READ THIS BEFORE OPENING THE LINK:
There's a really common misconception that you can put trial marks straight into ATAR calculators - and if you've done this, you'll probably notice a really disappointing ATAR that's much lower than what you expected. The reason for this is that ATAR calculators are actually designed for 'aligned' marks, which are the marks you get on the actual HSC results day. These aligned marks are entirely different to your raw mark in the exam, which aren't released unless you pay NESA $60 per subject. I won't go into too much detail, but basically alignment usually increases your marks (sometimes by as much as 30 marks!) to match NESA's band descriptors, but the long and short of it is that you can't use normal ATAR calculators with your trial/past paper marks.
To fill this hole I've been developing my own ATAR calculator, which allows you to input your raw marks (could be trial or past paper marks), converts them into aligned marks using extrapolated formulas based on data from https://rawmarks.info, and then follows a similar process to other ATAR calculators to convert your aligned marks into an ATAR.
https://docs.google.com/spreadsheets/d/1btYJ_CrnBl9mKI4jKoRW3ALxHKiKamtU5UtGawmbeOg/edit?usp=sharing
(you'll have to make a copy to use it)
DISCLAIMER: all data is based on the 2022 HSC unless indicated otherwise with italics or an *. If your trial was easier/harder than last years HSC then I obviously can't account for it, but you could just enter in a slightly lower/higher mark if you wish to - The ideal use for this calculator would be actually doing all of the 2022 HSC as past papers for near-perfect accuracy, but obviously that's a bit unrealistic. The other factor is that this is just an estimate of where you're at right now, and obviously things will change (usually for the better) over time, and your moderated School Assessment Mark will also be a factor in your marks.
DISCLAIMER 2: Just to clarify since people have been asking, this calculator will produce different results to UAC ATAR Compass, that is intended behaviour. The calculators are fundamentally different, ATAR Compass is intended for aligned marks while this calculator is for raw marks.
I hope this is helpful
Technical details (stop reading here if you're not interested)
Generally, the way the calculator itself functions is fairly simple - it's hidden normally but it's all visible if you open the "advanced" mode. The methodology for development was a little more interesting. This explanation will hopefully be helpful for anyone who wishes to understand how this calculator works or undertake a similar project in the future (and I just want to talk about it).
For the raw->aligned mark conversion, I found through research that the process of alignment is piecewise linear - NESA sets band cutoffs based on the band descriptors, and then linearly interpolates between marks (source here, also confirmed through my own testing). The data from https://rawmarks.info for many subjects includes multiple marks within each band range, and so I plotted all of the 2022 marks for each subject in desmos, and hence found the (linear) equation which resolved correct rounded aligned marks and matched to an exact rounded band cutoff for each available band (example), and then beyond available data I simply used a linear equation from 0 to the lowest known band cutoff. The accuracy of this method is dependent on the subject - for subjects with lots of raw marks data (e.g. most Mathematics subjects, English Advanced, Chemistry, Physics and Economics) this results in a perfect equation for the band 6 range and an equation which can theoretically be +/- 1 mark for the band 4/5 range. For most other subjects, the equation should theoretically be +/- 1 aligned mark - this is an inherent limit to inaccuracy once two data points are available from the middle/lower end of a band range as any further inaccuracy of band cutoff would result in an inaccurate result for the known data point. Below the available data range, the simple linear equation is theoretically not entirely valid, however given that the vast majority of students sit within or near the known data, its a sufficient compromise, which should provide results within a reasonable range that realistically is good enough given the low changes in scaled marks at low aligned marks, and it allows the calculator to properly function below known data where previous versions would simply output errors - though I still wouldn't advise usage of the calculator for a student with results in bands 1-3. Subjects which are marked with an asterisks required usage of multiple years of data - I resolved to only use this method when the data for one year was extremely scarce and newer data was fairly consistent, enabling a fairly limited degradation of accuracy, which should remain within the standard +/- 1 aligned mark in the vast majority of cases. Subjects which are marked with italics have data from long periods of time and/or a lack data within an included band range, and are only included due to requests - their data will be within +/- 2 aligned marks typically.
The equations found in desmos were then inputted into sheets through a relatively simple =IFS() formula to select the correct linear equation based on which band region a raw mark sits in, in addition to a simple MIN(x,100) function to remove the possibility of marks above 100 (or rather 50 for 1 unit subjects). The sheet uses two cells to store aligned marks, the first, row 3 is a rounded version of the aligned mark for the sake of creating a more simple user interface and preventing confusion given the rounded marks which a student is likely used to. However, row 7 contains the raw mark which is actually used for scaling calculations, as UAC has confirmed they use marks rounded to two decimal places.
The scaled mark conversion doesn't seem to follow any specific equation, rather a more complex system based on the results of each percentile of English marks within a subject, however, UAC provides significantly more data than NESA, and their data is much better separated by percentile cutoffs in the scaling report. Previously the calculator used a simple singular polynomial model for each subject, however this produced some inaccuracies due to the inherently inconsistent conversion, and furthermore Google Sheets limits their displayed quadratics to 3 significant figures (despite their own graphing using many more significant figures, implying they do exist), which was the primary concern because I found it causing some inaccuracies (as much as 2 scaled marks in some cases). As such, I coded a script in python (source code here) which uses numpy and scipy to find a polynomial equation to model subsets of each possible group of 3 data points, and then automatically inserts them into a sheets formula which calculates the scaled mark through individual subset polynomial models between the known data points. The script made it feasible to find this many individual subset models and allowed equations to 15 significant figures. Similar to the raw marks calculation, the script also uses a simple linear calculation below the 25th percentile which is unfortunately unavoidable, but by nature 75% of students and likely nearly 100% of users aren't in that region, so it is a relatively minor limitation.
