By introducing paths on the hypersurface of the band-energy contribution free energy to the magnetic anisotropy energy and of corresponding differences in the zz-like elements of the electric conductivity tensor, viewed as an implicit function of the free energy, experimental spin-polarized scanning tunnel microscope STM data, namely, the recording of a differential current as a function of an externally applied field, can be analyzed and facilitate a direct comparison between theory and experiment. It is shown that along different paths rather different flipping times of the direction of the magnetization can occur. In particular, discussed are in terms of "theoretical experiments" horizontal and vertical movements of the tip, the influence of the magnetic properties of the tip as well as of typical samples. Furthermore, it is claimed that because of different time scales in a presently still fictional time-resolved mode for spin-polarized STM experiments even particular paths on these hypersurfaces could be mapped out.