Paradox of limiting ranks (1 Viewer)

[Xanthi]

Suppose at a certain school, the top 4 students for a subject are listed as follows.

	Raw Internal Mark	External Raw Mark
Student A	70	90
Student B	70+δ	70
Student C	50	50
Student D	45	45

In the case δ << 0 student B scores substantially lower than student A. Student A always scores 90 points (moderated internal mark) until δ=0 where student A and B abruptly both score 80 points. However, as δ increases above zero by a small amount, there is an uncharacteristily large jump, with student B score increasing from 80 to 90.

This is paradoxical, seeing as one would expect any scaling processes to be continuous. I ask to satisfy curiosity at the seeming oddity.

 

[quickoats]

I’m pretty sure the internal marks (which are moderated exam marks) take into account the relative space between candidates minus outliers. This should smooth the “jump”

 

[Xanthi]

I think there is quite a high barrier to be considered an "outlier" though. The difference between a '90' and a '70' may not be sufficient and even if it is the paradox still holds upon reducing the mark difference.

It might take into account the relative spaces, in which case |δ|>0 but very small yields approximately 90 marks for both student A and B, but when δ=0 80 marks for both student A and B.* This is still quite a jump. In the former scenario marks are effectively "stolen" from the lower performing students, as 90+70<<90+90 and the marks have to come from somewhere. That doesn't seem particularly fair.

*If this is true then it is better for a student A to do slightly worse than student B. Upon decreasing their own internal slightly, their moderated internals jumps from 80 to almost 90. Surely that wouldn't occur?

 

[idkkdi]

*If this is true then it is better for a student A to do slightly worse than student B. Upon decreasing their own internal slightly, their externals jumps from 80 to almost 90. Surely that wouldn't occur?

If this is true then it is better for a student A to do slightly worse than student B. Upon decreasing their own internal slightly, their externals jumps from 80 to almost 90. Surely that wouldn't occur?


not following

 

[Xanthi]

If this is true then it is better for a student A to do slightly worse than student B. Upon decreasing their own internal slightly, their externals jumps from 80 to almost 90. Surely that wouldn't occur?


not following

Edited. "externals" was meant to say "moderated internals". Consider the following (the two students are the highest two ranked).

	Raw Internals	Externals	Moderated Internals
Student A	70.00	90	80
Student B	70.00	70	80
Student A'	69.99	90	Almost 90
Student B'	70.00	70	90

 

[Trebla]

Edited. "externals" was meant to say "moderated internals". Consider the following (the two students are the highest two ranked).

	Raw Internals	Externals	Moderated Internals
Student A	70.00	90	80
Student B	70.00	70	80
Student A'	69.99	90	Almost 90
Student B'	70.00	70	90

This is likely one of those exceptional cases in the moderating process where an exclusion occurs.

From

https://educationstandards.nsw.edu.au/wps/portal/nesa/11-12/hsc/about-HSC/moderation

Some students’ exam marks are not used in the moderation of school assessment marks if they are affected by certain circumstances, such as:

• Students with an upheld illness/misadventure application and an exam result that is relatively poor compared to their school assessment.
• Students whose performance in the exam is much lower than expected based on their performance relative to the group in the school assessment.
• Other special cases, as determined by NESA.

This suggests that the first scenario you provided above will lead to a similar moderated internal marks outcome to the second scenario instead (i.e. they both get moderated marks close to 90). The poorer performance in the externals is not fully ignored though, because it still makes up 50% of the final mark.

 

[Xanthi]

This is likely one of those exceptional cases in the moderating process where an exclusion occurs.

From [edited by Xanthi, can't post links]

Some students’ exam marks are not used in the moderation of school assessment marks if they are affected by certain circumstances, such as:

• Students with an upheld illness/misadventure application and an exam result that is relatively poor compared to their school assessment.
• Students whose performance in the exam is much lower than expected based on their performance relative to the group in the school assessment.
• Other special cases, as determined by NESA.

This suggests that the first scenario you provided above will lead to a similar moderated internal marks outcome to the second scenario instead (i.e. they both get moderated marks close to 90). The poorer performance in the externals is not fully ignored though, because it still makes up 50% of the final mark.

Edit: Never mind, the larger mark is always awarded so it doesn't become an issue