  It is shown that the symmetry under parity of the wavefunctions of two
identical particles with an arbitrary spin $s$ in three spatial dimensions
accounts for the appropriate wavefunction exchange statistics under the
permutations of particles. The standard properties of the angular momentum in
non-relativistic quantum mechanics account for the sign factor $(-1)^{2s}$ that
the wavefunctions acquire under the permutation of coordinates of the two
particles, without any additional requirements, directly relating spin and the
particle exchange statistics in the non-relativistic context.
