University admissions and the Z score

January 12, 2012, 12:00 pm , The Island.

Prof. R.O. Thattil

University of Peradeniya

The release of the GCE A/L results has led to many controversial issues regarding the method used to rank the students. The students and parents are in a dilemma whether to accept the results or not. Therefore, I decided to write this article to clarify matters since I was responsible for introducing the Z score as a basis for ranking a decade ago.

History

Admission to universities prior to the year 2000 was based on aggregate marks of 4 subjects obtained at the A/L examination. However, in that year the syllabus was changed and the new system required students to take only 3 subjects. Thus, there were 2 groups taking the A/L examination. One group (old syllabus) took 4 subjects while the other group (new syllabus) took only 3 subjects. The problem then was how to rank students for university admission.

Within a group of students tested for a given subject, the marks received are an indicator of who the better student is. However, the aggregation of marks of different subjects for the purpose of ranking is grossly unfair especially when students sit 2 different sets of subjects.

Distribution of marks is different from subject to subject. It is an exception rather the rule for marks of different subjects to have the same distribution in terms of location (measured by the mean) and dispersion (measured by the standard deviation). Discussions on what was the best way to rank students were held in the year 2000 chaired by the then secretary of Education Prof. R. P. Gunawardana. Many proposals were discussed and finally the proposal submitted by the author for using the Z score method of scaling marks was accepted.

The Z score

The scaling of different variables (some using different units of measurement) has been done using the standardized score Z for many decades. However, this was the first time it was to be used at a national examination. The Z score for a given subject is calculated as

Where X = raw mark of the subject,X = mean of the marks of the subject and S = standard deviation of the marks of the subject.

The Z score thus formed for a given subject is comparable to the Z score of another subject, while raw marks do not posses this attribute. A raw mark of 45 in a subject such as physics is an above average mark while in another subject it may even be below the average or very close to being so. However, a Z score of 1.2 in a given subject is equivalent to a Z score of 1.2 in any other subject. Although mean and variance of raw marks can differ from subject to subject, the Z scores are distributed with a mean = zero and variance = 1 for any subject. Thus, the Z scores of all subjects will have the same location and spread parameters. There is nothing called the perfect index.

Complications are avoided by not assuming any particular distribution for the raw marks. The Z score can be viewed as a scaling technique that makes the location and dispersion parameters for the marks of all subjects the same.

The present problem

A new syllabus was introduced in 2009 for the students sitting the A/L examination for the first time. Thus, there were 2 groups (new and old syllabuses) sitting for the A/L examinations in 2011 (similar to the year 2000!). A committee was appointed to decide on the method of ranking. The author was not a member of this committee. However, the author is aware that they pooled the mean and variances (square of the standard deviations) of a subject from the old and new syllabus. Pooling cannot be done for a subject since the 2 student groups should be considered as 2 populations. The mean and/or the standard deviation of 2 populations will be different and should have been treated separately.

Danger of pooling

Consider the means and variances of a subject for the 2 groups (new and old syllabus)

The standard deviations will necessarily be much lower than the means. The author has taken conservative values for the number of students (n). In some subjects the number can be much higher. I have used the formulas given by the recently appointed committee to obtain the pooled means xp and variances (S2p)

If these values are used to test the hypothesis, whether means of the 2 populations are significantly different or not, we can use the Z test (not to be confused with the Z score) since populations are large. This is a standard test of means of 2 populations.



The Z statistic is much larger than 2, which implies that the population means are significantly different and therefore pooled means cannot be used.

On first glance one may think that the mean differences are not very different. However, even a difference of 1.5 will lead to a significant difference. Now, consider the effect of pooling on the Z scores, for example a student receiving 80 marks in group 1 would have a Z score

if the unpooled mean and variance was used. However, if the pooled values are used the Z score will be equal to

 

which is higher than the un-pooled Z score. Therefore, students in group 1 will have an unfair advantage over the students in group 2 whose un-pooled mean is lower. In general the Z scores of the group with the higher mean will get elevated while the Z scores of the other group will be lowered. A case of the rich getting richer while the poor get poorer!

Solution

The solution is to consider the 2 groups as 2 different populations and calculate the Z score for each group separately using the (un-pooled) mean and variance for each subject. The average of the Z scores of the 3 subjects can then be taken to obtain the ranks. This solution is simple and elegant.

SB ends up with egg on face

January 12, 2012, 9:58 pm , The Island

By Shamindra Ferdinando

Higher Education Minister S. B. Dissanayake hadn’t even briefed the Cabinet about his controversial Quality Assurance, Accreditation and Qualification Frame Bill, aimed at regulating ‘private universities’, in spite of publicly vowing to present it in parliament, political sources told The Island.

