  The Davis-Chandrasekhar-Fermi (DCF) method is widely used to evaluate
magnetic fields in star-forming regions. Yet it remains unclear how well DCF
equations estimate the mean plane-of-the-sky field strength in a map region. To
address this question, five DCF equations are applied to an idealized cloud
map. Its polarization angles have a normal distribution with dispersion
${\sigma}_{\theta}$,and its density and velocity dispersion have negligible
variation. Each DCF equation specifies a global field strength $B_{DCF}$ and a
distribution of local DCF estimates. The "most-likely" DCF field strength
$B_{ml}$ is the distribution mode (Chen et al. 2022), for which a correction
factor ${\beta}_{ml}$ = $B_{ml}$/$B_{DCF}$ is calculated analytically. For each
equation ${\beta}_{ml}$ < 1, indicating that $B_{DCF}$ is a biased estimator of
$B_{ml}$. The values of ${\beta}_{ml}$ are ${\beta}_{ml}\approx$ 0.7 when
$B_{DCF} \propto {{\sigma}_{\theta}}^{-1}$ due to turbulent excitation of
Afv\'enic MHD waves, and ${\beta}_{ml}\approx$ 0.9 when $B_{DCF} \propto
{{\sigma}_{\theta}}^{-1/2}$ due to non-Alfv\'enic MHD waves. These statistical
correction factors ${\beta}_{ml}$ have partial agreement with correction
factors ${\beta}_{sim}$ obtained from MHD simulations. The relative importance
of the statistical correction is estimated by assuming that each simulation
correction has both a statistical and a physical component. Then the standard,
structure function, and original DCF equations appear most accurate because
they require the least physical correction. Their relative physical correction
factors are 0.1, 0.3, and 0.4 on a scale from 0 to 1. In contrast the
large-angle and parallel-${\delta}B$ equations have physical correction factors
0.6 and 0.7. These results may be useful in selecting DCF equations, within
model limitations.