(1/2)
There's a really common misconception that you can put trial marks straight into ATAR calculators - and if you've done this, you'll probably notice a really disappointing ATAR that's much lower than what you expected. The reason for this is that ATAR calculators are actually designed for 'aligned' marks, which are the marks you get on the actual HSC results day. These aligned marks are entirely different to your raw mark in the exam, which aren't released unless you pay NESA $60 per subject. I won't go into too much detail, but basically alignment usually increases your marks (sometimes by as much as 30 marks!) to match NESA's band descriptors, but the long and short of it is that you can't use normal ATAR calculators with your trial/past paper marks.
To fill this hole I've been developing my own ATAR calculator, which allows you to input your raw marks (could be trial or past paper marks), converts them into aligned marks using extrapolated formulas based on data from https://rawmarks.info, and then follows a similar process to other ATAR calculators to convert your aligned marks into an ATAR.
https://docs.google.com/spreadsheets/d/1btYJ_CrnBl9mKI4jKoRW3ALxHKiKamtU5UtGawmbeOg/edit?usp=sharing
(you'll have to make a copy to use it)
DISCLAIMER: all data is based on the 2022 HSC unless indicated otherwise with italics or an *. If your trial was easier/harder than last years HSC then I obviously can't account for it, but you could just enter in a slightly lower/higher mark if you wish to - The ideal use for this calculator would be actually doing all of the 2022 HSC as past papers for near-perfect accuracy, but obviously that's a bit unrealistic. The other factor is that this is just an estimate of where you're at right now, and obviously things will change (usually for the better) over time, and your moderated School Assessment Mark will also be a factor in your marks.
DISCLAIMER 2: Just to clarify since people have been asking, this calculator will produce different results to UAC ATAR Compass, that is intended behaviour. The calculators are fundamentally different, ATAR Compass is intended for aligned marks while this calculator is for raw marks.
I hope this is helpful
Technical details (stop reading here if you're not interested)
Generally, the way the calculator itself functions is fairly simple - it's hidden normally but it's all visible if you open the "advanced" mode. The methodology for development was a little more interesting. This explanation will hopefully be helpful for anyone who wishes to understand how this calculator works or undertake a similar project in the future (and I just want to talk about it).
For the raw->aligned mark conversion, I found through research that the process of alignment is piecewise linear - NESA sets band cutoffs based on the band descriptors, and then linearly interpolates between marks (source here, also confirmed through my own testing). The data from https://rawmarks.info for many subjects includes multiple marks within each band range, and so I plotted all of the 2022 marks for each subject in desmos, and hence found the (linear) equation which resolved correct rounded aligned marks and matched to an exact rounded band cutoff for each available band (example), and then beyond available data I simply used a linear equation from 0 to the lowest known band cutoff. The accuracy of this method is dependent on the subject - for subjects with lots of raw marks data (e.g. most Mathematics subjects, English Advanced, Chemistry, Physics and Economics) this results in a perfect equation for the band 6 range and an equation which can theoretically be +/- 1 mark for the band 4/5 range. For most other subjects, the equation should theoretically be +/- 1 aligned mark - this is an inherent limit to inaccuracy once two data points are available from the middle/lower end of a band range as any further inaccuracy of band cutoff would result in an inaccurate result for the known data point. Below the available data range, the simple linear equation is theoretically not entirely valid, however given that the vast majority of students sit within or near the known data, its a sufficient compromise, which should provide results within a reasonable range that realistically is good enough given the low changes in scaled marks at low aligned marks, and it allows the calculator to properly function below known data where previous versions would simply output errors - though I still wouldn't advise usage of the calculator for a student with results in bands 1-3. Subjects which are marked with an asterisks required usage of multiple years of data - I resolved to only use this method when the data for one year was extremely scarce and newer data was fairly consistent, enabling a fairly limited degradation of accuracy, which should remain within the standard +/- 1 aligned mark in the vast majority of cases. Subjects which are marked with italics have data from long periods of time and/or a lack data within an included band range, and are only included due to requests - their data will be within +/- 2 aligned marks typically.
The equations found in desmos were then inputted into sheets through a relatively simple =IFS() formula to select the correct linear equation based on which band region a raw mark sits in, in addition to a simple MIN(x,100) function to remove the possibility of marks above 100 (or rather 50 for 1 unit subjects). The sheet uses two cells to store aligned marks, the first, row 3 is a rounded version of the aligned mark for the sake of creating a more simple user interface and preventing confusion given the rounded marks which a student is likely used to. However, row 7 contains the raw mark which is actually used for scaling calculations, as UAC has confirmed they use marks rounded to two decimal places.
The scaled mark conversion doesn't seem to follow any specific equation, rather a more complex system based on the results of each percentile of English marks within a subject, however, UAC provides significantly more data than NESA, and their data is much better separated by percentile cutoffs in the scaling report. Previously the calculator used a simple singular polynomial model for each subject, however this produced some inaccuracies due to the inherently inconsistent conversion, and furthermore Google Sheets limits their displayed quadratics to 3 significant figures (despite their own graphing using many more significant figures, implying they do exist), which was the primary concern because I found it causing some inaccuracies (as much as 2 scaled marks in some cases). As such, I coded a script in python (source code here) which uses numpy and scipy to find a polynomial equation to model subsets of each possible group of 3 data points, and then automatically inserts them into a sheets formula which calculates the scaled mark through individual subset polynomial models between the known data points. The script made it feasible to find this many individual subset models and allowed equations to 15 significant figures. Similar to the raw marks calculation, the script also uses a simple linear calculation below the 25th percentile which is unfortunately unavoidable, but by nature 75% of students and likely nearly 100% of users aren't in that region, so it is a relatively minor limitation.
(1/2)
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