Dissimilarity or distance metrics between pairs of values I have cubes (objects) in which their volume was manually calculated (let's call this method the "manual method". Assume that the volume measures obtained by this method are considered the "true" measures. I am also using an automatization system that calculates volumes from digital image files (let's call this the "automatic method"). I have measured the same n cubes using both methods, and the automatic method is not 100% accurate. 
I have two sequences of positive integers (volume values) for each method (below I illustrate an output example with just 3 values, although I have hundreds of values):
manual method (considered the true values) - [35, 69, 40]
automatic method - [10, 68, 35]
Basically, for the first cube, the manual method yielded 35 (assume there is no unit) and the automatic method produced 10; for the second object, the manual method delivered 69 and the automatic method yielded 68, and so on...
I would like to calculate some distance or dissimilarity measures between the values generated by both methods to evaluate the automatic method's accuracy.
I have computed summary statistics, such as mean, median, standard deviation, percentage of differences in these values for a single object, etc... In addition to that, I have tested whether both sequences come from the same probability distribution or not. For this purpose, I employed the Kolmogorov-Smirnov and the Anderson-Darling tests. However, I would also like to include other type of statistics, such as distance or dissimilarity metrics, as mentioned above. Could you please recommend a statistical method that achieves this?
 A: I think you may have made this harder on yourself then it needs to be. In my opinion you could simply correlate the 2 measures to see how similar they are. If the correlation is high, then the differences in the raw values would be due to scaling effects. If it is low, than they do not measure the same thing.
An alternative to a simple correlation would be to use classical test theory. You could compute "reliability" metrics which would also provide similar information to that of correlation. However, some methods may be more appropriate depending on the nature of the distributions of the variables. See this page on inter-rater reliability.
If you are interested in dissimilarity and you have multiple vectors, as in you have a vector from each method for multiple observations. You could compute a "precision matrix" which would not only inform you of how dissimilar the methods are, but if the methods are more or less similar across your observations. A precision matrix in layman terms is the inverse of the covariance matrix. The covariance matrix represents the similarity of 2 variables, therefore the precision matrix provides the dissimilarity.
Distant metrics could also be used but are only useful in comparison. Because their scale will be arbitrary, they are only useful in comparing if you are comparing multiple methods. If method A has an inverse distance of X to method B, you could compare that distance to method C, if they are all scaled to the same unit.
