Observed polarization fraction (p) as a function of column density (N_H), for the cuts across the crest of the filaments derived from the boxes shown in Fig. 7. The small and large dots correspond to the background and filament regions, respectively. The three lines show linear fits for the filament regions of log p versus log N_H described in Sect. 3.4. The data uncertainties depend on the intensity of the polarized emission. They are the largest for low p and N_H values. The mean errorbar on p is 1.2% for the data points used for the linear fits. For smaller N_H values, the uncertainty on p is larger but does not account for the full dispersion of the data points.