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Comment by Narhem | Hacker News Reader

Like Tumors are higher dimensional objects than what human brains are trained to perceive.

For pedagogues and practitioners alike: there is a subtle connection between Simpson’s paradox and the wild geometry of relative entropy. This might be partly why effect sizes are also contentious.

Besides Ellenberg’s mind-altering discussion of that link[1], see hints on the second page of:

https://www.qeios.com/read/XB1N2A/pdf

[1] "[the point of Simpson’s paradox] isn't really to tell us which viewpoint to take but to insist that we keep both the parts and the whole in mind at once."

Ellenberg, from Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else (2021)

If the previous comment is right, then this one is plainly also true in some sense. I'm disappointed to see downvotes.

> If the previous comment is right

I actually coded a Z3 program to prove it! The 3-variables version takes too long to resolve, but I got results for the 2-variables version (tumor size + gender):

Results can be found in this GSheet: https://docs.google.com/spreadsheets/d/1tsBhElTgXjVTeas8quar...

Code is here: https://gist.github.com/TheMrZZ/c33927ca2cc917997a67d7f84b82...

I'm currently running the 3-variables version, hopefully I'll get results this afternoon.

We can clearly see the same problems that arise in the 1-variable Simpson's paradox (widely different population sizes).

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