Impact of increasing noise in the Faraday data on the HOG correlation between phase-separated H i structures and Faraday depth features for the case-study simulation along the mean field Each panel shows the 98th percentile of the normalized Rayleigh statistic (${\tilde{V}}^{98\%}$ as a function of Faraday depth, ϕ, for the CNM and WNM phases). The panels correspond to increasing signal-to-noise ratios (S/Ns) in Faraday space: from 1 to 6, as indicated. A higher S/N enhances the correlation amplitude for both phases, but the relative dominance of the WNM is preserved across all regimes.