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Comment by TicklishTiger | Hacker News Reader

That is not a paradox. It's just the fact that a theory about something might not hold when you take a closer look at that something.

In the articles example, the admission rates of a university seemed to indicate that there is a bias against women.

Zooming in and looking at the admission rates of the individual departments seem to indicate that there is a bias against men.

The article makes it sound like the first theory was wrong. And the second theory - the bias against men - is the real truth.

Zooming in further might indicate the opposite again.

Take two boxers. So far, one of them has won 86% of his fights and the other one has won 100%. According to the article, "The data is clear".

Now we add more data:

One fighter is Mike Tyson. He won 50 of his 58 fights. The other one is me. I did one fight in kindergarden and won it. But to be honest: I would not want to fight Tyson. As paradox as it sounds.

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It is a paradox. In common usage, a paradox is an apparent absurdity which nevertheless holds up upon deeper investigation. In this case the apparent absurdity is e.g. "Treatment A is better at treating kidney stones despite performing worse in both trials".

Sometimes the word paradox has a slightly different meaning. For example, Russell's paradox in mathematics is the opposite; it takes something apparently well-founded and shows that it is absurd.

It’s a paradox because many people find it counterintuitive. It’s the mathematical statement of why correlation does not imply causation. The existence of a confounding variable correlated both with the purported cause (eg gender) and the purported effect (school admissions) can lead to reversals in observed association when grouped or broken out. Thus it is challenging to draw causal conclusions from observational data.

That a pair of attributes doesn't necessarily exhibit independence within the universe at large, even if it exhibits independence within each sub-universe is a powerful observation, and it's a troubling one to anyone who has attempted to design a sales and marketing strategy, a drug trial, or frameworks to encourage social equality: To have it suggested I can say nothing less about these thousand students other than a thousand different things, just sounds so absurd, and yet here it is true.

Sometimes people use the term "paradox" simply to a contradictory statement which upon investigation turns out to be true. In that way, "Simpson's Paradox" is absolutely a paradox.

I don't know, but at some point, aren't we just running up against the definition of "probability"?