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I am considering the following question: when there are ties, how are ranks calculated?

In some references, they first rank them without repeating the ranks, and then average the ranks of those ties and assign the average rank to each one in the ties. I was wondering if that way is unanimously used in statistics for determining the ranks?

Are there other ways to determine the ranks in tie cases? If yes, when to use which way?

Thanks and regards!

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R lists 5 ways to calculate ranks. The first ("average") is by far the most commonly used: it has the advantage that the ranks computed this way are scale/permutation invariant

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  • $\begingroup$ Thanks! Are there some principles on when to use which way in statistics? $\endgroup$
    – Tim
    Apr 19, 2013 at 20:15
  • $\begingroup$ yea; as I wrote in my answer of all the methods listed there the average is the only one that yields scale/permutation invariants ranks (which means that the ranks of the observations is preserved even if you re-order or re-scale the original observations: this is a natural property to expect) so at least in the sense of invariance it is the best of the five. $\endgroup$
    – user603
    Apr 19, 2013 at 20:17
  • $\begingroup$ What about the other ways? when are they useful? $\endgroup$
    – Tim
    Apr 19, 2013 at 20:17
  • $\begingroup$ when you don't want to have ties in the ranks, even when the underlying data has ties. I guess. $\endgroup$
    – user603
    Apr 19, 2013 at 20:18
  • $\begingroup$ Do you have in mind some examples to use the other ways? $\endgroup$
    – Tim
    Apr 19, 2013 at 20:21

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