  At higher energies the present complex quantum theory with its unitary group
might expand into a real quantum theory with an orthogonal group, broken by an
approximate $i$ operator at lower energies. Implementing this possibility
requires a real quantum double-valued statistics. A Clifford statistics,
representing a swap (12) by a difference $\gamma_1-\gamma_2$ of Clifford units,
is uniquely appropriate. Unlike the Maxwell-Boltzmann, Fermi-Dirac,
Bose-Einstein, and para- statistics, which are tensorial and single-valued, and
unlike anyons, which are confined to two dimensions, Clifford statistics are
multivalued and work for any dimensionality. Nayak and Wilczek proposed a
Clifford statistics for the fractional quantum Hall effect. We apply them to
toy quanta here. A complex-Clifford example has the energy spectrum of a system
of spin-1/2 particles in an external magnetic field. This supports the proposal
that the double-valued rotations --- spin --- seen at current energies might
arise from double-valued permutations --- swap --- to be seen at higher
energies. Another toy with real Clifford statistics illustrates how an
effective imaginary unit $i$ can arise naturally within a real quantum theory.
