Simpson's Paradox: A Logically Benign, Empirically Treacherous Hydra

The Monist 84 (2):265 - 283 (2001)
An association between a pair of variables can consistently be inverted in each subpopulation of a population when the population is partitioned. E.g., a medical treatment can be associated with a higher recovery rate for treated patients compared with the recovery rate for untreated patients; yet, treated male patients and treated female patients can each have lower recovery rates when compared with untreated male patients and untreated female patients. Conversely, higher recovery rates for treated patients in each subpopulation are consistent with a lower recovery rate in the total population when data are aggregated. The arithmetical structures that underlie facts like these support surprising applications of them that invalidate a cluster of arguments that many people, at least initially, take to be intuitively valid. E.g., despite intuitions to the contrary, the following argument is invalid.
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