  We establish for the first time heuristic correlations between harmonic space
phase information and higher order statistics. Using the spherical full-sky
maps of the cosmic microwave background as an example we demonstrate that known
phase correlations at large spatial scales can gradually be diminished when
subtracting a suitable best-fit (Bianchi-) template map of given strength. The
weaker phase correlations lead in turn to a vanishing signature of anisotropy
when measuring the Minkowski functionals and scaling indices in real-space and
comparing them with surrogate maps being free of phase correlations. Those
investigations can open a new road to a better understanding of signatures of
non-Gaussianities in complex spatial structures by elucidating the meaning of
Fourier phase correlations and their influence on higher order statistics.
