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.
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