Z Score and Advanced Level results: The intricate story
The release of results of the GCE Advanced level examination was
delayed this time due to the controversy in calculation of Z score from
two different examinations under two different syllabi held in August.
The responsibility for the delay was thrown from the Department of
Examinations to the University Grants Commission back and forth
resulting in the students who sat for the examination to have sleepless
The issue appears to be a statistical problem which has not been
resolved quickly even by the panel appointed by the UGC. The Sunday
Observer interviewed an eminent scientist who has specialised in Spatial
Statistics for a clarification and answers for the unresolved problem
which determines the fate of students in the university entrance. Prof.
Ranjith Premalal De Silva, Vice Chancellor of Uva Wellassa University
and author of the text book on 'Spatial Statistics: Theory and Practice'
and several other publications related to spatial statistics, joins the
discussion to answer our questions.
Q: Can you explain the background and the reasons led to the
introduction of Z score for university admission in place of simple
aggregate mark used previously?
A: There is a diverse degree of variability in the nature itself so
is with the humans and their work. The scientific discipline called
statistics provides the conceptual and procedural approaches to
understand the variability and manage it in a fair and equitable manner.
Due to the inherent variability present in question papers and
evaluations, it was very well understood that the simple aggregate
obtained from the marks of different subjects is not a fare criterion to
determine the eligibility for university admission.
The degree of difficulty of the question papers in different subjects
varies significantly and also there are variations of the aptitude
measurement scale in different years. Therefore, it was not possible to
have a fixed cut off mark or simple aggregate solution to determine
eligibility for university admission.
For example, marks of one subject could have a range from 5 to 70
while the range for another subject spans from 45 to 99. A student who
obtained 70 is the best among the lot in the first case and the one who
obtained 70 in the second case is a mediocre student. When the simple
aggregate is taken for admission, the best student in the first case is
treated equally to a mediocre student who opted for a relatively easy
subject as in the second case. Within the general assumption that
students who sit for these two different subjects have more or less
equal level of competence, the disparity in relative difficulty of the
question papers or evaluation criteria definitely warrants some sort of
an approach for standardisation.
This issue was the theme for a series of discussions in academic
circles and in spite of several advanced methodologies available for
standardisation, Z score approach was adopted about ten years back as
the criterion for university admission due to its simplicity,
computational convenience, application efficiency and the need for only
two parametric estimates for its calculation.
Although the Ministry of Higher Education and the University Grants
Commission took the initiative to device the methodology and introduce
it for university admission, it is unfortunate that the school teachers
and students have not been educated properly on the use of Z score
standardisation approach. This has led to the circulation of several
myths and misinterpretations in schools and even most of the university
students (more than 90% is a very conservative estimation) are not aware
how this magic number was calculated in the selection process.
Q: If the calculation of Z score involves a simple methodology, can
you explain how it is computed?
A: The distribution of marks of the students in a given subject is
generally arranged to take the theoretical range of 0 to 100. The
calculation of Z score in fact does not need to have 0 as a lower bound
or 100 as the upper bound. It can be used to standardise any range of
values. Taking the individual mark of each and every student in a given
subject, the simple average of marks (mean) and the standard deviation
of the marks are calculated. These are the two parameters used for Z
Secondly, from each and every mark of the students, the mean or the
average value is subtracted and divided by the standard deviation. The
answer of this calculation provides the Z score corresponding to each
mark. Although, the calculation of the Z score is easy, its
interpretation should be done with caution since it transforms the marks
having a finite, discrete range to a new continuous distribution having
positive and negative infinity as the upper and lower bounds.
However, most of the values are found around the middle of the Z
distribution, which is 0 and 99.9% of the students have z score ranging
from -3 to +3. Also the actual calculation could lead to Z score having
several decimals, truncating to 4 decimals would not make any serious
issue in locating the relative position of the students. Since the Z
scores are standard values, simple the total of z scores in the three
subjects is a fair determinant of university admission qualification.
However, it should be emphasised that Z score is not a substitute for
district quota system and the disparities in accessing the education
facilities are intended to be compensated through the district quota
system although there are serious issues related to fairness in
allocating university admission quota to districts based on district
Q: If you have serious concerns on district quota system for
university admission, would you have a better approach to resolve the
issue of unfairness?
A: We still have a school-centered education system for Advanced
Level students. Although tuition plays a considerable role, it is not
possible to restrict individual's choice for tuition. Within a given
district, there are schools having a wide disparity in their teaching
and learning resources which are made available to the students in the
Although there are very good schools with all the facilities and
having excellent teaching and learning environments, there are also
resource poor schools within a very close proximity to the good schools.
