We consider the braid group representation which describes the non-abelian braiding statistics of the spin 1/2 particle world lines of an SU(2)$_4$ Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the $k=4$ Read-Rezayi quantum Hall state. We show that these braiding statistics are identical to those of Z$_3$ Parafermions.
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