The Impact of Spin Priors on Parameterized Tests of General Relativity
Spin priors play a fundamental role in gravitational-wave parameter estimation, yet their impact on parameterized tests of General Relativity (GR) remains insufficiently understood. We systematically investigate how spin-prior choices affect the 1.5PN deviation parameter $δ\hatϕ_3$ using real gravitational-wave events. Prior-induced effects are quantified through the Jensen--Shannon divergence and posterior median shifts. We find that $χ_p$ is significantly more sensitive to the spin prior than $χ_{\rm eff}$, while $δ\hatϕ_3$ is generally robust but can exhibit larger shifts in low-information regimes. GW231123_135430 shows particularly strong sensitivity, but its inferred properties are subject to waveform-model and event-specific systematics, warranting caution in interpreting results strongly influenced by this event. When $δ\hatϕ_3$ is included in the parameter-estimation model, a strong correlation emerges between the prior sensitivities of $χ_{\rm eff}$ and $δ\hatϕ_3$, consistent with their partial degeneracy at the 1.5PN order, whereas $χ_p$ remains weakly correlated. A leave-one-out test shows that GW231123\_135430 significantly affects the correlation strength, but the correlation persists when this event is removed. These results demonstrate that spin-prior choices can propagate into parameterized tests of GR and should be carefully accounted for when interpreting apparent deviations from GR.