Rank Correlation Statistic

A Rank Correlation Statistic is a test statistic that measures the relationship between rankings of different ordinal variables or different rankings of the same variable.

• Example(s):
  • Spearman's rank correlation, ρ
  • Kendall's tau rank correlation, τ
  • Goodman and Kruskal's gamma, γ
• See: Wilcoxon Signed-Rank Test, Statistic, Ranking, Ordinal Data, Statistical Significance, Nonparametric, Mann–Whitney U Test, Preference Learning; ROC Analysis; Preference Learning.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/rank_correlation Retrieved:2015-8-20.
  • In statistics, a rank correlation is any of several statistics that measure the relationship between rankings of different ordinal variables or different rankings of the same variable, where a "ranking" is the assignment of the labels "first", "second", "third", etc. to different observations of a particular variable. A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them. For example, two common nonparametric methods of significance that use rank correlation are the Mann–Whitney U test and the Wilcoxon signed-rank test.

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/rank_correlation#Correlation_coefficients Retrieved:2015-8-20.
  • Some of the more popular rank correlation statistics include
    1. Spearman's ρ.
    2. Kendall's τ.
    3. Goodman and Kruskal's γ.
  • An increasing rank correlation coefficient implies increasing agreement between rankings. The coefficient is inside the interval [−1, 1] and assumes the value:
    • 1 if the agreement between the two rankings is perfect; the two rankings are the same.
    • 0 if the rankings are completely independent.
    • −1 if the disagreement between the two rankings is perfect; one ranking is the reverse of the other.
  • Following , a ranking can be seen as a permutation of a set of objects. Thus we can look at observed rankings as data obtained when the sample space is (identified with) a symmetric group. We can then introduce a metric, making the symmetric group into a metric space. Different metrics will correspond to different rank correlations.

2011

• (Sammut & Webb, 2011) ⇒ Claude Sammut, and Geoffrey I. Webb. (2011). “Rank Correlation.” In: (Sammut & Webb, 2011) p.828
  • QUOTE: Rank correlation measures the correspondence between two rankings τ and τ′ of a set of m objects. Various proposals for such measures have been made, especially in the field of statistics. Two of the best-known measures are Spearman’s Rank Correlation and Kendall’s tau:

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