  A QCD analysis of the world data on inclusive polarized deep inelastic
scattering of leptons on nucleons is presented in leading and next-to-leading
order. New parameterizations are derived for the quark and gluon distributions
and the value of $\alpha_s(M_Z)$ is determined. Emphasis is put on the
derivation of fully correlated error bands for these distributions which 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 a
factorization-scheme invariant QCD analysis based on the observables
$g_1(x,Q^2)$ and $d g_1(x,Q^2)/d \log(Q^2)$ is performed in next-to-leading
order, which is compared to the standard analysis.
