The energy distributions I(E-1,E-2) of correlated electron pairs, excited from a single crystal of W(110) by 29 eV spin-polarized electrons, have been measured for two azimuthal orientations of the crystal: (a) the  direction is perpendicular to the scattering plane containing two-electron detectors and normal to the sample surface; (b) the sample was rotated by 90 degrees around the surface normal such that the  direction was perpendicular to the scattering plane. The polarization of the incident beam was chosen to be perpendicular to the scattering plane. The energy distributions were measured for spin-up I+(E-1,E-2) and spin-down I-(E-1,E-2) polarizations of the primary electrons and analyzed in terms of the spin asymmetry A=(I+-I-)/(I++I-). The asymmetry was visualized by extracting the energy sharing distribution for particular total energy of pairs from the two-dimensional distribution of the electron pairs. The asymmetry is nonzero due to a spin-orbit coupling and is different for the two azimuthal orientations of the sample. These results are discussed in terms of anisotropy of the spin-orbit coupling and anisotropy of the orbital moment in W(110). The relevance of these results to the magnetic anisotropy of thin Fe films on W(110) is discussed.