## Main Logo ## Sunday, 8 July 2012

### The Z score and the Supreme Court Judgment - Nonpublished

The Supreme Court has decided that the Z scores of the students who sat the GCE (A/L) Examination in the new syllabus and the old syllabus should be calculated separately as the candidates belong to two different populations. While respecting the judgment, it has to be pointed out that the Supreme Court has not given instructions to the UGC on a method to admit students to the Universities. Whoever calculates the Z scores it is finally the UGC that decides on admission of students.

In this respect there is no other way than pooling the two populations and devising a scheme to admit students to the Universities from a common list. Even if the Z scores are calculated separately one has to admit students to the Universities from one list prepared according to “merit” notwithstanding what is popularly known as the district quota system. There are various schemes that can be adopted in preparing the common list. Whatever the method is adopted it is going to be arbitrary as even lists prepared according to Statistical formulae are also arbitrary.

Suppose the UGC decides to prepare one list after calculating the Z scores separately purely on “merit”. In such a case the student who has the best Z score in a particular stream will be placed first whatever the population he/she belongs to. Then the second place will go to the student with the next best Z score again irrespective of the population. Then the third place and so on. However what is assumed in this particular method of preparing one list is that the Z scores of the two populations are equivalent. That is the Z score of x in population A carries the same weight as the Z score x in population B. Now how does one know that the Z scores of the two populations are equivalent?

Then there is the suggestion that a certain percentage of students in a particular stream should be from the population of students who sat for the examination in the new syllabus and the balance from those who repeated the examination. The percentages will not be the same for different streams but then there is again the problem of determining the percentages. Would it be based on the average of percentages of students admitted in the previous five years, ten years or what? In any event it also amounts to a pooling of students on some arbitrary Statistical basis and then compiling a common list.

The populations of students were different not only in the GCE (A/L) examination held in 2011 but also in the previous years. Though all students sat the same question papers in any particular subject in the previous years there were differences in quality of students with respect to those who sat first time and those who repeated the examination. Strictly speaking they belonged to two populations, though they were considered as one population for the calculation of the Z scores. Thus the students were considered to be of the same quality. In 2011 the repeat students were given different question papers and effectively they were sitting for a different examination. If the UGC decides to prepare the common list on a percentage basis depending on Statistics how would it account for the introduction of two sets of papers which was not the experience of the previous years. Then of course there are other problems such as the equivalence of the Z scores in different subjects that I had discussed in a previous article.

The expert committee appointed by the UGC came out with a formula to pool the two populations by first calculating a common variance and then finding the Z scores of the candidates. I do not agree with the formula as it is based on another formula for the calculation of variance of samples but a better a formula can be arrived at considering the populations themselves.

Once the Z scores are calculated separately as ordered by the Supreme Court for the two populations, in order to compile a common list it is also possible to derive a formula for a “common list Z score” as pooling is essential in admitting students to the Universities. Depending on the method of pooling different sets of students would be admitted to the Universities and there may be a series of court cases unless all stakeholders get together and arrive at a satisfactory solution.