Since Simpson's Paradox has been discussed here recently (and not so recently), I thought I'd share this interactive1 infographic that I found via the FlowingData blog. I already understood Simpson's Paradox pretty well, but playing with the sliders helped me get a more intuitive feel for it.
I expect similar tools would be helpful for explaining Bayes' Theorem and some of the other things we talk about on LW (like Pareto efficiency and Nash equilibria). Do such things exist?
1 The interactive part is farther down the page.
That's actually the first time I understood how Simpson's Paradox works. Nice one!
Great illustration! This is a nice alternative to the way I usually visualize Simpson's paradox, which involves the subgroup averages pulling the overall average proportionally to the sizes of the subgroups (then it's possible to decrease both of the subgroup averages, but skew the sizes sufficiently towards the higher subgroup average that the overall average goes up).
It should definitely be possible to make a similar interactive illustration for a Bayesian update, where you could tweak the prior and the likelihood ratio using sliders.