  The missing gravity in galaxies requires dark matter, or alternatively a
modification of gravity or inertia. These theoretical possibilities of
fundamental importance may be distinguished by the statistical relation between
the observed centripetal acceleration of particles in orbital motion and the
expected Newtonian acceleration from the observed distribution of baryons in
galaxies. Here predictions of cold dark matter halos, modified gravity, and
modified inertia are compared and tested by a statistical sample of galaxy
rotation curves from the Spitzer Photometry and Accurate Rotation Curves
(SPARC) database. Modified gravity under an estimated mean external field
correctly predicts the observed statistical relation of accelerations from both
the inner and outer parts of rotation curves. Taken at face value there is a
$6.9\sigma$ difference between the inner and outer parts on an acceleration
plane which would be inconsistent with current proposals of modified inertia.
Removing galaxies with possible systematic concerns such as central bulges or
special inclinations does not change this trend. Cold dark matter halos predict
a systematically deviating relation from the observed one. All aspects of
rotation curves are most naturally explained by modified gravity.
