Berkson’s Paradox (also known as Berkson’s bias or collider bias) is the observation of a counterintuitive and usually incorrect statistical result due to selection bias or sampling bias.
Specifically, Berkson’s Paradox pertains to situations where a group is selected based on the combination of two characteristics. One might observe within the group that those characteristics are negatively correlated – but those characteristics may in fact be positively correlated or uncorrelated in the population, and the observed negative correlation could be because those without those two characteristics were not selected to be in the group.
Example 1: Coin Collection
Let’s say you had a friend that likes to collect old coins and misprinted coins. If you observed your friend’s coin collection without knowing their selection criteria, it would seem that new coins are much more likely to be misprinted. But in reality, new coins that are not misprinted would simply not make it into the collection, which biases the result.
Example 2: Basketball Players
Take professional basketball players – you might observe that the taller players are less likely to be good shooters, and the good shooters are less likely to be tall.
You might come up with reasons why being taller makes it harder to shoot well, but more likely this negative correlation is spurious – there is a selection bias because short people that are not good shooters are unlikely to be professional basketball players in the first place! So when you see a short professional basketball player, they are more likely to be a good shooter, otherwise they would not have made it that far.
If you found Berkson’s Paradox interesting, you might also appreciate a related statistical phenomenon, Simpson’s Paradox.
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