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Comment by lisper | Hacker News Reader

"Inspection paradox" seems like a misnomer. It has nothing to do with inspection and it isn't a paradox. It's just selection bias [1] or more specifically, sampling bias [2]. In the case of class sizes, are you asking the average class size from the point of view of a student (N per class) or a teacher (1 per class)? Take the extreme case where you have one class with 99 students and one class with one student. From the student's point of view, the average class has 98 students. From the teachers' point of view, the average class has 50.

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[1] https://en.wikipedia.org/wiki/Selection_bias

[2] https://en.wikipedia.org/wiki/Sampling_bias

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It is called that because one of the most common places it turns up is managers/inspectors doing routine work. Typically if a manager checks in on their report they'll be stuck doing something that takes a lot longer than usual. If an inspector inspects ... I dunno, widgets, then the widget will typically be unusual because of selection biases.

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.

Could you elaborate more on the inverse correlation between degree and skill? Do you mean that usually people who did not go to university actually went straight to work and had the chance to get more skill as opposed to people with a degree that actually started later?

Simpsons paradox. People without qualifications have to be obviously competent to be hired to do a job. If someone is clueless they probably slipped in because they got certified somehow (like with a degree).

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.

That makes sense, but I would expect this paradox to vanish (or at least get weaker) as you go higher in the hierarchy of technical positions (i.e. from junior to lead, to senior, to principal etc.). I would expect the workplace to somehow naturally get rid of the incompetent people, so that after a certain point you're only left with [qualified, competent] and [unqualified, competent]

When a software engineer gets promoted to a senior role, their responsibility changes to impact a broader timescale. It's entirely possible that promotion is the very thing that masks their incompetence.

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.

One of the best ways to get rid of someone is to recommend them highly to an open position somewhere else. Sometimes a higher level position, or management.

See also: The Peter principle https://en.wikipedia.org/wiki/Peter_principle

It's a veridical paradox, because while it's logically consistent it still runs counter to most people's intuition.

A special case of selection bias is sampling bias (as you said with "specifically"), and the inspection paradox is a special case of selection bias — it is specifically about whether you “inspect” a member of a population or the population as a whole. The article you linked on sampling bias has a list of “types” — https://en.wikipedia.org/w/index.php?title=Sampling_bias&old... — and most of them don't fall under the category of inspection bias/paradox (while the example with class sizes does).

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.

> the inspection paradox is a special case of selection bias

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...

The inspection paradox in renewal theory that you linked (for every t the interval containing t is on average larger than the average interval) is an instance of the inspection paradox described in the article (the mean seen by a random observer can be very different from the true mean). Bus/train waiting times are in fact the third example in the article.

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...

> The inspection paradox in renewal theory that you linked ... is an instance of the inspection paradox described in the article

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.

Selection bias is something slightly different. This isn't a bias.

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.

> This is a misleading conclusion.

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?

Just because something isn't a logical paradox doesn't mean it shouldn't be allowed to be called a paradox...it can also just mean "apparently self-contradictory"

If you have 40 minutes to spare, jan Misali's video on paradoxes is a good breakdown of the many different things that we call paradoxes:

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".

It is very often used to mean simply "contradicts what seemed intuitive to me".

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