A New Weighted Rank Correlation
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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.
Copyright: © 2021 Tahani A. Maturi and Ezz H. Abdelfattah. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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- Weighted correlation
- top ranking
- top-down correlation coefficient
- weighted Kendall's Tau
- Blest’s correlation coefficient