Polarization fraction bias, normalized to the true value p₀, as a function of the S/N I₀/σ_I, plotted for three values of the polarization S/N, p₀/σ_p,G, and values of the effective ellipticity ε_eff covering the canonical (full line), low (dark grey shaded region), and extreme (light grey shaded region) regimes of the covariance matrix. The intensity correlation coefficients are set to ρ_Q = ρ_U = 0. We only consider the domain where (I₀/σ_I) > (p₀/σ_p,G).