  The observation of gravitational waves from compact binary coalescences is a
promising tool to test the validity of general relativity (GR) in a highly
dynamical strong-field regime. There are now a variety of tests of GR performed
on the observed compact binary signals. In this paper, we propose a new test of
GR that compares the results of these individual tests. This meta
inspiral-merger-ringdown consistency test (IMRCT) involves inferring the final
mass and spin of the remnant black hole obtained from the analyses of two
different tests of GR and checking for consistency. If there is a deviation
from GR, we expect that different tests of GR will recover different values for
the final mass and spin, in general. We check the performance of the meta IMRCT
using a standard set of null tests used in various gravitational-wave analyses:
the original IMRCT, parameterized phasing tests (TIGER and FTI) and the
modified dispersion test. However, the meta IMRCT is applicable to any tests of
GR that infer the initial masses and spins or the final mass and spin,
including ones that are applied to binary neutron star or neutron star--black
hole signals. We apply the meta IMRCT to simulated quasi-circular GR and non-GR
binary black hole (BBH) signals as well as to eccentric BBH signals in GR
(analyzed with quasicircular waveforms). We find that the meta IMRCT gives
consistency with GR for the quasi-circular GR signals and picks up a deviation
from GR in the other cases, as do other tests. In some cases, the meta IMRCT
finds a significant GR deviation for a given pair of tests (and specific
testing parameters) while the individual tests do not, showing that it is more
sensitive than the individual tests to certain types of deviations. In
addition, we also apply this test to a few selected real compact binary signals
and find them consistent with GR.
