Guide to how Study Scores and ATARs are calculated!

[FlorianK]

btw the system for the SAC scaling takes into account people that do excepionally good or bad. For Example: For Chemistry I was ranked last or maybe second last in a group of 10 of which the best got an A in Exam 1 and a B+ in Exam 2. The rest of the class got C+ or lower for both. I got a B+ for Exam1 and an A for Exam 2 and my SACs scaled up to a B+.

[Mao]

How are SAC GAs calculated

SAC GAs are often where most students get lost - and it is probably because most are not familiar with it.

First of all, what is important here is your overall SAC rank. This means that if you are ranked first, it doesn't matter if you are ranked first by a big margin or by a small margin. If you are ranked first, you are ranked first.

So now, say you are ranked nth. What VCAA will do is they will give you the nth exam mark in your cohort as your SAC mark.

So if there are three students, Thushan, Dan and Paul in a cohort and they each get an average SAC mark of 100, 70, 60 respectively, this means that Thushan will be ranked 1, Dan will be ranked 2 and Paul will be ranked 3. Say they all sit the exam, and on the exam day, Dan's beard has grown so much that he can't see his exam paper anymore, thus, their exam marks are 100, 20, 70.

This means that for the SAC GA - Thushan will get 100, Dan will get 70 and Paul will get 20.

I am almost certain this is not the case. This is an over-simplification of the statistical moderation process.

VCAA in 2010 published a flyer on this: http://www.vcaa.vic.edu.au/Documents/statmod2010.pdf

Here, they briefly outlined the method:
- The statistical distribution (measured by quartiles) for SACs and exams are calculated
- A scaling argument is used to align SACs quartiles and exams quartiles
- Students' internal SAC scores are moderated (presumably via linear interpolation) to the exam distribution.

Crucially:
- The relative rank is important only in the sense of finding the quartile ranges
- The unmoderated SAC rank is important for the actual statistical moderation
- Quartile populations are essentially moderated independently of each other. E.g. a student is only in competition with his/her quartile

To get the most benefit out of statistical moderation (i.e. for teachers to cheat the system):
- the top 25% of cohort should have scores in a tight group near the top of the distribution, while the last person of the first quartile should have a much lower SAC score. This skews the distribution of scores within the top quartile towards the maximum, while increasing the interquartile range.
- have at least 1 person of the cohort to achieve a near-perfect exam mark
- students in the top quartile who don't have glorious exam marks would now receive glorious SAC marks

TL;DR, OP's comments on statistical moderation of SACs is a misinterpretation.

[brenden]

I am almost certain this is not the case. This is an over-simplification of the statistical moderation process.

VCAA in 2010 published a flyer on this: http://www.vcaa.vic.edu.au/Documents/statmod2010.pdf

Here, they briefly outlined the method:
- The statistical distribution (measured by quartiles) for SACs and exams are calculated
- A scaling argument is used to align SACs quartiles and exams quartiles
- Students' internal SAC scores are moderated (presumably via linear interpolation) to the exam distribution.

Crucially:
- The relative rank is important only in the sense of finding the quartile ranges
- The unmoderated SAC rank is important for the actual statistical moderation
- Quartile populations are essentially moderated independently of each other. E.g. a student is only in competition with his/her quartile

To get the most benefit out of statistical moderation (i.e. for teachers to cheat the system):
- the top 25% of cohort should have scores in a tight group near the top of the distribution, while the last person of the first quartile should have a much lower SAC score. This skews the distribution of scores within the top quartile towards the maximum, while increasing the interquartile range.
- have at least 1 person of the cohort to achieve a near-perfect exam mark
- students in the top quartile who don't have glorious exam marks would now receive glorious SAC marks

TL;DR, OP's comments on statistical moderation of SACs is a misinterpretation.

Thank you for this.

[Dayman]

I am almost certain this is not the case. This is an over-simplification of the statistical moderation process.

VCAA in 2010 published a flyer on this: http://www.vcaa.vic.edu.au/Documents/statmod2010.pdf

Here, they briefly outlined the method:
- The statistical distribution (measured by quartiles) for SACs and exams are calculated
- A scaling argument is used to align SACs quartiles and exams quartiles
- Students' internal SAC scores are moderated (presumably via linear interpolation) to the exam distribution.

Crucially:
- The relative rank is important only in the sense of finding the quartile ranges
- The unmoderated SAC rank is important for the actual statistical moderation
- Quartile populations are essentially moderated independently of each other. E.g. a student is only in competition with his/her quartile

To get the most benefit out of statistical moderation (i.e. for teachers to cheat the system):
- the top 25% of cohort should have scores in a tight group near the top of the distribution, while the last person of the first quartile should have a much lower SAC score. This skews the distribution of scores within the top quartile towards the maximum, while increasing the interquartile range.
- have at least 1 person of the cohort to achieve a near-perfect exam mark
- students in the top quartile who don't have glorious exam marks would now receive glorious SAC marks

TL;DR, OP's comments on statistical moderation of SACs is a misinterpretation.

Honestly you need to voice your opinion louder because I think yours is the most accurate.

[Professor Polonsky]

I sort of got to that here as well.

- Students' internal SAC scores are moderated (presumably via linear interpolation) to the exam distribution.

I was actually told (by a fairly reputable source), strangely enough, that it's a quadratic function between quartiles. Take it with a pinch of salt, but yeah.

[chem-nerd]

it's a quadratic function between quartiles.

This.

[lala1911]

Good post Mao.
I was so shocked when I saw this thread. It just doesn't seem fair that if rank 1 scored 95% average SACs and rank 2 scores 94%, and the highest exam marks are 84% and 72%, that the rank 2 student would suffer 12%. There must be some complex equation to make it fairer.

[Dayman]

I sort of got to that here as well.
I was actually told (by a fairly reputable source), strangely enough, that it's a quadratic function between quartiles. Take it with a pinch of salt, but yeah.

Wait so in English please, I've only just delve into the world of quartiles so I don't understand what you said sorry.

[Mao]

I was actually told (by a fairly reputable source), strangely enough, that it's a quadratic function between quartiles. Take it with a pinch of salt, but yeah.

This.

That's very interesting. The problem with quadratic splines (interpolation) is that we must impose an arbitrary gradient at some part of the curve. Generally, we use cubic splines to avoid this (for reasons I won't explain here). I drew up a quick quadratic spline for a set of hypothetical but realistic interquartile ranges:


The boundary condition I chose were the extremes, but it does highlight how arbitrary the choice of boundary conditions can be. The brown curve is roughly what we expect, but it is really insignificantly different to a linear interpolation. I don't see the motivation behind the choice of a quadratic spline over linear interpolation. I also wonder what 'arbitrary' boundary condition they use.

TL;DR, I think quadratic functions are a terrible choice for this situation.

[hannah2013]

im confused because i was ranked about 4th or 5th in my cohort last year yet got the 2nd highest exam mark in my cohort and 2nd highest study score

[brenden]

im confused because i was ranked about 4th or 5th in my cohort last year yet got the 2nd highest exam mark in my cohort and 2nd highest study score

Seems appropriate. Why does that confuse you?

[hannah2013]

So its not the sac ranking in the cohort that determines your SS its your ranking in your cohort for the exam?

[brenden]

It's your exam mark and your SAC rank.

[nerdmmb]

Sorry, I know this is really late, but why is the highest atar 99.95? why cant it be 100?

[Zealous]

Sorry, I know this is really late, but why is the highest atar 99.95? why cant it be 100?

ATAR is a percentile score. A 90 ATAR means you performed higher than 90% of other students.

See why an ATAR of 100 does not work well?