# Sri Lankan University Admissions Demystified: Z-score, District Quota, and Other Factors

The Sri Lankan university admission system has been (and still is) the subject of much debate. It is surprising how many people are ignorant about how the z-score works; even among those who grasp the idea of the z-score, most are against the district quotas. This article aims to demystify the whole process.

## The Three Components

There are three components of the SL university admission protocol. They are:

(1) The z-score calculation,

(2) The district quota system, and

(3) The preference matrix.

## The Z-score: Basics

The first part, i.e., the z-score (also known as ‘standardisation’) is quite simple. It uses a basic Z-transformation which converts a gross score between 0–100 into a ‘standard score’, or ‘z-score’ between (-4.0 — +4.0). The formula is this:

The important point is that the **z-score is independent of the average mark or the spread of marks**. This allows us to compare between different papers. Consider two papers where one has an average of 53% and a spread of 21%, and the other with an average of 71% and a spread of 2%. Without the z-score, it would be impossible to bring these two scores to a common standard. Indeed, this is why the z-score is called ‘standardising’.

In a nutshell, the z-score tells you, regardless of the gross mark, how much ‘above’ or ‘below’ you are — compared to the average. This directly follows from the area under the Z-curve.

The graph makes it easier to visualise what I already described. A student who gets exactly the average mark for a paper gets a Z of 0.0. A negative score means ‘below average’, and a positive score means ‘above average’.

- +1.00 = better than ~84% of students
- +2.00 = better than ~97.5% of students
- +3.00 = better than ~99.5% of students

## The Z-score: Aggregation

Then there is the matter of aggregating the z-scores. Every student takes 03 subjects for A/Ls. The 03 scores are transformed into Z-scores. The Z-scores are then weighted by the average score and then summed up to give the final Z-score.

Weighting is important because not all papers are equally easy (or hard). A mark of 90% for a paper whose national average is 71% has to count more than a mark of 90% for a paper whose national average is 63%.

As an aside, this is why we see some students with ABB get a higher Z-score than those who score AAB (or even AAA, for that matter). Typically, the cutoff mark for an A is 75%. Therefore, a student scoring exactly 76% on all 03 papers will get AAA. However, another student might score 90% on one paper and 74% on the other 02 papers (leading to ABB). There is a higher chance for the second student to get a higher Z-score.

## The District Quota System: Why?

Now we come to the most hotly debated topic: the district quota system (DQS).

Not all districts produce the same number of qualifying students; some produce more while some, less. Specifically, rural districts show much lower Z-scores than urban districts. If we were to base admissions on the Z-scores alone, it would be impossible for them to enrol in a state university, ever. All state universities would be packed with students from Colombo, Jaffna, Galle, Matara, and Kandy; other students would never see the insides of a state university.

So what do we infer from this data? If we accept that the natural IQ of students does not depend on the district they study in, we are compelled to admit that the stark difference in performance is due to the vastly different facilities. If we admit this, then we must also admit that a correction is needed.

The common misconception (even among the more learned) is that the Z-score alone should determine university entrance. This would have been correct if all schools were equipped with equal facilities. Sadly, they are not. A surprisingly large number of people demand ‘meritocracy’, by which they want to abolish the DQS and make admissions solely on the Z-score. Meritocracy presupposes a level playing field with equal opportunities. When opportunities are not equal, meritocracy means nothing. Note that the word ‘equal opportunities’ does not mean the same paper, same marking scheme, etc. Even cursory research on a single facility — say the number of microscopes available in laboratories — would reveal that the playing field is far from ‘level’. What we need is a ‘correction factor’ — similar to how we adjusted the Z-scores of different papers by giving weights.

## The DQS: How?

Unfortunately, there is no satisfactory weighting formula for correcting for the ‘district effect’ so to speak. I have come up with only a handful of such proposals, of which the one by Verite Research in 2013 deserves special mention. You can read their excellent working paper here.

The current method solves this problem by assigning quotas.

- 40% of open positions by national merit (Z-score alone)
- 60% by district basis

In addition, there is a 5% quota for four specific degrees (which I will not go into detail for the sake of simplicity).

The repercussions are immediately seen. “Talented students from urban districts are left behind”, I hear.

Remember: we are not looking for talent alone: we’re looking for **relative **talent. Your Z-score must be “good in the context in which you studied”.

## Exceptions to DQS

While most courses will have two quotas — merit and district — there are certain courses whose entry is solely based on merit, i.e., the Z-score. For example, Arts entry (and related entries like Mass Media) in all state universities are merit-only. Social Work at Peradeniya, Conflict and Peace Studies at Kelaniya, and Islamic Studies at Batticaloa, are a couple of more examples.

Furthermore, certain courses will require students to pass an aptitude test — in addition to having exceeded the cutoff mark. Examples: Financial Engineering at Kelaniya, Architecture at Moratuwa, and Translation Studies at Kelaniya (among many others).

## DQS and the Cutoff Mark

If it were only for the Z-score, every faculty need to maintain one cutoff mark. Now, instead of ONE cutoff mark for a faculty, they must have 25 cutoffs for the 25 districts. This cutoff list is worth several pages in the ‘university handbook’. Here is a page from the 2019/2020 handbook for example.

Students from high-performing districts must clear a higher Z-score while those coming from rural districts must clear a lower Z-score. The cutoff Z-scores are not revealed beforehand — it is impossible to do so — but assuming that the overall student performance keeps increasing, the cutoff Z will be at least equal to the last admitted students’ Z (of the previous year).

## The Preference Matrix

Finally, we have the preference matrix. This is the dreaded “admission book” we all had to fill out when we got admitted to state unis. A student would fill in their preferred faculties and courses on a paper. Essentially, this is a **ranked order of preferences**. Since students do not know the cutoff marks by the time they apply for universities, they must submit a list of their preferences. This allows them to ‘fall back’ if their preferred faculty is not available. If your Z-score is sufficiently high, you may fill in just one faculty and be done with it. However, students will inevitably fill in several choices.

It is complex, but it gives students a LOT of choice.

## In Conclusion

Remember that we have a limited number of seats in each faculty. We **must **put some cutoff marks in place. Moreover, that mark has to be **fair and equalising **for less privileged districts.

To claim that “less talented people get in while more talented people stay out” is not right. Though a lot of people keep complaining that “talented students get left behind”, what they seem to forget is that if not for the district system, our faculties would be filled with only students from urban districts. I fail to see how that is better.

*Note: there is another myth that is being promulgated by certain extremists that the whole ‘standardisation process’ was put in place to demerit Tamil students and prevent them from getting into universities. Even the Wikipedia article claims the same — but one look at their references gives it away. I want to address this myth as well, but that is for another (lengthy) article.*

Peace.