  The ambipolar-diffusion theory of star formation predicts the formation of
fragments in molecular clouds with mass-to-flux ratios greater than that of the
parent-cloud envelope. By contrast, scenarios of turbulence-induced
fragmentation do not yield such a robust prediction. Based on this property,
Crutcher et al. (2009) proposed an observational test that could potentially
discriminate between fragmentation theories. However, the analysis applied to
the data severely restricts the discriminative power of the test: the authors
conclude that they can only constrain what they refer to as the "idealized"
ambipolar-diffusion theory that assumes initially straight-parallel magnetic
field lines in the parent cloud. We present an original, self-consistent
analysis of the same data taking into account the nonuniformity of the magnetic
field in the cloud envelopes, which is suggested by the data themselves, and we
discuss important geometrical effects that must be accounted for in using this
test. We show quantitatively that the quality of current data does not allow
for a strong conclusion about any fragmentation theory. Given the
discriminative potential of the test, we urge for more and better-quality data.
