  The direction dependence of the event rate in WIMP direct detection
experiments provides a powerful tool for distinguishing WIMP events from
potential backgrounds. We use a variety of (non-parametric) statistical tests
to examine the number of events required to distinguish a WIMP signal from an
isotropic background when the uncertainty in the reconstruction of the nuclear
recoil direction is included in the calculation of the expected signal. We
consider a range of models for the Milky Way halo, and also study rotational
symmetry tests aimed at detecting non-sphericity/isotropy of the Milky Way
halo. Finally we examine ways of detecting tidal streams of WIMPs. We find that
if the senses of the recoils are known then of order ten events will be
sufficient to distinguish a WIMP signal from an isotropic background for all of
the halo models considered, with the uncertainties in reconstructing the recoil
direction only mildly increasing the required number of events. If the senses
of the recoils are not known the number of events required is an order of
magnitude larger, with a large variation between halo models, and the recoil
resolution is now an important factor. The rotational symmetry tests require of
order a thousand events to distinguish between spherical and significantly
triaxial halos, however a deviation of the peak recoil direction from the
direction of the solar motion due to a tidal stream could be detected with of
order a hundred events, regardless of whether the sense of the recoils is
known.
