1. Secondary Analysis Method
Comparison of each subject with
School all-other-subjects average
and State average
This powerpoint file gives an overview of the Secondary Analysis presented in the HSC Analysis of Results.
While the primary analysis is a comparison of the results in each subject with what is typical of comparable students in the School Certificate, the secondary analysis is a comparison of the HSC results in a subject with the average of all other subjects taken by each student; the second part of the secondary analysis is a comparison with state average.
The secondary analysis is done using no School Certificate information.
The account of the process given in this presentation contains some over-simplifications, but does give the general thrust of what has been done.
The secondary analysis is done on the basis of marks re-scaled to TES (UAI) parameters. In this way, all marks lie on a common scale in a similar fashion to the common scale obtained by re-scaling to SC means and SDs.
This analysis technique was originally developed by Max Smith at DET. I am grateful to Max for permission to use it.
© JS DeCourcy 2004

2. All the students in this subject in this school - HSC marks
State Average Line
All the students in this
subject in this school -
HSC marks
First of all take all of the students in the study in this subject, and get their BOS one-unit mark.

3. This subject re-scaled to UAI values
State Average Line
This subject re-scaled
to UAI values
Re-scale the marks for each subject in each school to get the TES (UAI) value of those marks. (The mapping points to do this have been published by UAC each year on their website and in the Technical Committee on Scaling’s report.)

4. State Average Line Average for this subject
Find for each school the variation of the school from the all-of-state average. Note that this won’t be exactly the same as the “School/ State variation” published by BOS, as this analysis has put all subjects onto a common scale, the UAI scale.

5. Just a bit below state average State Average Line
Keep for this subject the difference as a UAI-based school / state difference.

6. School “all-others” Average Line
Now consider how each subject compares with all others in the school. The problem we have with BOS marks is that they lie on different scales. I.e., a mark of 70 in Physics may be more difficult to obtain than a mark of 70 in Senior Science. The UAI scaling process is intended to place all subjects on a common scale, so it is these marks that we use.

7. School “all-others” Average Line
Take one subject, and
re-scale it to UAI
Take one subject at a time. Say Biology.

8. School “all-others” Average Line
Consider one student’s
mark in this subject
Consider each student WHO TAKES BIOLOGY in turn. This first student we have found has a mark in Biology a bit above the average. Now for that student, consider his mark in……

9. School “all-others” Average Line
Look at this student’s
results in each of his/her
other (UAI-scaled) subjects
English Standard. He hasn’t done as well in English, the mark is a bit less.

10. School “all-others” Average Line
Look at this student’s
results in each of his/her
other (UAI-scaled) subjects
The green subject is Maths, and he has done quite poorly there.

11. School “all-others” Average Line
Look at this student’s
results in each of his/her
other (UAI-scaled) subjects
And in Business Studies – the yellow line – he has done better than Maths and English, but not as well as Biology.

12. School “all-others” Average Line
Look at this student’s
results in each of his/her
other (UAI-scaled) subjects
Religion is a bit less again

13. School “all-others” Average Line
Look at this student’s
results in each of his/her
other (UAI-scaled) subjects
The whole school did pretty terribly compared to State in the purple subject, say PDHPE.

14. School “all-others” Average Line
Look at this student’s
results in each of his/her
other (UAI-scaled) subjects
And he is definitely in the bottom part of the candidature in this school for his final subject in light green.

15. School “all-others” Average Line
Get the difference between the student’s mark in this subject and his/her mark in each other subject. (Note that in this example, this was the student’s best subject.)
School “all-others” Average Line
This demonstrates that for this student, Biology is his best subject. Now for this Biology student, measure the difference between his mark in Biology and his mark in each other subject…….

16. School “all-others” Average Line
Get the difference between the student’s mark in this subject and his/her mark in each other subject. (Note that in this example, this was the student’s best subject.)
School “all-others” Average Line
Considering just these differences, ………

17. School “all-others” Average Line
Find their average for this one Biology student.
Find the average of these differences for this student

18. School “all-others” Average Line
Find these average differences for all students in this subject
Repeat this process finding the average “all-other-subjects” difference for every Biology student.

19. School “all-others” Average Line
Find the average of the average differences for all students in the subject
Then find the overall Biology average of the average differences!

20. School “all-others” Average Line
Then, put this with what we had from comparison with state average to get.....
School “all-others” Average Line
This gives a measure of how Biology has compared with all of the other subjects in the school TAKEN BY STUDENTS OF BIOLOGY - hence it is a comparison on a common (UAI) scale, across common students.

21. School “all-others” Average Line
Then, put this with what we had from comparison with state average to get.....
School “all-others” Average Line
State Average Line
This value, with the value we worked out before for the comparison with state,

22. School “all-others” Average Line
State Average Line
Gives the point on the graph where we put

23. School “all-others” Average Line
State Average Line
..... this subject compared
to school and state averages
….. A little dot representing this subject compared to school and state averages. Note that this dot doesn’t have “uncertainties of measurement” around it. These are shown in the Trends Analysis, where these data are represented over time.

24. Thank you
……….. The end.