The example shows that the usual stats aren't enough to pin down the true data. But in practice I imagine / wonder if these stats really are reasonable "sufficient stats" because the probability of seeing data with strong structure is unlikely in most contexts. In other words...

p(data | stats) = p(stats | data) * p(data) / p(stats).

and p(data) is only strong for a "blob / cloud" of points, so when there's some correlation the observed stats tell you that you likely have a blob having some degree of correlation.

Thought this would be about the 'other' Anscombe:

* https://en.wikipedia.org/wiki/G._E._M._Anscombe

:)

I did a talk on Cognitive Biases in performance measurement and included Anscombe's Quartet (among other things) in the section on developer bias: https://speakerdeck.com/bluesmoon/we-love-speed-understandin...

I do STEM mentoring for high school kids. Bookmarking this, because it'll be a great teaching aid at some point.

Always visualize first. Human 'eyballing' is a good pattern detector.

Linear correlation is just one pattern the data can have.

Unfortunately many social science publications have reviewers who know only the basics and can't judge or accept statistically valid analysis that is outside their competence. Fit it into line or nothing.

This reminds that “visualize while thinking” will probably become an important part of reasoning as we move closer to AGI models.

This will require improvements to vision models, RL frameworks, etc, but will be interesting to see how much it can broaden current abilities.

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