Simpson's paradox is an extreme form of confounding, where the association between two variables in a full group is in the opposite direction of the association found within every subcategory of a third variable. This paradox was first described by G. U. Yule in 1903 and later developed and popularized by E. H. Simpson in 1951.

By way of example, consider a new drug treatment that initially appears to be effective, with 54% of treated patients recovering, as compared with 46% of patients receiving a placebo. However, when the sample is divided by gender, it is found that 20% of treated males recover compared with 25% of placebo males, and 75% of treated females recover as compared with 80% of placebo females. So the apparent paradox ...

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