Berkson's paradox

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:

• https://en.wikipedia.org/wiki/Berkson%27s_paradox

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.

Other 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.
• 2-star reviews: go to the coffee shops with two star reviews. Two star reviews only happen because they wanted to give one star (due to bad customer service) but couldn’t because of the coffee quality.