  The upcoming direct detection of gravitational waves will open a window to
probing the strong-field regime of general relativity (GR). As a consequence,
waveforms that include the presence of deviations from GR have been developed
(e.g. in the parametrized post-Einsteinian approach). TIGER, a data analysis
pipeline which builds Bayesian evidence to support or question the validity of
GR, has been written and tested. In particular, it was shown recently that data
from the LIGO and Virgo detectors will allow to detect deviations from GR
smaller than can be probed with Solar System tests and pulsar timing
measurements or not accessible with conventional tests of GR. However, evidence
from several detections is required before a deviation from GR can be
confidently claimed. An interesting consequence is that, should GR not be the
correct theory of gravity in its strong field regime, using standard GR
templates for the matched filter analysis of interferometer data will introduce
biases in the gravitational wave measured parameters with potentially
disastrous consequences on the astrophysical inferences, such as the
coalescence rate or the mass distribution. We consider three heuristic possible
deviations from GR and show that the biases introduced by assuming GR's
validity manifest in various ways. The mass parameters are usually the most
affected, with biases that can be as large as $30$ standard deviations for the
symmetric mass ratio, and nearly one percent for the chirp mass, which is
usually estimated with sub-percent accuracy. We conclude that statements about
the nature of the observed sources, e.g. if both objects are neutron stars,
depend critically on the explicit assumption that GR it the right theory of
gravity in the strong field regime.
