  We consider elastic reflection and transmission of electrons by a disordered
system characterized by a $2N\!\times\!2N$ scattering matrix $S$. Expressing
$S$ in terms of the $N$ radial parameters and of the four $N\!\times\!N$
unitary matrices used for the standard transfer matrix parametrization, we
calculate their probability distributions for the circular orthogonal (COE) and
unitary (CUE) Dyson ensembles. In this parametrization, we explicitely compare
the COE--CUE distributions with those suitable for quasi--$1d$ conductors and
insulators. Then, returning to the usual eigenvalue--eigenvector
parametrization of $S$, we study the distributions of the scattering phase
shifts. For a quasi--$1d$ metallic system, microscopic simulations show that
the phase sift density and correlation functions are close to those of the
circular ensembles. When quasi--$1d$ longitudinal localization breaks $S$ into
two uncorrelated reflection matrices, the phase shift form factor $b(k)$
exhibits a crossover from a behavior characteristic of two uncoupled COE--CUE
(small $k$) to a single COE--CUE behavior (large $k$). Outside quasi--one
dimension, we find that the phase shift density is no longer uniform and $S$
remains nonzero after disorder averaging. We use perturbation theory to
calculate the deviations to the isotropic Dyson distributions. When the
electron dynamics is no
