Top: normalized histogram of the vertical metallicity gradient for Z> 0 fields (red), shown in Fig. 7, and corresponding histogram (blue) of the permuted sample. The near complete overlap (0.27σ) between the two distributions indicates that the vertical metallicity gradient in the Z> 0 might as well be obtained by pure chance. Bottom: same as the top panel for the Z< 0 fields. The mean value of the observed distribution (red) is located at 3.82σ from the mean of the permuted sample, indicating that it is unlikely that the vertical metallicity gradient for Z< 0 was obtained by chance.