Research Article Open Access

A New Weighted Rank Correlation

Tahani A. Maturi1 and Ezz H. Abdelfattah1
  • 1 ,

Abstract

Problem Statement: There have been many cases in real life where two independent sources have ranked n objects, with the interest focused on agreement in the top rankings. Spearman's rho and Kendall's tau coefficients assigned equal weights to all rankings. As a result, the literature proposed several weighted correlation coefficients with emphasis on the top rankings, including the top-down, weighted Kendall's Tau and Blest's correlation coefficient. Approach: This article introduced a new weighted rank correlation coefficient that was sensitive to agreement in the top rankings. It presented the limiting distribution under the null hypothesis of independence and provided a summary of quantiles of the exact null distribution for n = 3(1)9. Results: The article summarized the power comparison between the new weighted coefficient and other weighted coefficients, and showed that the new weighted rank correlation coefficient provided the locally most powerful rank test. Conclusions/Recommendations: The new weighted correlation should be used along with other weighted coefficients when the interest focused on agreement in the top rankings, in order to make an effective inference.

Journal of Mathematics and Statistics
Volume 4 No. 4, 2008, 226-230

DOI: https://doi.org/10.3844/jmssp.2008.226.230

Submitted On: 30 June 2008 Published On: 31 December 2008

How to Cite: Maturi, T. A. & Abdelfattah, E. H. (2008). A New Weighted Rank Correlation. Journal of Mathematics and Statistics, 4(4), 226-230. https://doi.org/10.3844/jmssp.2008.226.230

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Keywords

  • Weighted correlation
  • top ranking
  • top-down correlation coefficient
  • weighted Kendall's Tau
  • Blest’s correlation coefficient