From Assignment to ATAR: How your Marks are CalculatedBy Jamon Windeyer in Study
29th of February 2016
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There is lots of content to know in the HSC. Formulae, statistics, quotes, pretty much any form of information under the sun. It can get a little boring after a while, trying to memorise buckets of information. One thing that everyone seems to manage to sit through without getting bored is an explanation of how the ATAR is calculated.
Now, the exact nitty gritty details of how the ATAR works are fairly complex. It’s quite well documented, with key details omitted by BOSTES to maintain a sense of mystery. There is definitely enough information to understand the process though, and while HSC Success does not rely on knowledge of this process, it Is pretty cool to know how it all works.
So, from your assignments, to your ATAR, let’s go through the process from start to finish.
Note: All information in this resource has been interpreted from BOSTES Documents. To the best of my knowledge, it is an accurate summary of a very complex process. To get all of the information directly from the source, visit the BOSTES website.
We begin of course with School Assessment Marks. The way these are calculated varies by school, but pretty much, it is just weighted marks added together to give a value from 0 to 100 for a 2 Unit Subject, and a mark from 0 to 50 for 1 Unit Subjects. This process is hardly a mystery, so we won’t dwell on it. You need only know that your school will send the Board a collection of School Assessment Marks. These, in turn, create the Internal Ranks, those things you fight and claw for all year. They can’t just submit ranks, because the marks themselves (well specifically, the distance between them) play into the moderation process.
Now, we come to the HSC Exam. There is even a bit of a process here, just in calculating your Examination Mark. The following occurs for all your exams.
First, obviously, your paper is marked and raw marks are obtained. This is literally what the marker gave you for each question on the paper. These marks are then linearly scaled in a manner such that the entire paper becomes a mark out of 100 (EG – a question worth 5 may be scaled back to be worth only 2 marks). This occurs in subjects like English, Physics, etc., where the exam is marked out of a value higher than 100. The sum of these becomes your total weighted mark (TWM).
Next, the Board examines the results of the Subject Cohort. They examine performances, sample scripts, statistical data, in an extremely detailed review of the exam. They then determine the Band Cut-Offs, the TWM which corresponds to each of the Band Performance Indicators. For example, it may be decided that for Legal Studies, a TWM of 86 will correspond to a Band 6, a TWM of 77 will correspond to a Band 5, etc. In this way, a Band 6 student may not necessarily have scored above 90% in the exam, even before all the scaling occurs in later stages.
If you are doing an Option, an additional process called Optional Question Scaling is applied. If the option/elective you have done has been deemed more difficult based on the marks of the entire cohort, the mark for that option is scaled to even the playing field. For example, if it is deemed that English Advanced Students who studied a specific text performed to a lower standard, those students’ marks are scaled up.
All of these processes finished, your TWM is then mapped to the Band Performance Indicators to give the Examination Mark (EG – in the scenario above, a TWM of 86 will result in an Examination Mark of 90, the Band 6 Cut Off).
So, quite a complex process already, but don’t worry. It gets worse.
Now we have a Raw Examination Mark and a Raw School Assessment Mark. Now that your examination mark has been determined, the Board needs to moderate your School Assessment Mark. Obviously, every school has different standards of success, different levels of competition. It is absolutely impossible for all of them to mark to the same standard. So, the Board moderates the marks before they are used. But how?
The Board moderates your School Assessment Mark for a subject using the Examination Marks obtained by the students who sat the exam for that subject at your school. That is, your HSC Physics mark is moderated based on the results of Physics students at your school.
2 Things Happen:
- The top assessment mark is immediately changed to equal the top examination mark in the cohort, and the bottom assessment mark is immediately changed to equal the lowest examination mark in the cohort (or if not exact, very close)
- The rest of the marks are shifted, maintaining rank and relative distances between marks, so that the mean of the school assessment marks is equal to the mean of the examination marks
Let’s consider an example. Say 4 students took Chemistry at your school; Lucy, Edmund, Peter and Susan. The school and exam marks are shown below:
|School Assessment Mark (Not Moderated)||Internal Rank||Exam Mark|
What will the moderated marks look like here? Well, Peter came first, so his assessment mark is immediately changed to the highest exam mark of 92, and Lucy came last, so her assessment mark is immediately adjusted to something very close to the lowest exam mark of 70. Susan and Edmund’s mark will be adjusted so the mean of the moderated marks equals the mean of the exam marks. Susan’s mark will go up and so will Edmund’s.
If you remember anything from this guide, remember these two points, because they have massive implications.
