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)

PhD in aviation ∩ climate science | Aviator, diver, ETH maxi, nexialist | 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

I think that would be the case if you randomly sampled *from the people you follow*, in which case it’s a classic illustration of the friendship paradox: on average, you are likely to have fewer followers than the people you follow, precisely because a few users account for a disproportionate share of all followers (https://en.wikipedia.org/wiki/Friendship_paradox).

If you truly randomly sampled users, e.g., sampling random numerical values across the entire range of FIDs, you would probably get an underestimate of the average number of followers, because high follower count correlates heavily with low FID, so the sample would be biased in the other direction.

Would be cool to run a simulation of both on Dune and compare the results

Geopolitics, web3 analyst, Art enthusiast

This paradox cannot be overemphasized.
Another example is asking random farcaster users about their followers. If you randomly survey users about how many followers they have, you might find that the average number of followers reported is higher than the platform's actual average. This happens because users with more followers are more likely to appear in your survey sample (since they have a larger presence on the network) leading to an over-representation of those with larger follower counts.

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229 $DEGEN

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Interesting. Not sure if related but I remembered about Pareto principle. These statistical phenomena always amaze me.

How I missed your casts! You didn’t show up on my feed for such a long time and I assumed you’ve stopped casting, I checked now and you didn’t. Feed is acting really weird lately. This one pushed me into a trans and I looked at a wall for couple of minutes like a crazy person 😂 enjoyed every second though.