An interesting paradox comes from the Selection bias regarding Collider variable. One of the best examples would be the attractiveness and talent as Wikipedia explains:
In figure 1, assume that talent and attractiveness are uncorrelated in the population. In figure 2, someone sampling the population using celebrities may wrongly infer that talent is negatively correlated with attractiveness, as people who are neither talented nor attractive do not typically become celebrities.
See also the explanation in Brilliant
A Numberphile episode by Hannah Fry explains this with books that are adapted into films: https://www.youtube.com/watch?v=FUD8h9JpEVQ
An article: http://www.the100.ci/2017/03/14/that-one-weird-third-variable-problem-nobody-ever-mentions-conditioning-on-a-collider/
Here are other nice examples: YouTube: Collider Bias (Berkson’s paradox): how ‘censored’ data leads to flawed conclusions and Lionel Page‘s Twitter thread: https://twitter.com/page_eco/status/1373266475230789633
See also Simpson’s paradox.
List of examples
- https://twitter.com/rlmcelreath/status/1386636052543283201: A new collider bias teaching example. Sample selects on marriage (not divorced) so: satisfaction ––> (not divorced) <–– children
- https://twitter.com/page_eco/status/1396101649802792965?s=20 - studies published in top journals that fail to replicate are cited more than those that replicate.