I suspectit may not be obvious why its survivorship bias.
The bicycle example lines up with this because the best cyclists survive the exervise longer, thus you have a samping bias towards those who survive the longest on the road,
Same with the friends examples... The most popular people tend to survive more friendships, meaning more popular people are more likely to have friends (including you).
@mjambon You may also be thinking the Cauchy-schwartz inequality, which describes the math behind the scenario re: friendship you mentioned. That is called the friendship paradox.
@freemo oh, interesting note regarding the friendship paradox:
> In contradiction to this, most people believe that they have more friends than their friends have.
I would explain this by the fact that we spend more time with people who have fewer friends than average. (not sure if it's a hard rule or if depends on the shape of the friendship graph)
@mjambon Yea its a bit harder to understand because its a bit of applying it in the opposite way you normally think of it.
So regression to the mean is explained one way that i think is not particularly counter intuitive to how it is applies but let me start with the basics.
Formally, regression to the mean is all about how if you take lots of samples of things with all sorts of bizzare distributions, in the end they will eventually average out to a normal distribution (thus explaining why normal distributions tend to be the default and crop up everyone)...
In practice though the fallacy aspect arrises when you pay attention to addressing outliers, and on resampling they appear to have been "fixed", when in reality they only cropped up as outliers in the first place due to random chance and nothing as changed.
A very typical example given is if you look at a city and pick the top 5 intersections where accidents took place last year and put additional safety measures in place the next year you will notice that those intersections have reduced the number of accidents significantly. You assume this is due to your safety measures when in fact that would have happened regardless since they were only outliers by random chance and they simple "regressed to the mean"...
So how does that apply here. Well like i said its a bit of what i just said but kinda in reverse. You are assuming your sampling is average, when in fact you are samping outliers. So while the reality tends to regress towards the mean (went home after their normal average length bike ride) those that remain are the outliers but you dont recognize them as outliers. So its the same principle of regression to the mean just, the inverse of it.
By the way there are so many terms you may have been thinking of please stop me if I actually hit ont he term you were trying to remember.
You were also describing "representativeness heuristic". Im sure there is a wikipedia page on that if you want to look it up. Basically just means you think someone is representative of the norm when it is not, It is a psychological concept not a statistical one as far as I know.
@mjambon If you can give me more insight on the term you are trying to remember I might be able to help you come up with it. I can think of sooooo many concepts you kinda touched on in some sense.
So many selection biases come to mind for example.
@mjambon This in no was dissuades me from wanting to figure out what your thinking of... this is kind of a treasure trove of fun logical/statistical ideas...
Honestly i think you may just be thinking of the term "confirmation bias"?
@freemo @dlakelan mentions "saliency bias". I have to digest all this stuff. My overall impression is that different paradoxes emerge from the way we model things (and go beyond their domain of applicability).
Paradoxes arent paradoxes, a very abused term and more often than not describes **apparent** paradoxes that are a paradox. So saying "paradoxes arise when" is really a kinda pointless thing to say if the word paradox hardly ever means anything consistent :)
@freemo Right, a paradox is usually a misunderstanding. A situation where a heuristic analysis fails but a systematic one reveals the correct answer. A lot of statistics is using formalism to find the consequences of what we know. At least, a lot of Bayesian statistics is that. @mjambon
Yea typically its used to describe a common seemingly obviously true assumption that is wrong, but typically resolvable.
But that is not a "real" or formal definition of a paradox in logic, which would be a **self-contradictory** statement that is neither true nor fase, and is generally non-sensical like "this statement is false" or "I will only speak lies"