  The detection of gravitational waves has offered us the opportunity to
explore the dynamical and strong-field regime of gravity. Because matched
filtering is more sensitive to variations in the gravitational waveform phase
than the amplitude, many tests of gravity with gravitational waves have been
carried out using only the former. Such studies cannot probe the
non-Einsteinian effects that may enter only in the amplitude. Besides, if not
accommodated in the waveform template, a non-Einsteinian effect in the
amplitude may induce systematic errors on other parameters such as the
luminosity distance. In this paper, we derive constraints on a few modified
theories of gravity (Einstein-dilaton-Gauss-Bonnet gravity, scalar-tensor
theories, and varying-$G$ theories), incorporating both phase and amplitude
corrections. We follow the model-independent approach of the parametrized
post-Einsteinian formalism. We perform Fisher analyses with Monte-Carlo
simulations using the LIGO/Virgo posterior samples. We find that the
contributions from amplitude corrections can be comparable to the ones from the
phase corrections in case of massive binaries like GW150914. Also, constraints
derived by incorporating both phase and amplitude corrections differ from the
ones with phase corrections only by 4% at most, which supports many of the
previous studies that only considered corrections in the phase. We further
derive reliable constraints on the time-evolution of a scalar field in a
scalar-tensor theory for the first time with gravitational waves.
