Revisiting the concept of a symmetric index of agreement for continuous datasets

Quantifying how close two datasets are to each other is a common and necessary undertaking in scientific research. The Pearson product-moment correlation coefficient r is a widely used measure of the degree of linear dependence between two data series, but it gives no indication of how similar the values of these series are in magnitude. Although a number of indexes have been proposed to compare a dataset with a reference, only few are available to compare two datasets of equivalent (or unknown) reliability. After a brief review and numerical tests of the metrics designed to accomplish this task, this paper shows how an index proposed by Mielke can, with a minor modification, satisfy a series of desired properties, namely to be adimensional, bounded, symmetric, easy to compute and directly interpretable with respect to r. We thus show that this index can be considered as a natural extension to r that downregulates the value of r according to the bias between analysed datasets. The paper also proposes an effective way to disentangle the systematic and the unsystematic contribution to this agreement based on eigen decompositions. The use and value of the index is also illustrated on synthetic and real datasets.