An aggregate trend reverses once you stratify. Which conditioning set is correct?

medium

Answer

$An association observed at the aggregate level reverses when data is split by a confounder.$
$Classic example: Berkeley admissions — men admitted at higher aggregate rate but women admitted at higher rate within every department (women applied to more competitive departments).$
$Resolution: pick the right conditioning set based on the causal DAG.$
$Blindly conditioning or ignoring a confounder both cause errors.$
$Textbook case for why 'always condition on more variables' is wrong.$

Check yourself — multiple choice

Not real
Aggregate association reverses when stratified by a confounder; requires causal DAG reasoning to know which set to condition on
Random
Same as p-hacking

Simpson: association reverses on stratification; need causal DAG to choose conditioning.

#causal-inference

215 interview questions in this topic.