The advantage of this property is that the value of the index can be immediately compared to r, which is a metric with which most practitioners are familiar. Any deviation from r indicates an increase in the differences in proportion to α. At this threshold, we can then calculate the logarithmic average of each agreement index that composes it. This is what can be said: among the time series selected in Figure 6, we can better detect the differences in the numerical value of the different metrics compared to the data analyzed (time profiles and dispersal diagrams). By focusing on the profiles of Figure 6c,d collected on very dry areas, the best performance of n compared to AC is clear. Both profiles have limited temporal variability and reduced correlation. AC has a negative (and a-bounds) value of €1,668 for profile c and a positive and higher value (0.227) for the d profile, which has a lower correlation and clear distortion. Rather, it shows a value below both correlations, and decreases for the d profile relative to c. It is interesting to note that the d profile tells us that the application of a linear transformation would greatly improve the agreement. Systematic additive and proportional distortions can interact. To illustrate this situation, column c) in Figure 2 shows the value between the index calculated for 2 vectors, with a given combination of distortions minus the value of the index calculated from the same vectors without bias. This only appears for a given correlation of.
This graphical representation can help illustrate the sensitivity of an index for small changes in b and m. Most indices react in the same way, with the notable exception of HQ. The AC Ji-Gallo index may be higher (i.e. more compliance) with a combination of small distortions than without any bias. The 100% differences have the same meaning as for the different agreements. Figure 2 shows how the four metrics analyzed for the generated datasets are cut based on the additive and multiplier distortion imposed and the initial correlation between X and Y. A first note about the plots in columns a) and b) in Figure 2 is that there is an intersection point of the iso lines for all metrics. It is assumed that metrics represent a correct decrease in compliance when there is an increased systematic disturbance for all types of correlations.