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I have two variables which represent two performance measures.
I ranked a finite set of elements according these two variables.
Therefore, I have to ranks. Suppose the ranks are performed in descending order (the highest the measure the highest the value in the decision process of each element).

For instance, an ordered set $\Omega$ of $10$ elements according the two measures A and B.

R#A = [5 3 1 9 2 10 6 7 4 8];  
R#B = [9 7 4 8 5 6 1 3 2 10];

Suppose that now I truncate R#A and R#B in order to select the "top 5" elements:

R#A_5 = [5 3 1 9 2];
R#B_5 = [9 7 4 8 5];

In your opinion it is still possible to get the Spearman's rho correlation coefficient with these two partial orders?

I know that
1) We are in the second step of the Spearman's because we are alrady dealing with ranks.
2) The Sample size is very low but it is just for explanation.

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I think you have one of two problems, depending on the what exactly R#A and R#B are. For example, does the 5 in R#A mean that the first element has a rank of 5, or does it mean that the fifth element has a rank of 1?

If it is the former, then you have not selected the top 5 elements. If it is the latter then R#A and R#B contain different elements.

You can certainly run a correlation on the two vectors; but what will the output mean?

Perhaps you can tell us what you are trying to accomplish.

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  • $\begingroup$ R#A and R#B are the ranked variables expressed by the element's position. In your example it means that the fifth element has a rankk of 1. $\endgroup$
    – Marco
    Oct 28, 2013 at 12:33
  • $\begingroup$ Then I don't see what a rho (or any other correlation) would actually mean. $\endgroup$
    – Peter Flom
    Oct 28, 2013 at 12:42
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    $\begingroup$ Nothing, I'm afraid. $\endgroup$
    – Marco
    Oct 28, 2013 at 15:34

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