Standard statistical analysis of the magnetic properties of the quiet Sun rely on simple histograms of quantities inferred from maximum-likelihood estimations. Because of the inherent degeneracies, either intrinsic or induced by the noise, this approach is not optimal and can lead to highly biased results. We carried out a meta-analysis of the magnetism of the quiet Sun from Hinode observations using a hierarchical probabilistic method. This method allowed us to infer the statistical properties of the magnetic field vector over the observed field-of-view, consistently taking into account the uncertainties in each pixel that are due to noise and degeneracies. Our results imply that the magnetic fields are very weak, below 275 G with 95% probability, with a slight preference for horizontal fields, although the distribution is not far from a quasi-isotropic distribution.