Reporting Under Pressure: Separating Factual and Tonal Sycophancy in LLM Statistical Analysis

Large language models are increasingly asked to analyze data and report what the results mean, a task distinct from the belief- or preference-alignment settings studied in most sycophancy research. We test whether editorial framing in the prompt, ranging from a neutral request to an explicit instruction to search exhaustively for reasons to discredit or to support a finding, changes not just the tone but the substance of a model's report. Across a 4 x 4 factorial design crossing four framing conditions with four ground-truth data patterns (a genuine effect, a confound that mimics an effect but fails a robustness check, a well-powered null, and an underpowered null), we collect 480 responses and score each along two independent dimensions: whether its factual claim about the data diverged from the correct interpretation, and whether only its tone diverged while the claim stayed correct. Factual misrepresentation is concentrated in two cells: brutally critical framing applied to a genuine effect, where the model talks itself into unwarranted skepticism (97% of responses), and significance-seeking framing applied to an underpowered null, where the model overstates confidence in a null conclusion the data cannot support (100% of responses). Tone shifts far more broadly than factual content does, with critical framing producing a defensive, hedge-heavy register across every data pattern regardless of what the data show, while significance-seeking framing shifts tone only where the data leave genuine ambiguity. A confound present in the data itself blocks both kinds of shift almost entirely under every framing condition tested. These results indicate that the risk of framing-induced distortion in LLM-assisted data analysis is neither uniform across framings nor uniform across data patterns, and that a model can hold a correct conclusion in place while its tone shifts substantially around it.