# HSC Scaling and ATAR calculation

Contents
What is scaling?

Scaling is the process by which UAC compares relative performance across different subjects. For example, an aligned mark of 88 in Maths Extension 1 can not be compared to a 94 in Physics. You can't say that a 94 in Physics is "better" than an 88 in Extension 1. One subject might be more difficult than the other, and each subject mark are not on the same scale. The only way we can compare marks across different subjects is to have a fair process which converts marks from different subjects into marks on a common scale. Specifically, this is done by converting the Raw Examination Mark (e.g. out of 120 for the Extension 2 exam, or 80 for Extension 1) into a scaled mark out of 50 for each unit of study (so 2 unit courses have a scaled mark out of 100). The conversion process itself is complex and does not need to be understood, but for those interested, read this.

So basically scaling converts Raw Exam Marks which are uncomparable, into scaled marks which are comparable. Easy.

What are Raw Exam Marks?

Raw Exam Marks is the BOS term coined for the actual mark in the external exam. Different subjects' exams are marked differently and have different totals. For example, the Maths Extension 2 exam is out of 120, but the Maths Extension 1 exam is out of 80. So if you scored 67/80 for Extension 1, that is your raw exam mark. As mentioned before, this is not your HSC mark (aligned mark) because it has not been aligned yet.

What do we mean by "scaled up" and "scaled down"?

Now when we talk about whether a subject is "scaled up" or "scaled down", this refers to whether the subject's raw examination mark tends to translate to a much higher or lower scaled mark. For example, for high-scaling subjects like Extension 2, students who score a raw mark of around 65 to 70 out of 120 still manage to score a 45 / 50 scaled mark. Of course, this is a rough guess because BOS does not normally release raw marks to the public. So all else equal, higher scaled subjects are preferable because they allow lower exam marks to be equated to higher scaled marks which are used for ATAR calculation.

Scaling and Aligning are different

One thing which often confuses students is the difference between the scaling process and the aligning process. When you get your HSC, you will get what are called "aligned HSC marks" which are out of 100. These are your final HSC marks, and are totally separate to ATAR calculation. They are called aligned marks because BOS aligns the raw exam marks into performance bands. E.g. a 92 in Chemistry is by definition band 6 because it falls between 90 and 100. Aligned HSC marks have nothing to do with ATAR calculation except that they are both calculated from raw exam marks.

Read more on HSC marks alignment process.

### Why are some subjects scaled higher than others?

Technically, how difficult a subject is has no effect on how well it scales. How well a subject is scaled depends on how well its candidature does relative to your whole cohort, if your whole cohort did that subject. This is the reason why English is compulsory, because it is used as a cohort benchmark, from which all relative candidature performances are statistically compared. More specifically, the better the candidature for a particular subject does in their other subjects, the better that subject will be scaled.

Example 1: if there are exactly 3,000 people who took Maths Extension 2 for a particular year, and all 3,000 just so happens to do Physics, Chemistry and English Advanced, then the better those students do at the latter 3 subjects relative to everyone else that does those latter 3 subjects, the better Maths Extension 2 will be scaled. I therefore re-iterate, the difficulty of the subject has no effect on how well it scales.

Example 2: suppose there were 9,000 Physics students and 9,000 Chemistry students, all of whom did English Advanced. All else equal, if the Physics students scored lower than the Chemistry students in English Advanced, then Physics will be scaled lower than Chemistry. The assumption is that because Physics students didn't do as well in their other subjects as the Chemistry students, a 90 in Physics is of lower achievement than a 90 in Chemistry.

In theory, using the first example, if all 3,000 students of Extension 2 are totally hopeless at all their other subjects, then Extension 2 will experience depressingly low scaling. But there tends to be a positive correlation between difficulty of subjects and their scaling. That is, people notice that harder subjects tend to scale better. The reason for this is that students who choose harder subjects tend to do better than their peers in their other subjects. This is also the reason why some uncommon language courses with a tiny candidature of 50 or less, would sometimes have massive scaling even higher than Maths Extension 2 - because the candidature just so happened to do very well in their other subjects relative to their peers.

How does scaling affect me?

Technically speaking, scaling shouldn't affect you at all because it is the mechanism which compensates for differences in subject difficulty and candidature quality. Having said that, as the table on the right (source: UAC 2007 Scaling Report) illustrates, in 2007 you would need to be in the top 10% in Geography or Legal Studies to score a similar scaled mark as you would if you were in the top 25% for Economics. This is because scaling has determined that due to the relative performances among all candidature, the Legal Studies and Geography candidature are "less able" than the Economics candidature, hence the need to be in a higher percentile bracket in those courses to be equivalent to a lower percentile in Economics. In other words, in theory your higher percentile requirement is compensated by the fact that your peers in Geography and Legal Studies is "less able".

