Comparisons of spatial distribution properties in the datasets. Left: histograms of the ratio of the differences between biased (black solid line), after iteration 1 (see text for a definition, blue dotted line), corrected (red dashed line), and true distance moduli to the true distance moduli, namely, the errors in percent on distance moduli. Middle: difference between true and biased (black diamonds), after iteration 1 (blue square) and at the end of the process or corrected (red circles) distance moduli versus true distance moduli. Right: ratio of the difference between assigned uncertainties and true errors to the true errors on distance moduli. Same colors and line styles as the left panel.