A rose by any other name: On basic scores from the 2x2 table and the plethora of names attached to them

Abstract

Forecast evaluation metrics have been discovered and rediscovered in a variety of contexts, leading to confusion. We look at measures from the 2x2 contingency table and the history of their development and illustrate how different fields working on similar problems has led to different approaches and perspectives of the same mathematical concepts. For example, Probability of Detection is a quantity in meteorology that was also called Prefigurance in the field, while the same thing is named Recall in information science and machine learning, and Sensitivity and True Positive Rate in the medical literature. Many of the scores that combine three elements of the 2x2 table can be seen as either coming from a perspective of Venn diagrams or from the Pythagorean means, possibly weighted, of two ratios of performance measures. Although there are algebraic relationships between the two perspectives, the approaches taken by authors led them in different directions, making it unlikely that they would discover scores that naturally arose from the other approach. We close by discussing the importance of understanding the implicit or explicit values expressed by the choice of scores. In addition, we make some simple recommendations about the appropriate nomenclature to use when publishing interdisciplinary work.