  The $k_\perp$-moment of a quark's Sivers function is known to be related to
the corresponding twist-three quark-gluon correlation function $T_{q,F}(x, x)$.
The two functions have been extracted from data for single-spin asymmetries in
semi-inclusive deep inelastic scattering and in single-inclusive hadron
production in $pp$ collisions, respectively. Performing a consistent comparison
of the extracted functions, we find that they show a "sign mismatch": while the
magnitude of the functions is roughly consistent, the $k_\perp$-moment of the
Sivers function has opposite sign from that of $T_{q,F}(x, x)$, both for up and
for down quarks. Barring any inconsistencies in our theoretical understanding
of the Sivers functions and their process dependence, the implication of this
mismatch is that either, the Sivers effect is not dominantly responsible for
the observed single-spin asymmetries in $pp$ collisions or, the current
semi-inclusive lepton scattering data do not sufficiently constrain the
$k_\perp$-moment of the quark Sivers functions. Both possibilities strengthen
the case for further experimental investigations of single-spin asymmetries in
high-energy $pp$ and $ep$ scattering.
