Weighted Z ? Score Based on Discrimination Factors

Abstract

Short comings in the current Z – score system were pointed out in the paper [1] presented at the last symposium. In this paper we show how these short comings can be minimized.In Sri Lanka, the results of the G. C. E. (Adv. Level) Examination are mainly used for the purpose of selecting students for university admission. There are two other purposes; one is to select personnel for non-graduate jobs and second is to select students for the courses conducted by professional, technical and private institutes. The results of the G. C. E. (Adv. Level) Examination, released in terms of grades based on the raw marks, serve the two purposes mentioned in the latter cases. To achieve the main purpose the results of the G. C. E. (Adv. Level) Examination are released, at present, in terms of the average of the three Z – scores obtained for the three subjects. The competition is very high for university admission due to the limited and small number of places available in the universities. As far as the streams such as Medicine, Engineering, Commerce & Management, and Law are concerned, the demand is very high. Usually the topmost group in Biological Sciences gets the opportunity to enter Medical faculties and the topmost group in Physical Sciences gets the opportunity to enter Engineering faculties. The criterion for selecting students especially to the highly competitive streams is a deciding factor for the future of students. Criteria used for this purpose should enable the authorities to select the best out of the groups. The main objective of this study is to find out a new system of measurement incorporating weights which could minimize the shortcomings in the present average Z- score method [1] that is used for selecting students for university admission [2]. In our study it is observed, from the last five years’ results, that the means and the standard deviations of the subjects vary significantly. The variations can be seen within and between subjects. These variations are mainly due to the variations in degrees of difficulty of the subjects. The degrees of difficulty of the papers of the same subject given in two different years are not the same. They too vary. Our main objective of this study is to find a way to incorporate this variation into the selection criteria. In our method a discrimination factor for each subject is considered. This factor is used to measure the discrimination between the cleverer students and the weaker students. For any combination of three subjects the recommended weights are computed based on the discrimination factors for the three subjects. We then consider the total of the weighted Z – scores of the three subjects as the criterion. This method gives due consideration to the students who perform well in difficult subjects; i.e. subjects with higher discrimination factors. It gives relatively less weight for the subjects that are easy to score in. For the identical aggregate of raw marks of the students the average scores of respective students vary widely. This range of variation is reduced by our method