four canonical statistical questions to five commercially prominent models across three linguistically distinct prompt formulations and five sampling temperature settings, yielding 3000 observations in a full-factorial design. In order to find an answer to our question, we design prompts that reflect how decision-makers with varying degrees of statistical knowledge would query AI in the absence of a trained statistician. We find that prompts that portray higher statistical competency can result in higher accuracy for some (but not all) LLMs; we also find that LLMs can fail catastrophically on tasks requiring quantitative precision. We connect these findings to architectural differences among models and to recent literature on epistemic mirroring in LLMs and argue that the observed patterns reveal models are performing linguistic pattern matching on statistically flavoured text rather than genuine statistical reasoning. We conclude that current LLMs cannot replace the statistician, though certain architectures approach useful performance on pattern-recognition subtasks.
