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).

#stats #statistics #math #paradox

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

@mjambon

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?

@freemo no, I didn't get the connection with regression to the mean.

@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?