Using spin-polarized scanning tunneling spectroscopy, we reveal how the standing wave patterns of confined surface state electrons on top of nanometer-scale ferromagnetic Co islands on Cu(111) are affected by the spin character of the responsible state, thus experimentally confirming a very recent theoretical result {[}L. Niebergall , Phys. Rev. Lett. 96, 127204 (2006)]. Furthermore, at the rim of the islands a spin-polarized state is found giving rise to enhanced zero bias conductance. Its polarization is opposite to that of the islands. The experimental findings are in accordance with ab initio spin-density calculations.