How to correlate a set of compositions to a same-sized set of estimates of these compositions?
-> composition(estimated) vs composition(real)
Imagine you have a mixture of 5 liquids A+B+C+D+E, which in total have a concentration of 1. You have a test (or heuristic) to determine the concentration of each liquid separately but the tests are quite vague: For an evaluation of the test, you measure 100 reference-mixtures with known real concentrations [A,B,C,D and E].
Here, as an invented example, the real A-content vs the "tested" one:
So you can show the correlation (real vs test) for each of the 5 contents separately!
But my question is now: How to combine the 5 individual correlations? Can you recommend a way to show the correlation to the combined composition? (composition = the ratios of the individual contents A,B,C,D and E, which together are always 1)
I want to show that the tests can estimate the overall composition, not the individual concentrations, which means: composition(estimated) vs composition(real)
I would prefer a statistical method that can be visualized and does not just give a single number as the output. I thought of using the sum of products (estimated vs real) (AxA + BxB + CxC + DxD + ExE) and comparing it to permutations of the same contents/estimates. But I don't know how to evaluate or visualize this approach. I am thankful for any ideas or references to established methods!