Bar fraction (f_bar) as a function of f_AGN for X-ray AGN (blue squares) and SED AGN (orange circles). Results are shown for S_bar, W_bar, and A_bar separately. The f_bar is calculated in f_AGN bins using bootstrapping with resampling. The values reported are the median f_bar (with 1σ standard deviations as uncertainties); the x-axis error bars indicate bin width. Overlaid are the best-fit merger fraction (f_merg)–f_AGN relations from LM24 for the MIR (solid red line), X-ray (dotted-dashed blue line), and SED (dashed orange line) AGN, parametrised as described in Appendix C. In each subplot, the grey-shaded area highlights the region where f_merg sharply rises as a function of f_AGN.