  A QCD analysis of the world data on polarized deep inelastic scattering is
presented in leading and next-to-leading order. New parameterizations are
derived for the quark and gluon distributions for the kinematic range $x
\epsilon [10^{-9},1], Q^2 \epsilon [1,10^6] \GeV^2$. The extrapolation far
outside the domain of the current measurements is given both to allow for
applications at higher values of $Q^2$ and to be able to calculate integral
properties of the present distributions. The values of $\Lambda_{\rm QCD}$ and
$\alpha_s(M_z)$ are determined. Emphasis is put on the derivation of the fully
correlated $1\sigma$ error bands for these distributions, which are also given
in terms of parameterizations and are directly applicable to determine
experimental errors of other polarized observables. The impact of the variation
of both the renormalization and factorization scales on the value of $\alpha_s$
is studied. Finally we perform a factorization--scheme invariant QCD analysis
based on the observables $g_1(x,Q^2)$ and $d g_1(x,Q^2)/d \log(Q^2)$ in
next-to-leading order, which is compared to the standard analysis. A series of
low moments of parton densities, accounting for error correlation, are given to
allow for comparison with results from lattice simulations.
