statistics

TIL about the inspection paradox, which arises whenever the probability of observing a quantity is related to the quantity being observed. For example, if you ask students about their class size, you might get an average of 40, when the real average is 30. This is because students from larger-than-average classes are, by definition, over-represented in your sample.

Source:

TIL about the inspection paradox, which arises whenever the probability of observing a quantity is related to the quantity being observed. For example, if you ask students about their class size, you might get an average of 40, when the real average is 30. This is because students from larger-than-average classes are, by definition, over-represented in your sample.

Source: https://allendowney.blogspot.com/2015/08/the-inspection-paradox-is-everywhere.html

Extending this concept is the waiting time paradox, which is a special case of the inspection paradox. Let's say you try to catch a bus whose average frequency is every 10 minutes. If you show up randomly at the bus stop, you might therefore expect to wait an average of 5 minutes. The reality is nearer to 10 minutes because late buses cause more passengers to wait, and thus you are more likely to be in that larger group of unlucky passengers.

Source: https://jakevdp.github.io/blog/2018/09/13/waiting-time-paradox/

(Caveat: the waiting time paradox only applies if the distribution of arrival times follows a Poisson process, which isn't necessarily the case for buses)

Aviator, diver, Etherean, nexialist, PhD in aviation ∩ climate science | Host of /diving /ethfinance /eth-staker /geopolitics /science /singapore /thomas

I always love finding those subtle ways in which our thin-slicing, system-1 thinking approximates the world in all the wrong ways and leads to unconscious biases and errors