Excuse my language, I am not a statistician so I will try to explain my question as a layman.

If we rank items into groups, let's say best={a,b,c}, good={d,e,f,g}, average={h,i,j} and we have a measurement showing that a>h>b>c>d>i>j>e>f>g, how can we measure the correlation between the two rankings? And how to measure correlation between two rankings into groups, let's say two opinions of good, average and bad?

An example in real world terms: sports expert A says that (a,b,c,d,e) are the elite teams. Expert B says that the elite teams are (a,b,d,f,g). Later we have a competition with participation of 8 teams, including some of the ranked as elite by experts. The results are 1st b; 2nd x; 3rd-4th a,f; 5th-8th e, c, y, z. How do I measure correlation of such rankings to see which of the experts was more precise?

Can I assign ranks "1" to everyone in the first group, "2" in the second and so on and try to do something similar to the Spearman correlation? If so, what to do with the equal ranked cases?


The conventional thing to do with equal ranks is to assign them the average of the ranks they would have got if they had been assigned separate ranks. So if expert A said {a, b, c, d, e} were the elite teasm and {x, y, z} were not then expert A has assigned rank 3 to the five elite teams (1+2+3+4+5)/5 and rank 7 to the other teams (6+7+8)/3. You can carry out the same procedure for the competition results and then compute Spearman's $\rho$.


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