Fig. 13

Sunglasses, with scores being the probabilities; \(n =\) 1300; Kuiper’s statistic is \(0.03597 / \sigma = 2.935\), Kolmogorov’s and Smirnov’s is \(0.03365 / \sigma = 2.745\). The reliability diagrams with only 10 or 30 bins each fail to resolve the very high deviation for probabilities greater than 0.9 (unlike the diagram with 50 bins)—the smaller numbers of bins average away interesting behavior, without warning. The scalar summary statistics detect some statistically significant deviation, yet both are blind to the serious deviation for the highest scores that the plot of cumulative differences displays prominently; the steep drop at the highest scores in the cumulative plot has little to no effect on the Kolmogorov-Smirnov or Kuiper metrics, unfortunately