Issue of ‘Average of Z scores’

Dilemma of two syllabi but one qualifying exam:

By Eng. K. A. S. G. Rajakaruna 

* Application of Z score method flawed

* Z score attached to respective p value, and not independent

* Dealing with p value the solution

The introduction of the new GCE A/L syllabi creates the dilemma of two syllabi but one qualifying-examination every two years because a portion of the student population faces the examination for the third time while others sit it for the first time, under the old and new syllabi, to qualify for university entrance. The failure on the part of the education authorities to make one ranking order is due to the improper application of the Z-score method.

This problem occurs every eight years when new syllabi are introduced and has led to court cases, as in the case of the GCE A/L results, in 2011 and 2019.

This situation occurs due to the Supreme Court judgment in Surendran Vs University Grant Commission, SC APEAL No 480/92 in 1993, which says both groups of students should be treated equally in respect of differences in examinations. Then, it was ‘Average of Percentage Markings’ method in practice. The two examinations, for due 1990 examination, were held in two occasions as 1990 August and 1991 March for the population of candidates due to the war in the North and the East. What is the difference between ‘two examinations under one syllabus’ and ‘two examinations under two syllabi’ in the same field of study for candidates who should get qualified to apply for university admission in the same academic year?

Since the introduction of ‘Average of Z-scores’, as the scaling method for the GCE A/L results in 2001, the dilemma of two syllabi but one qualifying examination came about in 2012 and 2020. It is clear that the introduction of ‘Average of Z-scores’ method has led to confusion. The problem is bound to recur in 2028 as well because the education authorities have failed to work out a solution, in keeping with the Supreme Court judgment, since 1993.

The wrong practice of treating differently the candidates who sit the GCE A/L, in the same year, continues against the 1993 SC ruling.

When the problem resurfaced in 2012, the University Grants Commission (UGC) admitted that the 2011 GCE A/L candidates must be treated as one population, but failed to convince the judiciary as per the SC (FR) case No. 29/2012. Delivering the SC judgment, the then Chief Justice Shirani Bandaranayake accepted the UGC argument as a mere statement.

The SC decided that two examinations, even in the same year, formed two distinct data populations, in its judgment of case No. SC(FR) 29/2012. It was only for the purpose of having two separate sets of data to calculate two sets of Z-scores. It is correct technically.

But, instead of complying with the SC rulings, in 2012 and 1993, the UGC has adopted the average of composite percentage, according to its letter, dated 8/4/2019, issued before the 2019 August examination, held under two syllabi. The prediction of the performance of candidates, facing the examination, based on the data of past five years performances, does not make sense because there was no relationship between two sets.

Indexes used as regards the GCE A/L results, according to the field of study, are flawed.

‘Average of Percentage Markings’, as well as the ‘Average of Z-sores’, are not technically correct terms defined and calculated, though in use. They are the two sides of the same coin as regards evaluations and rankings answer scripts. This may be the reason why ‘Average of Percentage Markings’ has been abandoned.

Dealing with p value is the solution and technically correct practice.

The application of average of Z- scores as the index is technically wrong for two reasons:

1. There is no such thing as ‘Average of Z-scores’. Instead, it is the pooled Z-scores which could not be calculated out of data of relative numbers produced in examination paper markings.

2. The combined-subject effect in the same field of study is not the sum of each subject markings therein.

More importantly, it not fair to work out countrywide rankings with only one combined-subject effect of candidate without considering other factors hindering and enhancing the subject effect unevenly, possibly throughout the country.

Z-scores is not independent and has bearings on p values. The application of average of Z-scores requires the continuation of Z-score method as per the use of respective p value under the normal and standard conditions regardless of the nature of data produced under the old and new syllabi and with data with uneven effect as per the case at hand.

Up to the marking of answer scripts, the management of each subject is independent. The probability of combined effect of independent events is the product of each event, as per the case-combined-effect of subjects in the field of study concerned.

Computer software is available to calculate respective p value, given that the Z values are calculated out of unavoidable percentage markings at examinations. It saves time and money and makes the exercise of ranking candidates in single order fair.

The proposed method p values of paper marking and combined p value according the field of study guarantee the following:

1. Different subject evaluation markings become comparable and convertible to read again as percentage markings.

2. Combined effect p value is read as single-subject p value as number between 0-1. P value could be converted into percentage figures for easy of understanding.

3. Intertangling of marking of different subject in combing is avoided.

4. Marking of dominant subject in the field of study influences rankings.

5. Any number of subjects could be considered as the field of study

6. Equal performances in all the subjects guarantee admission to professional degree programmes.

7. Relatively high performance in one of the subjects enables selection to particular degree programmes where knowledge of the high scoring subject matters.