Z score and university admissions

July 24, 2012, 12:00 pm, the island


By Nalin de Silva

The much-awaited new Z scores were released by the Department of Examinations over the weekend and it appears that many students who repeated the examination have been left on the street as a result. Their ranks have come down both country-wise and district-wise and as a result some students who would have been admitted to the universities under the old Z scores would be left out. The UGC is unable to intervene at present as the old Z scores have been cancelled as a result of a Supreme Court decision. In an article published in The Sunday Island of July 22, Dr. H. D. Goonetilleke of the Open University has shown that the percentage of repeaters who would be admitted to the universities under the new Z scores would be reduced roughly from about 55 to about 25. Since those who repeated the examination for the second time would not get an opportunity to sit the examination again it is a pity that those who would have been admitted on the previous Z scores (so called pooled scheme) would find themselves outside the university. Some of them would have ended up as western medical practitioners and engineers. These students and their parents have no option but to go before the Supreme Court and as I had mentioned in an article in Irida Divaina we are in for a series of court cases over university admissions. One of the tables given by Dr. Goonetilleke in The Sunday Island is reproduced below.

What many people including teacher trade union leaders and human rights campaigners in their rush to criticize the government and gain political mileage either forgot or failed to understand was that final admissions to the universities had to be based on a single list and not two lists. This is not only according to a previous decision of the Supreme Court but also happens to be the only available practical course of action that could be followed.

It is to the credit of the UGC that it understood the problem early and took action in the form of appointing a committee of university lecturers and professors who had specialized in statistics to advise the commission on the preparation of a common list. The committee came out with a formula to pool the two populations namely those of students who sat the examination in the new syllabus and of those who sat in the old syllabus. The first timers sat the new syllabus question papers while the repeaters sat the papers set in the old syllabus. The formula recommended by the committee of experts was accepted by the UGC that probably advised the Department of Examinations to calculate the Z scores in each subject and the mean Z scores of the students after pooling the two populations according to the formula. The teacher trade unions and the human rights groups organized a campaign to blame the ministers concerned for adopting a method that was not resorted to in 2001 when there were two populations of students who sat for papers in new syllabus and old syllabus. They were eager to criticize the ministers and the government for political reasons and blamed the ministers for adopting a so called new method, when the latter were not involved in the process. However there was a difference in 2011, which again escaped the minds of some journalists with party loyalties as well as the teacher trade unionists and other parties, as the number of subjects was reduced from four to three in the new syllabus. In addition subjects such as Pure Mathematics, Applied Mathematics, Botany and Zoology that were tested under the old syllabus were not found under the new syllabus. Instead new subjects such as Combined Mathematics and Biology had replaced those subjects. Thus, it was not possible to pool the populations in each subject as the subjects were different under the new syllabus and old syllabus at least in some cases. Hence I presume that the pooling was done not only after calculating the Z scores but also after finding the mean Z scores of the students. It has to be emphasized that it was a pooling of two populations and the students were selected to the universities from the list of pooled mean Z scores. Without pooling students cannot be selected in each stream as one has to find ultimately a way of ordering the Z scores on one list.

There are different ways of pooling and the method adopted by the UGC on the recommendation of the committee of experts was to pool and then calculate Z scores in each subject and compute the mean Z scores of students while in 2001 Prof. R. O. Thattil and others recommended the calculation of the Z scores in each subject separately for the new syllabus and old syllabus and find the mean Z scores of students first and then pool to prepare a common list from which admissions were made. In 2001, there would have been a reason for adopting the method of Prof. Thattil and others—it has to be remembered that Prof. Thattil only introduced the Z score standardization to Sri Lanka and not derived the Z score formula as some people believe—as the subjects were not common in the two syllabi. In 2011, there was no such problem and the UGC has to be commended for appointing a committee of experts to find other ways of pooling. I do not agree with the committee of experts on the formula suggested by them as it is not correct but I agree with the committee and the UGC that the pooling should have been done BEFORE Z scores were calculated.

As I have argued many times in the newspapers pooling after calculating the Z scores assumes that the Z scores in different subjects are equivalent. In the case of different subjects such as Combined Mathematics and Chemistry perhaps the Sri Lankan experts have not struck a formula to scale the marks in different subjects, though this was practised in some schools in the fifties and before, and we may excuse them for their unawareness. However, when the subjects are the same in the old and the new syllabi they could have easily derived a formula to pool the two populations even if no such formula is found in a text book or in a research paper published in a peer reviewed journal which are sought after by the Sri Lankan academics, without resorting to a formula that is not correct.

In any event there is a problem with finding the Z scores of students in each subject first. I am not sure whether the committee of experts or Prof. Thattil, who is also supposed to be an expert, has taken this aspect into consideration. A distribution of Z scores is already what is known as a normal distribution, with a mean of zero and standard deviation of one and it is not possible to pool two such distributions with weights attached to them to come out with a unique weighted pooled normal distribution. Using a little bit of Algebra taught in schools, let us assume that we have two distributions of Z scores given by z1 and z2 and let us construct another distribution formed with weights a1 and a2 attached to the two distributions respectively. Then the new distribution is given by a1 z1 + a2 z2. It is easy to show that the mean of the new distribution is also zero. However, there are no unique values for a1 and a2 that make the standard deviation of the new distribution equal to one. a1 = 1 and a2 =1 is only one such solution and it is arbitrary as one cannot impose conditions to arrive at this particular solution, except that the Z scores are equivalent which is the assumption that Prof. Thattil has made. It is not the case as the students in the new syllabus and the old syllabus clearly constitute two different populations not only with respect to question papers, but also with respect to their attitudes, experience, preparedness etc. That is the reason for the selection of about 55% of the students to the universities from the repeaters. The moment one considers the Z scores of the two groups to be equivalent the percentages of students admitted to the universities from the repeaters drop drastically and I would not be surprised if hundreds of repeat students and their parents go to courts thus delaying the whole process of admission to the universities not only this year but also in the years to come.