  We determine the uncertainty on the strong coupling alpha_S due to the
experimental errors on the data fitted in global analysis of hard-scattering
data, within the standard framework of leading-twist fixed-order collinear
factorisation in the MSbar scheme, finding that alpha_S(M_Z^2) =
0.1202^{+0.0012}_{-0.0015} at next-to-leading order (NLO) and alpha_S(M_Z^2) =
0.1171^{+0.0014}_{-0.0014} at next-to-next-to-leading order (NNLO). We do not
address in detail the issue of the additional theory uncertainty on
alpha_S(M_Z^2), but an estimate is +/-0.003 at NLO and at most +/-0.002 at
NNLO. We investigate the interplay between uncertainties on alpha_S and
uncertainties on parton distribution functions (PDFs). We show, for the first
time, how both these sources of uncertainty can be accounted for simultaneously
in calculations of cross sections, and we provide eigenvector PDF sets with
different fixed alpha_S values to allow further studies by the general user. We
illustrate the application of these PDF sets by calculating cross sections for
W, Z, Higgs boson and inclusive jet production at the Tevatron and LHC.
