  We study the consequences of limited recoil sense reconstruction on the
number of events required to reject isotropy and detect a WIMP signal using a
directional detector. For a constant probability of determining the sense
correctly, 3-d read-out and zero background, we find that as the probability is
decreased from 1.0 to 0.75 the number of events required to reject isotropy
using the mean angle statistic is increased by a factor of a few. As the
probability is decreased further the number of events required using this
statistic increases sharply, and in fact isotropy can be rejected more easily
by discarding the sense information and using axial statistics. This however
requires an order of magnitude more events than vectorial data with perfect
sense determination. We also consider energy dependent probabilities of
correctly measuring the sense, 2-d read-out and non-zero background. Our main
conclusion regarding the sense determination is that correctly determining the
sense of the abundant, but less anisotropic, low energy recoils is most
important for minimising the number of events required.
