A New Selection Index to Address within Course Competition and between Course Competition for Ranking Examination Scores

Different scenarios of examinations have to be handled separately when measuring the true performance of students. If examiners are required to compare the performance of different groups of students who follow different combinations of subjects in an examination, their combined raw scores have to be used. In this case the raw marks can be combined by using a linear equation called a selection index. A proper selection index should correctly address two types of competitions; namely within course competition and between course competition. Although different selection indices were introduced to address these issues in literature, these methods fail to fulfill the requirements expected from a proper selection method. The main objective of this study is to introduce a new selection index called Skewness based Common Currency Index (SCCI) which addresses both within course competition and between course competitions. The proposed method considers the relative subject effects, and these effects are identified by introducing a shape parameter to the selection index. The favorability of the proposed SCCI method is compared with three alternative selection indices. According to the statistical analysis it is found that there is a significant difference of ranks between the selected indices at 5% significance level. Further, the rank differences between the ranks of the SCCI method with the ranks of true student effects show smaller deviations with compared to the rank differences of the ranks of the other three selection methods. Based on the results of Wilcoxon rank sum test, it is revealed that the ranks of SCCI method are much closer to the ranks of the student effects than other three selection methods. Also the ranks of SCCI method have the highest correlation with the ranks assigned to the true student effects. According to the overall results it was confirmed that the new SCCI method can be used as a selection index to compare performance of examinees who follow different courses in an examination.