Top panel, in black: ⟨cos(Δ_S/V⟩ value from the data as a function of the fraction of the sample that is removed according to the R_P/p values of the data points (see text). The red line and shaded regions indicate the mean and the one and two sigma contours from the observational errors on the polarization position angles (dust and quasar). The gray shaded regions correspond to the one and two sigma deviations around the expected value (black dot horizontal line), assuming a uniform distribution of Δ_S/V angles. Bottom panel: under the hypothesis of uniform distribution of Δ_S/V, the black line is the p-value of the observation as a function of the removed fraction of the sample. The red line and shaded region correspond to the p-values computed for the mean and the one standard deviation from the mean of the observation accounting for the position angles uncertainties.