It can be useful and intuitive to illustrate the paradox in a chart. For example: https://twitter.com/remiemonet/status/984893903605321729?s=20
If we look at the population as a whole, the best fit line points in a certain direction. If we break down the same data into key groups, it’s clear that the best fit line for each group would point in a completely different direction. Our interpretation of the data can be different or even reversed, depending on whether we include group identification as a feature.
That sounds like base rate fallacy, so now I’m doubting whether I understand either of them :)
This one is also useful to visualize: https://byrdnick.com/wp-content/uploads/2020/07/Base-rate-box-problem-drug-test-diagnostic-reasoning-nick-byrd-512x446.jpeg
In the base rate fallacy, the correct interpretation is a straight-forward application of Bayes’ rule, which turns out to be unintuitive for the lay-person. Essentially, even if you have a very accurate test or detector, when you have a very low “base rate” or true prevalence of the condition in the population, the results of your test can turn out to be uninformative.
The Wikipedia article on Simpson’s paradox does a good job of illustrating it with examples. If anything, it’s a caution (beyond those which already exist) against reading too much into base rates.