# Willmott Index Of Agreement

Through numerical analysis of different proposed metrics, this document shows that a modified version of The Mielke Index is preferable to the others. This index, cited here, is adimensional, limited, symmetrical, easy to calculate and directly interpretable in relation to the commonly used pearson coefficient of correlation r. This index can in principle be considered as a natural extension to r that regulates the downward r value depending on the distortion that occurs in the data. Limited between a lower limit (z.B 0) that does not correspond to an agreement and a ceiling (for example. B 1) A perfect match. One consequence is that higher values should always indicate greater agreement. Quantifying the proximity of two data sets is a common and necessary undertaking in the field of scientific research. The pearson-moment r correlation coefficient is a widespread measure of the degree of linear dependence between two sets of data, but gives no indication of the similarity of the values of these series in size. Although a number of indices have been proposed to compare a dataset to a reference, little data is available to compare two datasets with equivalent (or unknown) reliability. After a brief review and numerical testing of the metrics designed to accomplish this task, this document shows how an index proposed by Mielke can, with a minor modification, satisfy a number of desired characteristics, namely a dimensional, limited, symmetrical, easy to calculate and directly interpretable in relation to r.

We therefore show that this index can be considered a natural extension to r, which regulates the downward r value according to the distortion between the data sets analyzed. The document also proposes an effective way to unravel the systematic and non-systematic contribution to this agreement on the basis of own decompositions. The use and value of the index are also illustrated on synthetic and real data sets. similarity to the equation (7) and the simplified expression of the Mielke permutation index. As shown in Figure 3, the index obtained is identical to that of positively correlated vectors, while it remains at 0 if . Table of indexes of agreements and agreements on the data sets examined in this paper, with different correlations and systematic additive or multiplier distortions. An important point about the non-cryptic index is that, although it does not take into account any bias, it does not mean that it corresponds to the correlation. The two also do not correspond α in the case of Difference can be appreciated by looking at a cloud of dots and turning it. This changes their correlation, but thanks to the clean fences, will remain the same. This also leads to positive values for when, which can be interpreted as noise levels in the data.