Now here's the thing with scaling: it's up to you what you want to do. Subjects with low scaling indicate a "less able" candidature, so getting a higher percentile in lower scaled subjects is, in theory, easier. Therefore you should always pick subjects you will be good at. There's no point choosing Maths Extension 2 if you have no talent in Maths. If you are passionate about Legal Studies and are able to score in the top 1%, that is so much better for your ATAR than doing something you're not interested in, but with better scaling, and scoring in the bottom 10%.

What is a scaled mean?

Each subject has a scaled mean. The scaled mean is, as its name suggests, the average scaled mark for that subject. The scaled mean is a number out of 50, and describes the average scaled mark per unit of study scored by the candidature of that subject. For example, in 2008, Maths Extension 1 had a scaled mean of 40, meaning the average scaled mark received by students of Extension 1 was 40/50.

Generally, the scaled mean is the most important statistic to notice because it is a measure of how high a subject scales. The higher the scaled mean for a subject, the better it scales. To give you an idea of some scaled means of common subjects, Mathematics Extension 2 had a scaled mean of 44.5 in 2008, making it the highest scaled commonly chosen subject. This has been the case since the inception of the 2001 HSC. English Advanced's scaled mean was 31.3, Chemistry's was 31.6, and Physics was 30.4 for the same. Scaled means change year to year because the relative performance of candidatures across subjects also change each year. However, judging from past data, scaled means have remainedr relatively stable, and we can expect the scaling reputations of most subjects to hold into the future.

A table of scaled means is published by the UAC in their annual Scaling Report, found in Table A3.

Note that the effects of scaling are not constant throughout the percentiles. For example, if you're at the 99th percentile (top 1%) of Maths (2 unit), an aligned mark of 98/100 equates to a scaled mark of around 94/100 (note that the raw mark % may be lower). However at the 75th percentile (top 25%), an aligned mark of 86/100 translates to a scaled mark of around 76/100. Therefore the relationship between marks and scaled marks is definitely not linear. Generally speaking, for the highly scaled subjects, if you are in the top 1% of your candidature, your scaled mark will be around 49/50 or 50/50.

How is my ATAR calculated?

Now that we've discussed scaling in fair detail, we can fully understand the steps in which to calculate ATAR.

1) Firstly, your raw HSC mark used for scaling is calculated from your Raw Examination Mark and your raw moderated school assessment mark.

The HSC mark to be scaled is the average of your Raw Examination Mark (i.e. the mark you received in the external exam) and your raw moderated school assessment mark. The latter is determined through the process known as the HSC moderation process. (We recommend that you read more on moderation if you don't know the process of how school assessment marks are treated)

This raw HSC mark will be scaled according to that particular subject's scaling for that year. The scaled mark arrived at will be out of 50 per unit of study.

2) UAC takes the best 10 units (i.e. highest scaled marks for 10 units) including at least 2 units of English and adds up all scaled marks to form an Aggregate mark out of 500.

For example, if after scaling, your scaled marks were: 92/100 for English Advanced, 93/100 for Chemistry, 93/100 for Physics, 99/100 for Maths Extension 1, 99/100 for Maths Extension 2, your aggregate would be 92 + 93 + 93 + 99 + 99 = 476 / 500, (those marks correspond to top 1% in all subjects) and your ATAR would be a perfect 99.95. Note that if you do English Extension 1 or 2, any combination of 2 or more units of English can count to your ATAR. For example, 1 unit from English Advanced, 1 unit from English Extension 2.

3) The Aggregates of the entire cohort are compared and ATARs are assigned corresponding to the percentile of each Aggregate.

The percentile position of each Aggregate score relative to the entire cohort (including those who have left school at the end of year 10) corresponds to the ATAR given to that student, after rounding to the nearest 0.05 intervals. The final adjustment process effectively accounts for how the early school leavers would have done had they continued schooling and received a ATAR. Typically each year there are 21-23 students who achieve the perfect 99.95 ATAR, followed by around 41-43 students for each 0.05 increment thereafter.

So in simple terms, if your aggregate places you in the 99.85th percentile among your entire cohort, your ATAR would be 99.85.

Summary

WOW! What a mouthful that was. Actually the entire process is not that hard to understand in principle. What makes it difficult are the mathematical details, especially those on scaling and raw-mark conversion. But basically the scaling system operates according to statistical principles and is technically fair.

What you need to know

What students and parents ought to know how to read and interpret scaled means of various subjects. This is critical information for year 10 and younger students who are about to select their subjects for year 11. Table A3 is published by the UAC in their annual scaling report (see HSC scaling statistics) and contains the most recent scaling data on all subjects. Having said that, students should do the subjects for which they have a talent for. There is no point in choosing a subject purely for its high scaling, if the student has no aptitude or interest for the subject.

HSC Scaling statistics (including recent scaling reports and Tables published by the UAC)

Scaling and Subject selection (for those who need to choose subjects for year 11)

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