Firstly, consider the student in first place. If you are 1st in your school, your school assessment mark is automatically maximised. This is a huge advantage. Fight for 1st place where you can.
Secondly, this forces us to recognise the importance of helping students in your school. The moderation process is based on the mean of the marks. So, the higher the average, the more favourable the process will be to your school. This is why students are “dragged up” by high achievers; they are pushing up the mean, and thus, pushing up everyone’s marks. You want the freakishly talented student in your year; it actually helps you.
Now, interestingly, the Board can choose to exclude certain exam results from this moderation calculation. They do exclude, for example, students who perform markedly worse than expected. This means that students who “bomb” the exam do not impact on the results of their peers.
In this way, the Board adjusts the individual School Assessment Marks, maintaining the order of rank, and maintaining (as much as possible) the shape of the distribution curve. That is, if 2nd place was very close to 1st, they will remain very close to 1st. Relative differences will be reflected in the moderation.
So, we now have Raw Examination Marks and Moderated School Assessment Marks. Now, the part we’ve all been waiting for:
How Does Scaling Work?
Yes, it happens. But how does it work? The following is an extract from a BOSTES Report on Scaling of the 2014 HSC (my own year):
The model underpinning the scaling algorithm specifies that the scaled mean in a course is equal to the average academic achievement of the course candidature where, for individual students, the measure of academic achievement is taken as the average scaled mark in all courses completed. The model specification leads to a set of simultaneous equations from which the scaled means of 2-unit courses are calculated.
What the hell does that mean?
Well, in as simple as I can state it for a very complex process, it means that the mean of all marks in a course (the average), is adjusted so it matches the average overall performance of the candidature in that course. This “overall performance” is measured for each individual, as the average scaled mark in all the courses they did. So, the average mark of all Physics students in other subjects, is used to determine how well Physics is scaled. This, as stated, creates a (massive) set of simultaneous equations, where the scaled mean of each course is solved based on the scaled mean of other courses.
If that didn’t make sense, take away one thing: How well your subject scales depend on how well the candidature does in the HSC as a whole. It is not based on difficulty, content, or anything about the course itself. The fact that Chemistry scales extremely well is because its candidature, on the whole, does really well in the HSC.
Now this process differs slightly for Extension subjects, where the scaled means are adjusted based on the performance of the related 2-unit course (EG – English Extension scales based on the performance of the English Advanced Cohort).
From here, your marks (School and Exam) are scaled to make everything suit these new scaled means. Basically, it is just a linear transformation, preserving the deviation in the marks (the shape of the mark curve).
How is my ATAR Calculated?
The marks now match what will appear on your HSC Credentials at the end of the year. But how do they translate to an ATAR?
You should know that your best 10 units count towards an ATAR. For every student, their best 10 units (each marked from 0-50, where this mark is the average of your Exam and Assessment Mark) are added to give an aggregate (just the sum of the marks). For example, a mark of 40/50 for every unit would yield an aggregate of 400. Now, there is some extremely complex mathematics at play here, beyond what is necessary to know, so I’ll simplify it slightly.
Essentially, BOSTES puts these aggregates in order, to determine an ATAR-Eligible-Percentile for each student. In my year, an aggregate of 450 meant an ATAR-Eligible-Percentile of 98.90: This means that 98.90% of students achieved an aggregate of 450 or less.
From here, the complex math I mentioned above kicks in. These ATAR-Eligible-Percentiles are adjusted slightly using a two parameter logistic function. Essentially, it adjusts the ATAR Eligible Percentiles based on the number of ATAR eligible students, so that approximately 1/2000 students achieve a score of 99.95. In my year group, this was 47 students. The remaining ATAR Categories are progressively allocated to students in order, to meet target frequencies calculated in the aforementioned function.
The impact is that the curve is ‘stretched’ and ‘pushed up.’ It’s a good thing. Most student’s marks will increase as a result.
As a comparison, here is a table of aggregates, ATAR Eligible Percentiles, and ATARS, for 2014.
|Aggregate||ATAR Eligible Percentile||ATAR|
This calculation increases the performance of the ATAR eligible cohort based on the presence of non-ATAR eligible students, either those who completed their HSC, or those who didn’t (these are based on Year 10 cohort numbers, so it includes consideration of students who left school).
And there is your ATAR! This is a huge, complex process, and it is not important to understand it in depth. What you should take away from it is that overall performance is key: The entire cohort does well, then you do well. HSC is a collaborative effort to drive the scaling process to work in your favour. Help each other, because it is helping yourself as well!
If you have any additional questions (which is pretty likely given how confusing all of this is), you can ask them here for a quick answer!