  Since the x dependence of the axial-anomaly effect in inclusive polarized
deep inelastic scattering is fixed, the transformation from the $\bar{MS}$
scheme to different factorization schemes are not arbitrary. If the quark spin
distribution is demanded to be anomaly-free so that it does not evolve with
$Q^2$ and hard gluons contribute to the first moment of $g_1(x)$, then all the
moments of coefficient and splitting functions are fixed by perturbative QCD
for a given $\gamma_5$ prescription, contrary to the commonly used
Adler-Bardeen (AB) or AB-like scheme. It is urged that, in order to correctly
demonstrate the effect of factorization scheme dependence, the QCD analysis of
polarized structure functions in next-to-leading order should be performed,
besides the $\bar{MS}$ scheme, in the chiral-invariant factorization scheme in
which the axial anomaly resides in the gluon coefficient function, instead of
the less consistent and ambiguous AB scheme.
