Berkson’s Paradox is a counterintuitive or unexpected trend observed in a sample due to a particular type of selection bias. This bias arises when the sample is selected based on the combination of two characteristics.
Also known as Berkson’s bias or collider bias, Berkson’s Paradox pertains to situations where a group is selected based on the combination of two characteristics and results in some false observation of correlation between the two characteristics – the correlation might be observed in the sample only because those without those two characteristics were not selected to be in the group in the first place.
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.