Angular correlations in four-jet events from hadronic decays of the Z$^0$
have been compared with second-order matrix element calculations by
Ellis, Ross and Terrano, using the LUND string
fragmentation model. Such comparisons can be used to determine the fraction 
of four-quark events contained in the data, which we call apparent fraction, 
since this type of measurement does not actually identify real four-quark 
events. It relies only on the relative shapes between measured and calculated 
distributions. We find the overall ratio of the experimentally measured 
apparent fraction of four-quark events to the theoretical prediction to be 
$R_{4\mathrm{q}}$ = 1.28$\pm0.12$(stat)$^{+0.97}_{-0.95}$(syst).
Differences in shape between the correlations of the 
data and the second-order theory have  been observed  as a function  of 
$m_{34}$, the invariant mass formed by the system of the two least energetic 
jets. These differences, expressed by the value of  
$R_{4\mathrm{q}}$($m_{34}$), exhibit a shallow maximum in the region of 
20 GeV and become negative at higher values of  $m_{34}$.
Some of these features can also be  qualitatively observed in models which 
include higher order effects such as  a combination of matrix elements with  
a parton shower.