  We apply the marked correlation function test proposed by Armijo et al.
(Paper I) to samples of luminous red galaxies (LRGs) from the final data
release of the Sloan Digital Sky Survey (SDSS) III. The test assigns a
density-dependent mark to galaxies in the estimation of the projected marked
correlation function. Two gravity models are compared: general relativity (GR)
and $f(R)$ gravity. We build mock catalogues which, by construction, reproduce
the measured galaxy number density and two-point correlation function of the
LRG samples, using the halo occupation distribution model (HOD). A range of HOD
models give acceptable fits to the observational constraints, and this
uncertainty is fed through to the error in the predicted marked correlation
functions. The uncertainty from the HOD modelling is comparable to the sample
variance for the SDSS-III LRG samples. Our analysis shows that current galaxy
catalogues are too small for the test to distinguish a popular $f(R)$ model
from GR. However, upcoming surveys with a better measured galaxy number density
and smaller errors on the two-point correlation function, or a better
understanding of galaxy formation, may allow our method to distinguish between
viable gravity models.
