= Simpson's paradox
{c}
{wiki}
= Simpson paradox
{c}
{synonym}
A comparison can have the same direction within every background stratum but reverse after pooling strata with different group compositions. For example, let unexposed event risks be $0.001$ in a low-risk stratum and $0.05$ in a high-risk stratum, and multiply the odds by $2.7$ for exposure within each stratum. The exposed risks are then approximately $0.002695$ and $0.124424$. If 80% of unexposed subjects but only 1% of exposed subjects belong to the high-risk stratum, the pooled unexposed risk is $0.0402$ while the pooled exposed risk is about $0.003913$. Every conditional <odds ratio> is above one, yet the pooled exposed risk is smaller. The differing background distributions create the reversal; this example does not identify a <causal effect> without assumptions on how exposure was assigned.
Back to article page
