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This happens to students on a fairly consistent basis. Suppose a project is worth 10% of the student's final mark while a midterm is worth 30% and the final ex

by canistr 15y ago

This happens to students on a fairly consistent basis. Suppose a project is worth 10% of the student's final mark while a midterm is worth 30% and the final exam is worth 60%. If the student performs well on the project, average on the midterm, but poorly on the Final Exam, their mark is still going to be poor due to the heavier weighting of the exam and midterm over the project. EDIT: I know it's not a perfect example, but comparing marks between different students based on how they are weighted is essentially the idea.

jmilloy 15y ago
Is this really the same thing? That just sounds like whoever chose the weightings got the result they wanted - a student who couldn't master the final exam got a poor mark.
afhof 15y ago
The point wasn't the weighting, it was that group A can get a better average in every category, while group B has the best overall.
- canistr 15y ago
  Well the comparison would be between different students. But the weightings essentially account for this difference. However, the better comparison would probably be if different students had different marking schemes.
bdhe 15y ago
This is not the same thing as the Simpson's paradox. Specifically, as stated in wiki, you need to show a grouping (that is classically anti-causally related) with one correlation, but overall, upon combining the data, the correlation is reversed. This does not happen in your example. But you do hint at something similar, i.e., the weights assigned are different to different groups and that is necessary for the Paradox to occur.
orangecat 15y ago
That's not quite right. The "paradoxical" version would be something like: Alice and Bob are taking a course where their grades are determined by 5 essays and/or presentations, and they can choose how many of each to do. Alice does one essay where she earns 80%, and 4 presentations where she earns an average of 90%. Bob does 4 essays earning an average of 85%, and one presentation where he earns 95%. For each assignment type Bob has a higher average than Alice, but Alice's overall grade (assuming equal weighting) is higher than Bob's: Alice gets 88% ((80 + 4 * 90)/5) and Bob gets 87% ((4 * 85 + 95)/5).
- deleted 15y ago
  [deleted]

by canistr 15y ago

jmilloy 15y ago

Is this really the same thing? That just sounds like whoever chose the weightings got the result they wanted - a student who couldn't master the final exam got a poor mark.

afhof 15y ago

The point wasn't the weighting, it was that group A can get a better average in every category, while group B has the best overall.

canistr 15y ago
Well the comparison would be between different students. But the weightings essentially account for this difference. However, the better comparison would probably be if different students had different marking schemes.

bdhe 15y ago

This is not the same thing as the Simpson's paradox. Specifically, as stated in wiki, you need to show a grouping (that is classically anti-causally related) with one correlation, but overall, upon combining the data, the correlation is reversed. This does not happen in your example. But you do hint at something similar, i.e., the weights assigned are different to different groups and that is necessary for the Paradox to occur.

orangecat 15y ago

That's not quite right. The "paradoxical" version would be something like: Alice and Bob are taking a course where their grades are determined by 5 essays and/or presentations, and they can choose how many of each to do. Alice does one essay where she earns 80%, and 4 presentations where she earns an average of 90%. Bob does 4 essays earning an average of 85%, and one presentation where he earns 95%. For each assignment type Bob has a higher average than Alice, but Alice's overall grade (assuming equal weighting) is higher than Bob's: Alice gets 88% ((80 + 4 * 90)/5) and Bob gets 87% ((4 * 85 + 95)/5).

deleted 15y ago
[deleted]