Probability of finding the true polarization fraction p₀ inside the interval , where and are the 1σ lower and upper limits, respectively. We plot this for each estimator: true σ_p,0 (top left); conventional σ_p,C (bottom left); geometric σ_p,G (top right); and arithmetic σ_p,A (bottom right). These are plotted as a function of the S/N p₀/σ_p,G. Monte Carlo simulations have been carried out in the canonical (solid line), low (dark grey), and extreme (light grey) regimes of the covariance matrix. The expected 68.27% level is shown as a dashed line.