More to the story: The curious case of Simpson’s Paradox

Simpson’s Paradox is a statistical phenomenon that can occur when trying to make comparisons between groups.

Let’s say we have two schools, School A and School B. We want to compare the success rates of the schools by looking at the percentage of students who pass their exams.

At first glance, it appears that School A is doing much better than School B. Out of 100 students, 90 passed their exams at School A, while only 80 passed at School B. So it seems like School A is the better choice, right?

But if we look a little closer, we’ll see that there’s more to the story:

It turns out that School A has a much higher percentage of students who are struggling academically. In fact, 50% of the students at School A are considered to be at-risk of failing, compared to just 20% at School B.

So when we take this into account, the picture looks a little different. If we compare the success rates of just the at-risk students at each school, we see that School B is actually doing much better. Out of the 20 at-risk students at School B, 16 passed their exams (a success rate of 80%), while only 35 out of the 50 at-risk students at School A passed (a success rate of just 70%).

This is Simpson’s Paradox in action — by just looking at the overall success rates of the two schools, we would have come to the wrong conclusion. It’s important to remember to always consider all the relevant factors when making comparisons, or you might end up falling victim to this paradox!