Top: normalized histograms of the projected radial (R_gcd) metallicity gradient of original sample (red), and the normalized histograms of the projected radial gradient of the permuted samples (blue). Bottom: same as the top panel for the vertical (|Z|) metallicity gradient. The lack of overlap between the two (red and blue) histograms qualitatively indicates that neither the projected radial nor the vertical gradient can be explained by chance. Quantitatively, the two observed distribution means are at 3.2σ and 8.2σ from the permuted distribution means, reassuring that neither gradient is likely to have been reproduced by chance.