The failure on the part of Minister Dissanayake to discuss such a critical issue with his Cabinet colleagues before making public pronouncements was pointed out during Wednesday’s Cabinet meet chaired by President Mahinda Rajapaksa.

Asked whether the government had succumbed to protests launched by the University community and the Opposition, ministerial sources emphasized that the issue had never been discussed. A minister pointed out the absurdity in the Cabinet not taking up the issue, whereas the entire country was talking about it.

Minister Dissanayake was in Jaffna to meet the Jaffna University community. Ministers remarked that universities were on fire, while the Higher Education Minister was touring Jaffna.

Sources alleged that Dissanayake’s private university project couldn’t be allowed at the expense of the SLFP-led coalition. Asked whether the government was likely to take up the contentious issue, sources said that it would be a grave mistake on the part of the UPFA to give a rallying point for those agitating against the administration.

In spite of recent break-up of the JVP, its student arm, the IUSF (Inter University Students Federation) is engaged in a major campaign against Dissanayake’s move, with the rebel group spearheading the initiative.

FUTA won’t trust President

January 12, 2012, 10:02 pm , The Island

by Dasun Edirisinghe

Despite President Mahinda Rajapaksa directing Higher Education Minister S. B. Dissanayake to put on hold the ‘private university bill’, university teachers yesterday warned the government that education would become a commodity under the proposed bill.

President of the Federation of University Teachers’ Associations (FUTA) Dr. Nirmal Ranjith Devasiri told a press conference that their main demand this time was for the withdrawal pf the proposed bill which would enable private universities to operate here.

"We don’t trust President Rajapaksa’s words as we have been cheated by him several times," he said.

Dr. Devasiri said that Higher Education Ministry refused a discussion on higher educational reforms, but when FUTA threatened trade union action on Jan. 17 the ministry offered a discussion today (13).

He said that according to the agreement which FUTA entered into with the Higher Education Ministry, when temporarily suspending trade union action on July 21, the ministry promised to consult university teachers when taking decisions on the higher education sector in the future.

"But, they never consulted us when drafting the private university bill," Dr. Devasiri said adding they have a moral right to be involved in decisions concerning the university sector, as stakeholders.

The senior academic said that Higher Education Ministry Secretary Dr. Sunil Jayantha Navaratne did not give them a copy of the draft bill even after they they made a request for it.

"Currently, the professor who made the ‘Z’ score formula a decade ago, insists that the ministry didn’t consult him when combining the ‘Z’ score of the old and new syllabuses of the recently released GCE (A/L) results," Dr. Devasiri said adding that it was another problem created due to the non-involvement of the correct experts in the field.

He said that FUTA also requested the government to consider allocating approximately 6 per cent of GDP to the education sector and that too was in the agreement.

But the government had cut down the funds for the higher education sector this time disregarding their request, he said.

Private universities - Dons to strike on Tuesday

Thursday, 12 January 2012 21:46, Dailymirror

While students of several universities were continuing protest campaigns, university teachers said today they would launch a countrywide strike next Tuesday in protest over the Private University Bill which they said should only be brought to Parliament after the government discussed the matter fully with university teachers and other stakeholders.

The Federation of University Teachers Associations (FUTA) said the government should not introduce the proposed Quality Assurance Accreditation and Qualification Frame Bill without the approval of all stakeholders in the higher education sector.

Meanwhile the government said it had no intention of introducing the Private University Bill at least in the foreseeable future.

FUTA, which comprises university lecturers in Sri Lanka said now that the bill has been postponed, the provisions of the bill should be discussed with all stakeholders and obtain their consent before the Bill was brought to Parliament. FUTA President Nirmal Dewasiri said provisions in the bill related to university autonomy, proposals to create a council to regulate non-state universities and other conditions which were not suitable for the educational structure in the country.

He said the employability of graduates; quality of higher education and the involvement of private capital were issues that needed to be given priority.

“There should be dialogue among the stakeholders first and then the policies should be introduced based on the dialogue. The authorities think they can make decisions on behalf of the education sector but it doesn’t work that way. It is the wrong attitude and the wrong decisions made which can be detrimental to the education system in the country,” Dr. Dewasiri said.

University teachers will also demand the salary increments and benefits which were proposed and approved by the Treasury Secretary last year but were still not given. They are also demanding that funds allocated to the education sector be increased to six per cent of the GDP.“Some of the many burning issues we are facing today in universities is because of low investments in the education sector, which has an allocation of some two per cent of the GDP, and this is much lower than Ethiopia which has an allocation of four per cent of the GDP,” Dr. Dewasiri said. (Olindhi Jayasundere)