This article provides an in depth look at KS5 residuals in the KS5 Reports of Analytics and how it is calculated. This can help with troubleshooting figures or for those who are interested in the detail behind the calculations.
What is a Residual?
Residuals are used to compare the relative performance of faculties, qualifications, classes, or students. They aim to represent how well a faculty, qualification, or class has performed in comparison with how the same students have performed across all of the qualifications they have taken, or how well a student has performed in one qualification compared to all of their qualifications on average. They’re based on the performance of your students in the report you’re currently viewing.
| Note: As residuals are based on student performance, Analytics will include all students (including guests) and all grades. Grades that have been discounted and do not count towards headline measures will still be included in residuals. |
In KS5 reports, the average points used to calculate residuals for L3 qualifications and Tech Certificates will be calculated separately, using respective qualifications. This is due to these qualifications being awarded different grades and therefore not being directly comparable.
You also have access to the ‘Residual Exclusion’ functionality, which can be used to exclude certain qualifications from the average points scores used to calculate the residuals. For example, this could be useful if you wanted to exclude vocational qualifications and see the impact this has on your student’s residuals. For more information on how to use this, see Appendix 1 - Residual Exclusions further on in this article.
Student Residuals
Student residuals can be used to compare a student’s performance in a particular qualification with how they’re performing on average across all of their qualifications.
1 / Calculate Average Points
Residual calculations begin with separating the Level 3 grades from Tech Cert grades and will be calculated for L3 and Tech Cert qualifications separately. For example, if a student takes three Level 3 qualifications and two Tech Cert qualifications, they will be treated separately based on the points awarded for these.
| In the below examples, Level 3 grades are used however the process for calculating residuals for L2 Tech Certificates is the same. |
Once separated, the grade points for the appropriate qualifications (L3 or Tech Certs) will be totalled, and the entries for those qualifications will be totalled. The average points score will then be calculated, using the formula below:
|
Average Points Score = (Total Grade Points – Total Entries)* *Calculated separately for Level 3 and Tech Cert Qualifications |
2 / Standardise Grade Points
The next step would be to standardise the actual grade points for the qualifications included, to make them equivalent to one full entry. This is because some Level 3 qualifications are worth more than 1 full A Level for example, and therefore would need to be standardised to be treated fairly against the A Level qualifications. The same will apply to Level 2 Tech Certificates that will be standardised, to make sure all grades count as 1 entry towards residuals and are treated equally.
For example, if a student took BTEC Engineering worth 70 points and 2 entries, the points will be divided by 2 and therefore equal to 35 when equivalent to one entry.
3 / Calculate Residuals
Once the average points are calculated and the actual points are standardised, residuals will be calculated using the formula below for each qualification the student is taking. In our example, we have a student taking three Level 3 qualifications, so you can see their individual residual for each qualification.
|
Student Residual = (Standardised Point Score – Average Point Score)* *For that specific qualification |
The student’s residuals would indicate how well they are performing in each of their Level 3 qualifications, compared to all L3 qualifications they take.
In KS5 there are 10 points difference between the whole grades, so based on the above example, a residual of 2.5 in Engineering would indicate that the student is performing approximately a quarter of a grade better in Engineering than they are performing across all L3 qualifications they take.
Class Residuals
Class Residuals compare the performance of students in a class to how those same students are performing overall, across all of their Level 3 or L2 Tech Certificates. These are calculated by taking the sum of the individual student residuals and dividing this by the number of students in the class.
| Class Residual = (Sum of Student Residuals in Class / Count of Students in Class) |
For example, there are 6 students in the Maths class (13A/Ma2), shown in the table below.
The class residual calculation is as follows:
13A/Ma2 Residual = 42.5 ÷ 6
= 7.08 (2dp)
Qualification Residuals
Qualification residuals compare the performance of students in a qualification to how those same students are performing overall, across all of their L3 or Tech Cert qualifications. These are calculated by taking the sum of the individual student residuals and dividing this by the number of students in the qualification.
| Qualification Residual = (Sum of Student Residuals in Qualification / Count of Students in Qualification) |
For example, there are 19 students in our Maths qualification, partly shown in the table below.
The qualification residual calculation is as follows:
Maths Residual = 51.37 ÷ 19
= 2.7 (2dp)
Faculty Residuals
Faculty Residuals compare the performance of students in a faculty to how those same students are performing overall, across all of their Level 3 or Tech Cert qualifications. These are calculated by taking the sum of the individual student residuals and dividing this by the total number of student residuals in the faculty.
| Faculty Residual = (Sum of Student Residuals in Faculty / Count of Students in Faculty) |
For example, there are 22 student residuals in the qualifications included in the Humanities faculty, partly shown in the table below.
The faculty Residual calculation is as follows:
Humanities Faculty Residual = -65.19 ÷ 22
= -2.96 (2dp)
Admin only - Faculties must be created in the CONFIG. area and selected in the FACULTY column of the Matching page for this analysis to be available in the reports.
Appendix 1 - Residual Exclusions
Residuals can be found on various report views. By default Analytics will include all qualifications shown on the view you are working with but you can temporarily exclude selected qualifications from this calculation if you wish to. Please note this will affect residuals calculations only, and you can do this by clicking the filter icon within the ‘Residual’ column header.
A panel will expand, listing all qualifications with a grade in that data set’s report. If you wish to exclude qualifications, tick the boxes next to the relevant qualifications and click ‘Apply’. Once applied, these qualifications will be excluded from the average points step of the calculation (covered on step 1 of this article).
Thanks for reading!