Final-state effects on angle-resolved photoemission extended fine structure (ARPEFS) chi(k) curves were studied using previously published normal-emission experimental data from the S 1s and S 2p core levels of c(2x2)S/Ni(001). The two chi(k) curves appeared to be approximately 180 degrees out of phase, as predicted by Tong and Tang. However. in contrast to the expectations based on plane-wave theory, the Fourier transforms of the experimental S 1s and S 2p data sets are quite different, with a generalized Ramsauer-Townsend splitting present in the 1s but not in the 2p data. Multiple-scattering spherical-wave calculations were carried out to study the final-state effects. On the basis of the calculations, an approximate method for analyzing ARPEFS data from a non-s initial-state using only the higher-l partial wave was proposed and successfully tested with the experimental S 2p ARPEFS data.