As far as the university admission criteria based on district quota is
concerned, the students of resource rich and poor schools have to
compete for the same admission slots made available for the same
district. This is not a level playing field.
District quota system is based on the underlying assumption that all
schools in a given district have the same standards of education
facilities and it is obvious that this assumption is not realistic and
hence, the quota system is also not fair. The schools should be
categorised based on the available teaching and learning resources
available evaluating the related attributes of schools and a
stratification or a grading system should be introduced to rank the
schools. The quota should be awarded for university admission not to
districts but to each category of schools depending on the total number
of students sitting for Advanced Level in each year from each stratum of
schools. Private candidates should also be affiliated to their original
school of education. A quota system based on the school classification
is very much fair and equitable measure of the aptitude of the student
for university admission.
Q: What is the issue for the delay in releasing results of the
Advanced Level examination this year?
A: There were two separate examinations held this year for Advanced
level based on old and new syllabi. For each subject, there have been
two sets of questions papers one for old syllabus and the other for the
new syllabus. The Department of Examinations has no intellectual
capacity to determine how the Z scores should be calculated to determine
university admission from these two separate examinations on a single
It is not fair to blame the Department of Examinations for not having
the capability and capacity to propose an acceptable solution to the
problem, yet they cannot be excused for not realising the problem until
they were about to release the results.
The arrangements to hold two separate examinations were initiated
more than 6 months ago and this problem should have been brought for
discussion several months earlier rather than later, putting the
innocent students in dilemma due to the delay in releasing the results.
The Director General of Examinations forwarded the question to
University Grants Commission at the last minute expecting an immediate
The Chairman of UGC, being a veteran academic wanted to have a
consensus solution from a group of experts.
The Minister of Higher Education also demanded a solution which is
fair and just for everybody and also emphasised the urgency in finding
An expert committee was appointed but UGC did not receive a prompt
However, UGC was advised to request Z-score marks of the candidates
in three different ways i.e. one for the old syllabus, one for the new
syllabus, and a common Z-score for both the categories. The error free
calculation marks with several cross checks in three different formats
obviously take time and that made the delay in releasing the results.
Q: As a Professor involved in teaching spatial statistics, can you
propose a fair solution to this problem?
A: It is not at all difficult to propose a solution for this problem
provided you have the necessary conceptual and theoretical background
and a sound understanding of the education system in Sri Lanka. I do not
believe that anybody could propose a fair solution to the problem only
reviewing marks in the requested three different formats. Let me explain
this in detail. In exploring a solution to this problem, the underlying
assumptions made in calculating the Z scores need to be re-examined.
One of the assumptions is that the aptitude of knowledge and skills
of the student population opting for different subjects or subject
streams are not significantly different.
This assumption should be validated now because almost all the
students in the old syllabus except for those with valid medical or
other reasons have made a failed attempt to enter university earlier.
Those who qualify from the new syllabus are the fresh group who took the
examination for the first time. Assuming the equal knowledge and skill
background for these two diverse groups obviously introduce an error
into the fair selection process.
Before processing marks, the hypothesis of statistically non
significant difference between these two student groups needs to be
validated with at least past data for a period of 10 years.
If this hypothesis cannot be proved, then the degree of dissimilarity
needs to be assessed in order to determine a fair ratio for university
admission from these two groups of students.
The second issue is whether the relative difficulty of two questions
papers in both old and new syllabi is significantly different.
It is obvious that the calculated z scores are of no use to propose a
solution for this problem and it is required to analyze the raw marks of
the old and new question papers to make a mean comparison. If means are
found to be different, then an adjustment needs to be made to equalize
the two sets of marks.
The subject matter expert's opinion is also a choice that can be
considered in decision making. In fact, in the fundamental level of
statistics courses, we give a lesson to our students that they should
propose a valid statistical methodology before they collect their data
for research to ensure the compatibility of data with the statistical
techniques to be employed in the analysis.
Unfortunately, the Department of Examinations could not stick to this
advice and only seeks statistically valid solution after collecting the
data from student examinations.
Once the data are collected, it is not possible to employ the best
methodology but to reach a compromise to find a reasonable solution
without creating a serious injustice to any group.
Reviewing the situation from its apparent background, it is obvious
that the Z score calculated from the data combined from old and new
syllabi or individual Z scores for each examination as requested by the
expert panel have no practical relevance or validity in determining the