Simpson's paradox
An easy answer?
In a neighborhood of London, highschool students pass their A-levels. In 2023, 1446 women obtained the A-level, whereas 1368 men obtained theirs.
Question 1a. Which group performed best, men or women?
Question 1b. Does this make sense?
We now know that they were 1647 women who took the examination. There were also 1542 men.
Question 2. Does this change the answer? Why?
Finally, we obtain even more information. Many subjects can be studied in order to obtain the A-level. In order to simplify, let us consider that students fall into one of the categories "Humanities", "Economics" and "Sciences".
- In Humanities
- 321 women obtained their A-level out of 419.
- 187 men obtained their A-level out of 250.
- In Economics
- 458 women obtained their A-level out of 521.
- 393 men obtained their A-level out of 451.
- In Sciences
- 667 women obtained their A-level out of 707.
- 788 men obtained their A-level out of 841.
Question 3. Who performed best in Humanities? Economics? Sciences?
Question 4. Try to explain why the result is different when we look at the numbers without knowledge of the subjects studied.