Consider the following scenario:

• There are five students at Suzanne Cory High School completing Subject X. 

• There are five students Sumutha High School also completing Subject X.

A summary of their SAC scores are shown in the diagram below.

You can see the average SAC score at Sumutha High School is higher than the average SAC score at Suzanne Cory High School. Does this mean we performed worse than Sumutha High School? No it does not! Maybe our SACs were more difficult?

How could you really tell which school performed better? The only way is for both schools to do identical assessments, and then use this assessment as a standard to compare SAC results. The only assessment that all students from all schools complete is the external exam. 

Below is a diagram of what each of the students at Suzanne Cory High School achieved in the external exam for Subject X.

As shown, the average examination scores are significantly higher than the internal SAC scores. This indicates that the SACs were considerably more difficult than the external examination. It is important to recognise that internal SACs assess students only within their own school cohort, whereas external examinations assess students across all schools statewide.

Consider the example of the student Vegeta. Although Vegeta achieved 39% relative to his peers within the school, he achieved 93% when compared to the broader state cohort in the external examination. As a result, it would be unfair for Vegeta to be disadvantaged simply because the school’s SACs were set at a much higher level of difficulty.

If Study Scores were calculated directly from raw SAC results, schools would be incentivised to design easier assessments in order to maximise student scores, ultimately undermining the integrity and purpose of assessment. To ensure fairness and consistency across all schools, SAC scores undergo statistical moderation so that they are aligned with external examination performance. This process adjusts the internal SAC results to better reflect the relative achievement demonstrated in the statewide examinations.

The diagram below illustrates this moderation process.

As shown, all SAC scores have been adjusted so that their distribution aligns with the external examination results. Notice that Vegeta was ranked 4th within his cohort for the internal SACs, achieving a raw score of 39%. Following statistical moderation, his SAC score is adjusted to match the 4th-ranked examination score, which in this example is 76%. In other words, his moderated SAC score increased from 39% to 76%.

In contrast, Vegeta’s examination score remains unchanged. Since the external examination already provides a fair and standardised comparison of performance across all students in the state, no moderation is required. Vegeta’s exam score therefore remains at 93%.

Assume that, for this subject (Subject X), the overall performance weighting consists of 40% internal SACs and 60% external examination. Using these weightings, a student’s Statistically Moderated Score can be calculated. For Vegeta, this would be:

Statistically Moderated Score = 76% x 40% + 93% x 60% = 86.2%.

The Statistically Moderated Scores for all students undertaking Subject X are then ranked from highest to lowest, forming a normal distribution curve, as illustrated below.

Just to reiterate the philosophies behind the ATAR calculation:

1. A student’s results should not depend on the school they attend.

One school should not gain an advantage over another simply because its internal SACs are easier or more leniently assessed. To address this, VCAA applies Statistical Moderation (commonly referred to as SAC scaling), which aligns internal assessment results with external examination performance.

2. A student’s results should not depend on the subjects they choose.

One subject should not provide an advantage over another simply because it is easier to achieve high percentage scores. To address this, VCAA applies Subject Scaling, which adjusts Raw Study Scores so that results are mathematically comparable across all subjects.

Now imagine if the state average Statistically Moderated Score (not raw study score) for:

• Chemistry is 50%

• General Maths is 80%

Which subject was easier for students to score better in?

In this case, General Maths was easier to perform better in. If raw study scores were blindly accepted to calculate the ATAR, then everyone would prefer to do all of the ‘easier’ subjects. Therefore, we need a way to ensure that all subjects are scaled in a way so that all subjects become equivalent.

The way this is done is by first calculating the average Statistically Moderated Scores for all subjects. See the diagram below as an example.

As shown in the diagram, the distribution curves for multiple subjects can be compared. The darkest distribution curve, representing Subject X, has a higher average Statistically Moderated Score than the overall average across all subjects.

This indicates that students undertaking Subject X, on average, achieved stronger performance relative to students in other subjects. To ensure fairness and comparability between all subjects, Subject X would therefore undergo downward scaling so that its results are mathematically aligned with the statewide standard across all subjects.

The diagram below illustrates this scaling process.

As illustrated, when the distribution curve for Subject X is shifted downward to align with the overall distribution curve for all subjects, Vegeta’s Raw Study Score of 32 decreases to a Scaled Study Score of 28. In other words, his Raw Study Score is scaled down by 4 points through the scaling process.

It is important to emphasise that this is a hypothetical example intended solely to demonstrate the effect of scaling on Study Scores. In practice, a reduction of 4 study score points is relatively large and uncommon for most subjects.

It is also important to note that university prerequisite requirements are based on Raw Study Scores rather than Scaled Study Scores. Therefore, when a university specifies a minimum study score requirement for a subject, the requirement refers to the student’s Raw Study Score before scaling has been applied.

Once a Scaled Study Score has been determined for each subject, the Aggregate Score can then be calculated by combining the relevant Scaled Study Scores. When calculating the Aggregate Score, the following rules apply:

• A maximum of six subjects can contribute towards the Aggregate Score.

• Of these six subjects, the two lowest-performing subjects (excluding the required English-based subject) contribute only 10% of their Scaled Study Score.

• An English-based subject must be included among the four subjects that contribute their full Scaled Study Score towards the Aggregate Score.

The example below demonstrates how an Aggregate Score is calculated.

Once the Aggregate Score has been calculated, the Aggregate Scores of all students are ranked in numerical order across the state. A student’s ATAR is then determined by identifying the percentile ranking of their Aggregate Score relative to all other students.

For example, in Vegeta’s case, his Aggregate Score of 162.3 corresponds to the 85th percentile statewide. This means that his Aggregate Score is higher than that of 85% of all other students. Consequently, Vegeta’s ATAR would be 85.00.

The diagram below illustrates this percentile ranking process.