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Z-Score in University Admission:

2014 Jun 04

No better alternative

Professor Ranjith Premalal De Silva

Vice Chancellor, Uva Wellassa University

This is a response to the article appeared in Editorial: Analysis Commentary of the Daily Island on March 30 on Z-score by Dr. S. M. Poruthotage. Some of the misconceptions, incorrect assumptions, irrelevant example and erroneous conclusions in the said article warrant clarification in order to avoid misinformation to the readership. It demonstrates an example where individuals propose solutions for problems without having a sound understanding and knowledge of the background of the problem or the issue at hand.

Firstly, it must be emphasized that the Z-score computation was not introduced to resolve the issue of having two separate examinations held under two different syllabi in 2011 for university admission. In fact, Z-score concept was introduced for university admission in 2001 by Professor R.O. Thattil when there was a conflict in 3 subject and 4 subject combinations available for university admission. Z-score was used to convert the raw marks in different subjects to a common scale while weighting factor was used to adjust the discrepancy arising from different number of subjects.

Z-score was particularly recommended due to questions raised by a publication of the University Grants Commission, which stated that studies have shown, that when using the aggregate of the raw marks in selecting students to university, "undue competitive advantage may accrue to some students by virtue of the subjects they offer." This was due to the fact that examination papers in all subjects are not of the same level of difficulty. Hence, raw mark was not obviously an acceptable indicator of their relative performance at the A/L examination. There are better techniques than Z-score to provide a much equitable and fair evaluation for university admission from the advanced level results. However, in terms of the simplicity, computational efficiency and conceptual identity, Z-score is the best solution to provide a fair and just evaluation of student performance in diverse subjects.It only requires two parameters to provide standardized results which are possible to be compared upon a continuous scale.

However, a totally different approach was adopted to alleviate the differences of the results of new and old syllabus examinations held in 2011 for university admission although Z-score was used to bring the raw mark of each subject to a comparable scale as has been practiced since 2001.

Secondly, the hypothetical example detailed by Dr. Poruthotage is completely irrelevant to the current issue at hand and therefore is obviously misleading the readers. In the said example, the underlying populations are distinctly different and represent extreme tail ends of a population. Anybody having a basic knowledge in statistics would agree that two groups; one representing the best group of students from a population and the other accounting for the weakest students in the population cannot be ranked by simple merging the Z-scores calculated from these two groups of students separately. The knowledge in the best student in the weak group may be lower than the weakest student in the best group. When the evaluation of distinctly different populations needs to be considered, a common yardstick for measurement is the best choice. Although the situation was not so polarized as the hypothetical example of Dr. Poruthotage, this was the exact problem faced for the university admission in 2011. Two different populations (old and new syllabus students) were evaluated using two sets of questions papers and there was no common parameter to standardize the evaluations to a common scale. Further, the quoted example of Dr. Poruthotage with 10 students in each group is by no means an acceptable application of Z-score for ranking students as the Z-scores are obviously at too discrete levels.

In contrast, in Advanced Level, Z-score is used to obtain a standardized score for the students who opt for different subject combinations. The assumption made here is that the groups of students choosing different subjects are randomly derived from a large population. However, the application of Z-score for subjects like English Literature and Latin should be made with caution since the number of students in these groups is relatively small and may not comply with the assumptions. Further, it must be noted that the application of Z-score does not require the assumption of normality in the data series.

The aggregation of Z-score for the three subjects is not at all complicated or harder to justify. When the underlying assumption that the student group for each subject is chosen randomly from a large population is true and all three subject are equally important, ranking the students from the aggregated Z-score is perfectly valid and justifiable. It must be understood that Z-score claims a strong stake only when there are different combinations possible. Subject streams for Medicine and Engineering where a fixed three subject combination is only available, Z-score ranking does not deviate much from the ranking based on aggregated mark.

However, it should be emphasized that Z score is not a substitute for district quota system. The disparities in accessing the education facilities are intended to be compensated through the district quota system although there are serious issues related to fairness in allocating university admission quota to districts based on district populations. The other criticism is that the Z-score of every student can change after re-correction results are released. Since Z-score is a ranking or a relative position of a student in a population, when the mark of some other students changes due to re-correction, the ranking of others also should change in order to reflect the new positions. This happened even when the aggregate mark was used although it was not visible due to non-releasing of ranks with the raw mark.

The issue at hand when the syllabus was changed was the violation of the fundamental assumption in the application of Z-score that the students of these two syllabi were obviously different in terms of their capabilities and knowledge.

One of the assumptions is that the aptitude of knowledge and skills of the student population opting for different subjects or subject streams are not significantly different. This assumption should be validated now because almost all the students in the old syllabus except for those with valid medical or other reasons have made a failed attempt to enter university earlier. Those who qualify from the new syllabus are the fresh group who took the examination for the first time. Assuming the equal knowledge and skill background for these two diverse groups obviously introduce an error into the fair selection process. If this hypothesis cannot be proved, then the degree of dissimilarity needs to be assessed in order to determine a fair ratio for university admission from these two groups of students.

For subject streams like Engineering, more than 60% of the successful students were first timers and for Medicine, majority of the successful students were in their second or third attempt. The application of Z-score blindly would have obviously favoured the underdogs and hence an approach was recommended to evaluate the statistics of past years and proportionate the admission opportunities based on a quota in order to reflect the historical trends.

Accordingly, it is incorrect to assume that Z-score standardization arose due to sudden existence of new and old syllabus. Further clarifications are available in my interviews in Sunday Observer ( and published even before the Z-score fiasco staged drama creating headlines in the national media. The solutions which I proposed in my contributions to Sunday Observer interviews are included in the final approach adopted by the UGC with the concurrence of the Supreme Court for university admission in 2011 resolving the much debated crisis.

Dr. Poruthotage believes that curricula should evolve rather than change. In my opinion as agreed by many educationists around the world that the curriculum revision process should be continuous but the change of curriculum should happen at discrete times (every five to ten years) in order to be transparent and applicable in practice. Text books, instructor’s manuals and other teaching aids cannot be produced every year. Continuous change in curricula leads to confusion not only among students but also among teachers and other stakeholders. However, this subject should be left with education experts to make a decision.

Finally, it is highlighted that proposing solutions for most of the issues related to the use of Z-score and other statistical techniques in university admission require not only a sound understanding and knowledge in statistics but also a comprehensive knowledge of the problem at hand.A national workshop must be organized to showcase the issues related to the use of Z-score and all the stakeholders and experts should be invited to have a debate on these issues to reach consensus solutions.

(The writer is a member of the Expert Committee appointed by President Mahinda Rajapaksa to make recommendations on the Errors in A/L Results in 2011. He is also the Co-Chairman of the Committee appointed by the Minister of Education to make recommendation to improve the performance of mathematics at O/L examinations. He also pioneered in developing the curriculum and has been teaching Spatial Statistics as a subject for postgraduate study programmes at University of Peradeniya since 1998. He is also the Founder President of the Geo-informatics Society of Sri Lanka.)

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