  Fitting the model "A" to dark matter direct detection data, when the model
that underlies the data is "B", introduces a theoretical bias in the fit. We
perform a quantitative study of the theoretical bias in dark matter direct
detection, with a focus on assumptions regarding the dark matter interactions,
and velocity distribution. We address this problem within the effective theory
of isoscalar dark matter-nucleon interactions mediated by a heavy spin-1 or
spin-0 particle. We analyze 24 benchmark points in the parameter space of the
theory, using frequentist and Bayesian statistical methods. First, we simulate
the data of future direct detection experiments assuming a momentum/velocity
dependent dark matter-nucleon interaction, and an anisotropic dark matter
velocity distribution. Then, we fit a constant scattering cross section, and an
isotropic Maxwell-Boltzmann velocity distribution to the simulated data,
thereby introducing a bias in the analysis. The best fit values of the dark
matter particle mass differ from their benchmark values up to 2 standard
deviations. The best fit values of the dark matter-nucleon coupling constant
differ from their benchmark values up to several standard deviations. We
conclude that common assumptions in dark matter direct detection are a source
of potentially significant bias.
