Scatter plot for the linear-to-circular polarization fraction relation p_L − p_V. In red, the observations of (a) Herpin et al. (2006) and (b) Surcis et al. (2011) are reported. In panel (a) the blue points come from our simulations of the J = 2−1 transition at B = 1 G, with the kinetic temperature of the maser T = 1000 K. In (panel b) the blue points come from our simulations of the isotropically pumped water maser at v_th = 1.0 km s⁻¹ and B = 200 mG. To generate these scatters, we computed the polarization fractions from (a) 200 (b: 30) isotropically pumped masers with a randomly selected a luminosity between (a) T_bΔΩ = 10⁶−10¹¹ (b: T_bΔΩ = 10^8.5−10¹¹) and a randomly selected propagation angle θ. In the scatter plot, we do not include masers that show polarization <0.5% (b: < 0.1%). In (panel a), we also report the linear regression analysis result from Herpin et al. (2006).