  The direct detection of gravitational waves (GW) from merging binary black
holes and neutron stars mark the beginning of a new era in gravitational
physics, and it brings forth new opportunities to test theories of gravity. To
this end, it is crucial to search for anomalous deviations from general
relativity in a model-independent way, irrespective of gravity theories, GW
sources, and background spacetimes. In this paper, we propose a new universal
framework for testing gravity with GW, based on the generalized propagation of
a GW in an effective field theory that describes modification of gravity at
cosmological scales. Then we perform a parameter estimation study, showing how
well the future observation of GW can constrain the model parameters in the
generalized models of GW propagation.
