Hi Vaniver! =D
On the commentary: your eyeballing seems good, but I don't think I ever said anything about relative comparisons between correlation coefficients (namely just overall correlation is positive). As you observed, I could easily make all 3 correlations (blue-only, green only, or blue+green) positive. I don't have any interesting things to say about their relative degrees.
I don't quite see the difference in interpretation from this writing. I agree with basically all the stuff you've written? The fact that the slicing "behaves as a filter", if I interpret it correctly, is exactly the problem here.
I don't know what "have a different origin than Simpson's paradox" means exactly, but here are a few ways they differ and why I say they are "different":
a fundamental assumption on Simpson's paradox is that there's some imbalance with the denominators; in your 2x2x2 matrix you can't arbitrarily scale the numbers arbitrarily; all the examples you can construct almost relies on (let's say we are using the familiar batting averages example) the fact that the denominators (row sums) are different.
the direct cause of the reversal effect is, as you said, the noise; I don't think Simpson's paradox has anything related to the noise.
Idea: my steel-man version of your argument is that reversal effects arise when you have inhomogenous data, and this is definitely the more general common problem in both situations. In that case I agree. (this is how I teach this class at SPARC, at least).
Haha hey QC. Remind me sometime to learn the "get ridiculously high points in karma-based communities and learn a lot" metaskill from you... you seem to be off to a good start here too ;)
I am Yan Zhang, a mathematics grad student specializing in combinatorics at MIT (and soon to work at UC Berkeley after graduation) and co-founder of Vivana.com. I was involved with building the first year of SPARC. There, I met many cool people at CFAR, for which I'm now a curicculum consultant.
I don't know much about LW but have liked some of the things I have read here; AnnaSalamon described me as a "street rationalist" because my own rationality principles are home-grown from a mix of other communities and hobbies. In that sense, I'm happy to step foot into this "mainstream dojo" and learn your language.
Recently Anna suggested I may want to cross-post something I wrote to LW and I've always wanted to get to know the community better, so this is the first step, I suppose. I look forward to learning from all of you.
I'm glad it was helpful. =)