In this paper we will take a careful look at the well-known fact that a complete 2π rotation in three dimensional space, while leaving vectors, tensors and generally the integral representations of the rotation group unchanged, causes a sign change in the half-integral spinor representations of the rotation group. First, in a brief introduction, we review the origin of the sign change of spinors by a 2π rotation. Next, we analyze Aharonov and Susskind's (hereafter referred to as A. & S.) (1967) original proposal for detecting such a sign change and compare it with a later proposal^{1} for detecting the sign change using neutron beams that are coherently split and recombined. While the A. & S. experiment is, we think, conceptually more interesting, the neutron beam experiment has actually been carried out. And finally, we discuss the philosophical significance of the rotationally induced spinor sign change.