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Indeed, much better described at: https://en.wikipedia.org/wiki/Simpson%27s_paradox https://en.wikipedia.org/wiki/Simpson%27s_paradox
by internet_user 8y ago
Indeed, much better described at: https://en.wikipedia.org/wiki/Simpson%27s_paradox https://en.wikipedia.org/wiki/Simpson%27s_paradox
- gerdesj 8y agoI agree. To really get into the "paradox", start with the WP article. Pearl is heavily referenced and linked in it anyway. For me, this is pretty much the core argument that makes the paradox vanish: For instance, naive students of probability may expect the average of a product to equal the product of the averages (OP pdf page 4) It's not too hard to convince yourself that you can't stir numbers together at random and get away with it, even if it nearly looks sensible at first. The language says it all: "average of products" and "product of averages". The Vector Interpretation in the WP article gives a pretty decent visual explanation. If you find the maths a bit off putting just squint past the notation. You can pretty much replace all occurrences of funky symbols and vector with the word "line", accept that you can add these special lines together and you should be able to get the gist of what is going on.
- shadowmatter 8y agoI appreciate how the characters in the example are named Bart and Lisa.
- titzer 8y agoYep, the first picture in the upper right of the wikipedia article is worth a thousand words. In it we can clearly see there is a third hidden variable which is somehow getting mixed in with x.