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. © 2008 Science Publications.
Highlights
Every year many students want to apply for postgraduate courses and research, leading to a large number of applicants to universities
A new weighted rank correlation: Let (Xi, Yi), (1 i n) be an i.i.d. sample from a bivariate distribution and let (i, qi), i = 1, 2,..., n, be paired rankings of n objects, where qi is the rank of the Y values whose corresponding X has rank i among all {Xj}
This article proposed a new weighted rank correlation coefficient that was sensitive to agreement in the top rankings
Summary
Every year many students want to apply for postgraduate courses and research, leading to a large number of applicants to universities. Postgraduate committee can choose only few of them, according to some criteria such as GPA and the average of their grades in the major courses that they have studied before. Since the number of the applicants is large, the aim is to minimize the effort and the cost of interviewing all the candidates while choosing the best among them. In such cases, a measure which gives more weight to those who have higher grades is required. A couple of panels of judges in one of the Olympic game wants to choose the best participants
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