Weighting Lower and Upper Ranks Simultaneously Through Rank-Order Correlation Coefficients
Two new weighted correlation coefficients, that allow to give more weight to the lower and upper ranks simultaneously, are proposed. These indexes were obtained computing the Pearson correlation coefficient with a modified Klotz and modified Mood scores. Under the null hypothesis of independence of the two sets of ranks, the asymptotic distribution of these new coefficients was derived. The exact and approximate quantiles were provided. To illustrate the value of these measures an example, that could mimic several biometrical concerns, is presented. A Monte Carlo simulation study was carried out to compare the performance of these new coefficients with other weighted coefficient, the van der Waerden correlation coefficient, and with two non-weighted indexes, the Spearman and Kendall correlation coefficients. The results show that, if the aim of the study is the detection of correlation or agreement between two sets of ranks, putting emphasis on both lower and upper ranks simultaneously, the use of van der Waerden, signed Klotz and signed Mood rank-order correlation coefficients should be privileged, since they have more power to detect this type of agreement, in particular when the concordance was focused on a lower proportion of extreme ranks. The preference for one of the coefficients should take into account the weight one wants to assign to the extreme ranks.
KeywordsMonte Carlo simulation Rank-order correlation Weighted concordance Signed Klotz scores Signed Mood scores van der Waerden scores
Research was partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal – FCT, under the projects PEst-OE/SAU/UI0447/2011 and UID/MAT/00006/2013.
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