  By using the full density matrix approach to spectral functions within the
numerical renormalization group method, we present a detailed study of the
magnetic field induced splittings in the spin-resolved and the total spectral
densities of a Kondo correlated quantum dot described by the single level
Anderson impurity model. The universal scaling of the splittings with magnetic
field is examined by varying the Kondo scale either by a change of local level
position at a fixed tunnel coupling or by a change of the tunnel coupling at a
fixed level position. We find that the Kondo-peak splitting $\Delta/T_K$ in the
spin-resolved spectral function always scales perfectly for magnetic fields
$B<8T_K$ in either of the two $T_K$-adjusted paths. Scaling is destroyed for
fields $B>10T_K$. On the other hand, the Kondo peak splitting $\delta/T_K$ in
the total spectral function does slightly deviate from the conventional scaling
theory in whole magnetic field window along the coupling-varying path.
Furthermore, we show the scaling analysis suitable for all field windows within
the Kondo regime and two specific fitting scaling curves are given from which
certain detailed features at low field are derived. In addition, the scaling
dimensionless quantity $\Delta/2B$ and $\delta/2B$ are also studied and they
can reach and exceed 1 in the large magnetic field region, in agreement with a
recent experiment [T.M. Liu, et al., Phys. Rev. Lett. 103, 026803 (2009)].
