Re: Math trivia
Simpson's Paradox moreover gets promoted from freaky quirk of some situations to general badass problem in statistical reasoning, once we take on board the general empirical availability of a partition that will create this just this sort of reversal of inequalities. I.e., P(X)>P(Y) within the partitions, and P(Y)>P(X) in aggregate. This is one of the phenomena I harp on when I'm selling my students on the idea that good statistical reasoning requires much more than formal virtuosity in calculating probabilities. Which axiom or theorem of probability tells you how to partition the data perspicuously? I ask them.
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