# Perils of Generalizing from One's Social Group

I see people make statements of the form, "In my experience with people I encounter, X is correlated with ...".  The problem is, there's an excellent chance that the people they deal with are very unrepresentative of the population they want to generalize about, and I rarely see them show awareness of the possibility that selection bias has created the effect they're describing.

Scott has [written](https://slatestarcodex.com/2014/09/30/i-can-tolerate-anything-except-the-outgroup/) about the strength of social group filter bubbles.  But there's a systematic effect I want to highlight: [Berkson's paradox](https://en.wikipedia.org/wiki/Berkson%27s_paradox).  Following Wikipedia's example:

Suppose that people become famous either by being pretty, or by being talented.  Let's say these are all-or-nothing, binary traits.  Then, *among* the population of famous people, being pretty will be *anticorrelated* with being talented.  If a famous person is pretty, then they might or might not be talented, whereas if they're not pretty, then they *must* be talented—otherwise they wouldn't be famous.  So this anticorrelation between talent and beauty is guaranteed to exist among famous people, no matter how highly correlated they might be among the general population.[^99ay2rf9zc6]

If we use numbers instead of a binary, then we might imagine that talent and beauty scores are numbers from 0 to 10, and we'll say one becomes famous if those scores add to at least 12.  It follows that, if we see a famous guy and observe that his beauty is 10, then his talent could be anything from 2 to 10, but if we see his beauty is 2, then his talent must be 10.  So the selection effect will likely create a big anticorrelation between the two traits.[^t7dulmcduzp]

One can directly apply that model of "popularity ≈ beauty + substance ==> beauty anticorrelates with substance among the popular" to lots of areas.  (In fact, if we treat it like a real equation, we can subtract and get "substance ≈ popularity - beauty".)  For example, if games become popular by having a combination of good graphics and good gameplay, then, if you see a popular game with awful graphics, you know it has great gameplay.  A successful movie that looks ugly probably has a great storyline.  And, as Don Norman tells us, a product that looks like "it probably won a prize \[for aesthetics\]" may still be [horribly unusable](https://www.lesswrong.com/posts/yepKvM5rsvbpix75G/you-don-t-exist-duncan?commentId=BvGfgdBrEzjzxXSZ4).

But the idea applies to any case where you're selecting on one trait that's (approximately) determined by adding up other traits.  The original case Berkson wrote about may be presented thus: you end up in the hospital either by having diabetes, or by having a worse problem like an inflamed gallbladder; and therefore, *among* those who end up in the hospital, having diabetes is correlated with better health, even though diabetes itself obviously causes worse health.[^bokdjqcgcq]

Now let's consider colleges.  They sort by some metric of student impressiveness.  Let's suppose that the biggest determinants of that are intelligence and motivation.  Again, let's give each of them a number from 0 to 10.  Suppose you're at a mid-tier college, where those traits add to 12 for all students.  (The selection effect is stronger here, due to having both a lower cutoff and an upper cutoff.)

Among these students, anyone with an intelligence of 10 must have a motivation of 2; if they had higher motivation, they would be at a higher-tier college.  And anyone with intelligence 2 must have motivation 10; if they had less motivation, they would be at a lower-tier college.  Thus, in this simplified and exaggerated illustration, intelligence and motivation are *perfectly* anticorrelated among students at this college.

More realistically, there won't be an exact number but an accepted band, like "(intelligence + motivation) is between 11 and 13", and the boundaries won't be hard cutoffs but more like "The farther away you are from the accepted band, the higher the probability you'd go elsewhere",[^gr3mri1w9r] which is partly because college acceptance and choice are probabilistic, and partly because there are other impressiveness-affecting traits that aren't perfectly correlated with intelligence or motivation.  Taking these caveats into account weakens the effect, but I expect the result to still be "Intelligence and motivation are significantly anticorrelated among students at this college."

Next, social groups.  I think social circles are significantly grouped by financial success.  If your friend is a billionaire, and you're not, this will tend to create awkwardness and friction; your friendship *may* survive, and sometimes does, but chances are high that it will not.  Lesser versions of this apply at lesser wealth disparities.

It's reasonably common wisdom that intelligence and motivation, again, are some of the biggest contributors to financial success.[^86v8xnuuvq2]  Also, many people met many of their friends in college, so the above stuff about college tiers carries over.  Therefore, *among* your friends, we expect a selection effect that causes intelligence to anticorrelate with motivation, and, generally speaking, both will anticorrelate with other positive factors.

Your smartest friend probably has low executive function, ADHD, etc., because if he was highly motivated then he'd become a zillionaire and ascend to a higher social plane.  Your hardest-working friend probably has chronic health issues and other bad luck, as well as not being particularly smart.  And, for that matter, "bad luck" will correlate with success-promoting traits—otherwise they'd descend to a lower social plane.

All the above can be expected as a simple statistical effect, *completely* independently of what is correlated with what in the general population.  You can easily end up with local correlations that are the *opposite* of the overall pattern.  (Not to mention the difficulty of deducing the right causation from a correlation, viz. "band-aids cause injuries".)

I expect that >90% of people who make generalizations about the associations between certain success-relevant traits and others have failed to realize this.  And I'm not sure how one *could*, in general, "correct for" this selection effect—because, by definition, you don't know who you're excluding from your sample because you don't know them—except by doing a serious representative survey.

[^99ay2rf9zc6]: To illustrate with numbers: 10% of people are pretty and talented, 1% are pretty and not talented, 1% are talented and not pretty, and 88% are the non-famous masses.  Among the whole population, only 1.1% of the non-pretty are talented, while 91% of the pretty are talented—a huge correlation.  Yet, among the famous, 100% of the non-pretty are talented, while the fraction of the pretty who are talented remains 91%. 

[^t7dulmcduzp]: You can come up with very unusual distributions, e.g. where the population consists of a bunch of non-famous people among whom talent and beauty are uncorrelated, and famous people who are all "8, 8" or "9, 9", in which case talent and beauty are actually more correlated among the famous.  In the real world, there are forces that would partly push towards this: fame tends to yield money, which can enable improving one's appearance.  But there exist famous people who don't bother with that, enough that I expect the net selection effect is still an anticorrelation. 

[^bokdjqcgcq]: If this article is to be believed, there are lots of purportedly serious medical researchers who write about apparent protective effects of obesity among certain subpopulations without seeming to realize the possibility of selection bias.  (The abstracted example they give: if hepatitis C and obesity both tend to cause diabetes, and hepatitis C is worse for you than obesity, then that will skew the results towards "obesity correlates with better health among diabetes patients".)This makes me want to execute some kind of hostile takeover of the medical research community.  I should bear in mind that this case is selected for notability—someone bothered to write an article about it, and then I think I saw it because it was upvoted somewhere.  Still, the alleged "obesity paradox" seems to be a thing. 

[^gr3mri1w9r]: Also, one could argue that, at the very top colleges, it's no longer true that "If your motivation were higher, then you'd be at a higher-tier college", because there aren't any.  Though one could counter-argue that such a high-achieving person would likely instead enter that top-tier college at a younger age, and/or drop out to form a startup. 

[^86v8xnuuvq2]: I think it's more like a product than a sum, but the result is similar for our purposes.