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by Narhem 671 days ago
Like Tumors are higher dimensional objects than what human brains are trained to perceive.
2 comments
gradschoolfail 671 days ago
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)

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oh_my_goodness 671 days ago
If the previous comment is right, then this one is plainly also true in some sense. I'm disappointed to see downvotes.
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TheMrZZ 671 days ago
> 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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