Which method is more accurate? or errors have error bars

This document is my attempt at distilling some of the information in two papers published by Anthony Nicholls (J. Comput. Aided Mol. Des. 2014, 28, 887; ibid 2016, 30, 103). Anthony also very kindly provided some new equations, not found in the papers, in response to my questions. The paper describes how one determines whether the difference in accuracy of two methods in predicting some properties for the same data set is statistically significant using root-mean-square errors, mean absolute errors, mean errors, and Pearsons r values.