  The observations of gravitational-wave signals from astrophysical sources
such as binary inspirals will be used to test General Relativity for self
consistency and against alternative theories of gravity. I describe a simple
formula that can be used to characterize the prospects of such tests, by
estimating the matched-filtering signal-to-noise ratio required to detect
non-General-Relativistic corrections of a given magnitude. The formula is valid
for sufficiently strong signals; it requires the computation of a single
number, the fitting factor between the General-Relativistic and corrected
waveform families; and it can be applied to all tests that embed General
Relativity in a larger theory, including tests of individual theories such as
Brans-Dicke gravity, as well as the phenomenological schemes that introduce
corrections and extra terms in the post-Newtonian phasing expressions of
inspiral waveforms. The formula suggests that the volume-limited
gravitational-wave searches performed with second-generation ground-based
detectors would detect alternative-gravity corrections to General-Relativistic
waveforms no smaller than 1-10% (corresponding to fitting factors of 0.9 to
0.99).
