Simpson’s paradox is a phenomenon in which a trend appears in several groups of data but disappears or reverses when the groups are combined. It is caused by confounding variables.

Example

A famous study shows Simpson’s Paradox in analyzing the effect of smoking on mortality rates in women. The combined data seems to suggest that smoker has less mortality than non-smokers.

Simpsons Paradox 1.png When we split the sample by age groups, the trend reversed, and we see that smokers have higher mortality rates for virtually every age group!

Simpsons Paradox 2.png

The confounding variables here is the age. As there are more young women who smoked than older women, and as younger women are expected to live longer than older women, adding all the groups together makes smoking appear to be beneficial.