Scanning tunneling spectroscopy (STS) on the system of isolated oxygen atoms adsorbed on the double layer of Fe on W(110) shows highly anisotropic spatial oscillations in the local density of states in the vicinity of the adsorbates. We explain this in terms of a single-particle model as electron waves being scattered by the potential induced by the presence of the oxygen atoms. Analysis of the wavelength of the standing electron waves and comparison with ab initio spin-resolved electronic structure calculations reveal that minority-spin bands of d-like symmetry are involved in the scattering process. By applying spin-polarized STS, we observe this standing wave pattern on one particular type of magnetic domain of Fe on W(110) only, thereby proving that the standing electron waves are highly spin polarized.