  We compute the accuracy at which a LISA-like space-based gravitational wave
detector will be able to observe deviations from General Relativity in the low
frequency approximation. To do so, we introduce six correction parameters that
account for modified gravity in the second post-Newtonian gravitational wave
phase for inspiralling supermassive black hole binaries with spin precession on
quasi-circular orbits. Our implementation can be regarded as a subset of the
ppE formalism developed by Yunes and Pretorius, being able to investigate also
next-to-leading order effects. In order to find error distributions for the
alternative theory parameters, we use the Fisher information formalism and
carry out Monte Carlo simulations for 17 different binary black hole mass
configurations in the range 10^5 Msun < M < 10^8 Msun with 10^3 randomly
distributed points in the parameter space each, comparing the full (FWF) and
restricted (RWF) version of the gravitational waveform. We find that the
binaries can roughly be separated into two groups: one with low (< ~10^7 Msun)
and one with high total masses (> ~10^7 Msun). The RWF errors on the
alternative theory parameters are two orders of magnitude higher than the FWF
errors for high-mass binaries while almost comparable for low-mass binaries.
Due to dilution of the available information, the accuracy of the binary
parameters is reduced by factors of a few, except for the luminosity distance
which is affected more seriously in the high-mass regime. As an application and
to compare our research with previous work, we compute an optimal lower bound
on the graviton Compton wavelength which is increased by a factor of ~1.6 when
using the FWF.
