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The Davis-Chandrasekhar-Fermi (DCF) method provides an indirect way toestimate the magnetic field strength from statistics of magnetic fieldorientations. We compile all the previous DCF estimations from polarized dustemission observations and re-calculate the magnetic field strength of theselected samples with the new DCF correction factors in Liu et al. (2021). Wefind the magnetic field scales with the volume density as $B \propto n^{0.57}$.However, the estimated power-law index of the observed $B-n$ relation has largeuncertainties and may not be comparable to the $B-n$ relation of theoreticalmodels. A clear trend of decreasing magnetic viral parameter (i.e., increasingmass-to-flux ratio in units of critical value) with increasing column densityis found in the sample, which suggests the magnetic field dominates the gravityat lower densities but cannot compete with the gravity at higher densities.This finding also indicates that the magnetic flux is dissipated at highercolumn densities due to ambipolar diffusion or magnetic recennection, and theaccumulation of mass at higher densities may be by mass flows along themagnetic field lines. Both sub-Alfv\'{e}nic and super-Alfv\'{e}nic states arefound in the sample, with the average state being approximatelytrans-Alfv\'{e}nic.

Magnetic fields in star formation: a complete compilation of all the DCF estimations