Examples of the adopted methodology to assess the robustness of the correlations presented in Appendix E. Both panels show the cumulative distribution of Kendall’s τ obtained from 10⁴ Monte-Carlo simulations, where for each realisation the involved variables were perturbed according to their error-bars. The green dotted line shows the median of the distribution, which is adopted to calculate p₀, whereas the blue dashed lines show the upper- and lower quartile. The solid red line shows the critical τ value according to Eq. (E.2). Both panels show the cumulative distribution of τ for the relation between v_shear/σ₀^obs and $f_{\text{esc}}^{\text{Ly}\alpha }$, but the distribution in the left-hand panel is obtained for the sample of N = 38 galaxies analysed in Sect. 3.6 (exclusion of galaxies with double component Hα profiles), whereas the distribution in the right-hand panel is obtained for the subsample of N = 33 galaxies that is analysed in Sect. 4.1.1 (galaxies without upper limits in their Lyα observables).