If half of an airline's flights are full and half are empty, passengers will complain that the flights are full every time, contrasting with the assessment of the crew who report that half of the flights are empty. How do you call this effect/paradox? (I forgot)

The same effect explains that if you have an average number of friends (= popularity), more than half of your friends are more popular than you.

Or when your doctor tells you you're in average physical condition but each time you go cycling, most cyclists you come across are faster than you (because the fast cyclists are also the ones who spend the most time on the roads and are encountered disproportionately).

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@mjambon You are describing quite a few things.. namely survivorship bias, and regression to the mean are most notable.


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.

@mjambon Is it obvious why i mentioned regression to the mean, or should i elaborate on that?

@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.

Make sense now?


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.

@freemo I skimmed the Wikipedia article about representativeness heuristic. Seems to connect to the notion I had of stereotypes vs. averages.

@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.

@freemo the original example was a "clever" post by a shitposting page on Facebook, something like this:

"It's not possible that every time we call your customer service you're experiencing a higher amount of calls than usual".

@freemo i.e. not something I need for urgent or professional purposes ๐Ÿ™‚

@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"?

@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 :)


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.


I actually responded to this out of thread.

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"


@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 this seems more like a social element than a statistical one.. but yea i get that.

Another concept here is "saliency bias" basically people focus on things that they notice and not things that seem normal. So the passengers find the crowdedness salient, because they kind of don't think about it when the plane is half full... Whereas the workers find it abnormal when there are very few people. In addition to there being more passengers who experience crowded conditions.

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