Eli5: What is the Simpson’s paradox in statistics?

Question

Can someone explain its significance and maybe a simple example as well?

In: 3585

Answer 1

Here’s an example just about anyone asking this question is familiar with:

Suppose both your math and your science classes assign grades based (only) on a combination of test scores and homework grades.

In your math class, test scores are weighted 80% and homework is weighted 20%. Your test average was a 90% and homework average was 50%, so your overall grade is .9*80% + .50*20% = 82%.

In your science class, test scores and homework scores are both weighted 50%. Your test average was 94% and homework average was 60%, so your overall grade is .94*50% + .60*50% = 77%.

So even though you scored better in science in both test taking (90%->94%) and homework (50%->60%), the change of weights made your overall science grade lower than your math grade (82%->77%).