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.
