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Simpson’s Paradox Explained

Mehdi Daoudi, et al, have a nice explanation of Simpson’s Paradox:

E.H. Simpson first described the phenomenon of Simpson’s paradox in 1951. The actual name “Simpson’s paradox” was introduced by Colin R. Blyth in 1972. Blyth mentioned that:

G.W. Haggstrom pointed out that Simpson’s paradox is the simplest form of the false correlation paradox in which the domain of x is divided into short intervals, on each of which y is a linear function of x with large negative slope, but these short line segments get progressively higher to the right, so that over the whole domain of x, the variable y is practically a linear function of x with large positive slope.

The authors also provide a helpful example with operational metrics, showing how aggregating the data leads to an opposite (and invalid) conclusion.