  Submillimeter dust polarization measurements of a sample of 50 star-forming
regions, observed with the SMA and the CSO covering pc-scale clouds to
mpc-scale cores, are analyzed in order to quantify the magnetic field
importance. The magnetic field misalignment $\delta$ -- the local angle between
magnetic field and dust emission gradient -- is found to be a prime observable,
revealing distinct distributions for sources where the magnetic field is
preferentially aligned with or perpendicular to the source minor axis.
Source-averaged misalignment angles $\langle|\delta|\rangle$ fall into
systematically different ranges, reflecting the different source-magnetic field
configurations. Possible bimodal $\langle|\delta|\rangle$-distributions are
found for the separate SMA and CSO samples. Combining both samples broadens the
distribution with a wide maximum peak at small $\langle|\delta|\rangle$-values.
Assuming the 50 sources to be representative, the prevailing source-magnetic
field configuration is one that statistically prefers small magnetic field
misalignments $|\delta|$. When interpreting $|\delta|$ together with an MHD
force equation, as developed in the framework of the polarization-intensity
gradient method, a sample-based scaling fits the magnetic field
tension-to-gravity force ratio $\langle\Sigma_B\rangle$ versus
$\langle|\delta|\rangle$ with $\langle\Sigma_B\rangle = 0.116 \cdot
\exp(0.047\cdot \langle|\delta|\rangle)\pm 0.20$ (mean error), providing a way
to estimate the relative importance of the magnetic field, only based on
measurable field misalignments $|\delta|$. The force ratio $\Sigma_B$
discriminates systems that are collapsible on average ($\langle \Sigma_B\rangle
<1$) from other molecular clouds where the magnetic field still provides enough
resistance against gravitational collapse ($\langle \Sigma_B\rangle >1$)
(abridged).
