(1) x's average absolute error (MAE) averaged over 100 points sampled from a normal distribution with standard deviation σ. The black dashed line is defined by |ε| = √ 2/πσ coresponding to the MAE of a Gaussian error distribution with standard deviation σ. The Spearman rank correlation coefficient is 0.56 and 1.0 for the dots and x's, respectively. (b) Same as in (a) but in intervals of 0.01σ. The blue and orange lines are defined by |ε| = 2σ and |ε| = 3σ, respectively. The Spearman rank correlation coefficient is 0.55 and 0.99 for the dots and x's, respectively Notice that this does not imply a strong correlation between ε and σ since individual random errors can fluctuate significantly. For example the Spearman rank correlation (ρ rank ) for 10 points, each randomly sampled from a normal distribution with increasing standard deviations, shown in Figure is only 0.56. More fine grained sampling (Figure ) leads to a ρ rank of 0.55. As we will see in the results section, a more reasonable σ-range for uncertainty estimates on chemical data has the highest uncertainties roughly three times higher than the lowest uncertainties. Looking at the σ-range of 0.5-1.5 (grey shaded area, Figure ) leads to ρ rank = 0.31.