  We continue the program started in cond-mat/9809384 and explain the
statistics of the excitations for the generalizations of the paired states in
the quantum Hall effect in terms of the parafermion statistics. We show that
these excitations behave as combinations of bosons and parafermions. That
generalizes the prior treatment of the paired (Pfaffian) state where the
excitations behave as combinations of bosons and fermions. We explain what it
means, from a quantum mechanical point of view, for a particle to be a
`parafermion' rather than a boson or a fermion and work through several
explicit examples. The resulting multiplets coincide exactly with the angular
momentum multiplets found numerically for the $k+1$ particle interaction
Hamiltonian on a sphere. We also present a proof that the wave functions found
in cond-mat/9809384 are indeed the correlation functions of the parafermion
conformal field theory.
