> My favorite example (true in many European countries): most families have a single child, but most kids have siblings.
> you actually are, on the average, in the slower lane, because slow lanes are (on average) the ones that have more vehicles in. So you are more likely to be in these lanes than in the faster moving ones which more vehicles are in.
https://leightonvw.com/2019/04/04/the-slower-lane-paradox-in...
How many cars pass a sign over an hour-long period?
It should be equal to speed (miles/hour) X density (cars/mile) (say that speed and density are constant over the hour)
So more cars in the fast lane will pass that sign than cars in the slow lane will over the hour if speed (fast) / speed (slow) > density (slow) / density (fast)
Also, this relates to renewal theory: https://en.wikipedia.org/wiki/Renewal_theory#Inspection_para...
The Inspection Paradox is Everywhere: a surprising statistical illusion - https://news.ycombinator.com/item?id=20665234 - Aug 2019 (4 comments)
Inspection Paradox (2015) - https://news.ycombinator.com/item?id=18342560 - Oct 2018 (13 comments)
But my complaints about flights being too full is based only on my own experience. I don't think people are upset about airplanes crowdedness because they surveyed a bunch of people and concluded from the survey that airplanes are crowded.
This is still falling prey to the error described in the OP.
Imagine that 99% of all flights were totally empty, and the remaining 1% of flights were completely full. Despite the fact that 99% of all seats are vacant in this scenario, 100% of all flyers will have the experience of being on exclusively packed flights.
(And this was Seattle to Orlando, not some puddle jumper to Bumphuck, Nowhere.)
And you can find more recent posts at his newer blog: https://www.allendowney.com/blog/ where again there are similar links for each month.
---
I'd expect that since this is the usual workplace introduction to the economic value of knowing about the bias it got its name there. A lot of confused people trying to work out why their data makes no sense.
The other fun workplace paradox would be if HR ever tries to be data driven, does some metrics over the engineering department and works out that a degree is inversely correlated with any attempted at measure of skill. Fortunately most HR persons are not interested enough in stats to try that approach.
Expect a negative correlation between certification and competence (in the workplace) because the workplace only reliably excludes people who are incompetent and unqualified. So the population sampled is made up of [qualified, competent], [unqualified, competent] and [qualified, incompetent]. And anyone who isn't ready for that will get very confused when they try to work out how much value a degree adds in their pool of programmers. Or any department, really.
For example, a junior developer is expected to manage implementation details, while a senior developer is expected to manage business logic. Incompetently designed business logic is noticed later, and can often be blamed on trivial implementation failure.
So it's actually useful to have this article that collects many examples of this specific kind of sampling bias (and specific kind of selection bias). I especially like the one on relative speeds:
> when I overtook slower runners, they were usually much slower; and when faster runners passed me, they were usually much faster.
Nope. Turns out that there actually is such a thing as the "inspection paradox" but this ain't it.
https://en.wikipedia.org/wiki/Renewal_theory#Inspection_para...
It's a standard term in the literature (both in stochastic processes and probability more generally); look at the first dozen or so results in books search: https://www.google.com/search?q=%22inspection+paradox%22&udm...
I think that's debatable. The standard definition of the IP is intimately bound to random processes, and there is nothing random about class sizes. So while I do see the similarity, I think that saying that the class-size example is an instance of the IP is at best misleading because it discards an essential feature of the actual IP, namely, randomness.
It might be useful as a pedagogical tool, i.e. "here is an analogous result in a deterministic system" but to say that they are the same is very misleading IMHO.
Here is the relevant quote from the Wikipedia article on renewal theory:
"The resolution of the paradox is that our sampled distribution at time t is size-biased (see sampling bias)"
So the resolution of both "paradoxes" is the same, i.e. they are both examples of sample bias. But that doesn't mean that the problems are the same, or that one is an instance of the other.
This is a misleading conclusion. The data is correct, but the very act of inspecting that data leads to a confounding result.
I think the work "paradox" is imprecise, but it does fit the spirit of the problem well. A layperson may expect that data will draw a useful conclusion. The fact it does not feels paradoxical.
No, there is nothing misleading about it. There are two equally valid conclusions. It depends entirely on what you take to be a data point. If you are asking about average number of students per class, and you have 100 students and 2 classes, do you have 100 data points to consider or 2?
https://www.youtube.com/watch?v=ppX7Qjbe6BM
If you don't have 40 minutes, just pause the video at 15 seconds in and read the screen, you'll get the gist of it. This one is category 3: "counterintuitive fact" or "veridical paradox".