ON COMPARING THE POWER OF WEIGHTED AND UNWEIGHTED RANK CORRELATION COEFFICIENTS

Procedures are required which are robust (insensitive to changes in extraneous factors not under test) as well as powerful (sensitive to specific factors under test). Our objective is to review some weighted and unweighted measures of rank correlation and compare their power, through a simulation study. A weighted rank correlation is one that emphasizes items with low rankings and de-emphasizes those with high rankings, while unweighted rank correlation assigns equal weight to all levels. In this paper, we aimed to compare the power of 13 different weighted rank correlation coefficients and 9 unweighted rank correlation coefficients for various sample sizes in the presence of outliers. The results show that within the weighted measures, Mature-Abdelfattah 0.9, Blest, Mango, and Costa -Soares have the highest power. It shows also that, within the unweighted measures, the coefficients average slope, median slope, and Spearman Rho have the highest power values. In general, we note that weighted measures own highest power values in the presence of outliers in compare with the unweighted measures, and that quadrant association, Fechner, and Gideon -Hollister have the lowest power values among all the coefficients tested, while in our previous study (Abdelfattah [1]), we found that unweighted measures are more robust than weighted measures.