I have a list of numbers that I want to measure how well are sorted/decrease. I want something more detailed than simply inversion, I want to know how uniformly they decrease.
For examples, the list (10,8,6,4,2,0) should have a higher score than (10,9,8,,3,2,1).
(10,8,6,4,2,0) and (10, 8, 6, 7, 4, 2) should both have a higher score than (10.5,10.4,10.3, 10.1, 8, 6).
In other words, I want to measure how well the numbers descend, and also I want to favour the magnitude of descending.
My idea is to assign each number an index, and then to measure the correlation. However, what kind of correlation would I want? Should it be Pearson since I am looking for a linear correlation. Or is there a better method?
More info: In some tests I have done Pearson gave the list [10.91, 4.84, 4.75, 4.75, 4.397, 4.37, 3.85, 3.05, 3.05] a lower correlation than the list [14.71, 14.71, 14.71, 10.15, 10.15, 10.17, 10.22, 10.22, 10.22].
The first list is more desirable to me since the range is bigger - we can see the list is descending more strongly. Should I use spearmans rank instead? If so, why?