Variations of the CCs with σ_α based on the Monte Carlo simulations. Panel a: results of the normalization method. Panel b: results of the binned fitting method. Panel c: results of the unbinned fitting method. The blue and red dotted curves depict the best-fit of the tilt angle scatter and correlation coefficients for the linear form and the square-root form of Joy’s law, respectively. Error bars represent one standard error for 10 000 correlation coefficients sets in each tilt angle scatters.