Unified schemes attempt to classify radio loud quasars and Fanaroff-Ri
ley Class II radio galaxies as a single type of object, whose properti
es depend on the orientation of the jet axis relative to the line of s
ight. We describe a new test of such unification schemes using observe
d jet opening angles as orientation indicators and apply it to existin
g data. Opening angles were measured for a subset of the 3CR catalogue
, consisting of all identified extragalactic sources with P178 MHz> 10
(25) W/Hz and for which high resolution radio maps were found. This pr
ovided a sample relatively free of orientation effects. The observed d
istributions of opening angles for the quasars were compared with thos
e of the galaxies, and with Monte Carlo simulations. We find that the
observed jet opening angles of quasars tend to be larger than those of
the galaxies; this result is consistent with, and supports, the unifi
ed scheme. Detailed Monte Carlo simulations suggest the observations a
re inconsistent with a simple unified scheme where a single orientatio
n angle sharply distinguishes between quasars and galaxies. We modify
Barthel's [ApJ, 336, 606 (1989)] unification scheme by introducing a r
ange of orientation angles that differentiate quasars from galaxies; t
his yields more consistent results. However, neither Barthel's unifica
tion, nor the modification presented here, are fully able to account f
or the observed differences in quasar and galaxy redshift distribution
s. Finally, we demonstrate the existence of a loose anticorrelation be
tween jet opening angle and source linear size, confirming that these
parameters are useful as orientation indicators.