# gjm comments on How my school gamed the stats

• It’s certainly possible that I’m underestimating the level of privilege here. But I guarantee that the area is not at all “the very upper part of the upper middle class”. In particular, I know a lot of the parents-with-PhDs, and I’m pretty sure none of us is upper-upper-middle-class by any reasonable definition. To whatever extent the school sounds startlingly privileged rather than merely distinctly more than averagely privileged, I think it’s more likely that my estimates of the parents are skewed than that the school is really super-duper-elite. (For instance: I’m an academic sort of person, the people I know will tend to be academic sorts of people, and so it would be very unsurprising if I overestimated how many parents have PhDs. Also, I am consistently trying to overestimate rather than underestimate, because I want to be honest about the fact that this school is serving a pretty “good” population.)

I don’t think I agree with your second paragraph. I have a super-handwavy model in my head according to which populations like “Cambridge graduates”, while of course both well-educated and high-status, are less high-status than you would expect from e.g. seeing where they sit in the distribution of education and assuming they’re in the same place in the distribution of social status. Let me try to make it a bit more concrete and see whether I still disagree with you.

Effect #1: education and status are correlated but not at all the same thing. Toy model: status = education + otherstuff, both are uniform(0,1). If status ⇐ 1 then status quantile = status^2/​2; if status >= 1 then status quantile = 1 - (2-status)^2/​2. If your education quantile (= your education) is 0.9 then your status is uniform between 0.9 and 1.9, so your average status quantile is (if I’ve got the calculations right) about 0.78. If your education quantile is 0.97 then your average status quantile is about 0.82. High, but not that high.

Effect #2: when you condition on somewhat extreme values of one variable, its correlations with other correlated variables tend to go away. Toy model: same as above. If I’ve done my calculations right, the (Pearson) correlation coefficient between education and status in the whole population is 1/​sqrt(2); in the population with education >= 0.9 it’s 1/​sqrt(101).

Effect #3 (I’m much less sure about this one): education and status are correlated because of a bunch of causal links (e->s, s->e, other->{e,s}), and in a population like the Cambridge-area one you get more people who are highly educated for less-status-linked reasons. I won’t bother with a toy model because it’s obvious how this works, and the questionable bit is whether I’m right about the local population. I’m not at all sure I am.

Effect #4: while education and status correlate, I’m not so sure even of the sign of the correlation at the extremes. Very able people with ambitions that aren’t strictly academic don’t (I think) usually do PhDs. I wouldn’t be surprised to find that wealth and status are higher on average for people whose academic performance would have got them a PhD place if they’d wanted one but who preferred to do something else, than for people who actually did a PhD. I wouldn’t be surprised to find it the other way around, either.

• I’d agree with most of your models, and agree that there is divergence at the extremes of a distribution—but that’s at the very extremes, and usually doesn’t lead to strong anti-correlation even in the extreme tails.

But I think we’re better off being more concrete. I don’t know where you live, but I suspect that your postal code is around the 90% income percentile, after housing costs—a prediction which you can check easily. And that implies that the tails for income and education are still pretty well correlated at only the 97th percentile for education—and implying the same about status more generally. (Or perhaps you think the people who attend the school are significantly less rich than the average in the area?)

• I checked. Annoyingly, the tool you linked to only tells you which 10%-sized block of percentiles the area is in. It says 70-80 before, and 80-90 after, adjusting for housing costs. (If you’re trying to measure social status, upper-middle-class-ness, etc., then I claim you should actually use the figures before adjusting for housing costs.)

That’s the village where I live and where the school is located, but it takes pupils from other places too; the neighbouring village that I think provides the largest number of other pupils is in the 70-80 percentile by both metrics.

The same page has a thing that gives finer-grained percentiles but only for the before-housing-costs figure (which, again, I think is actually the more relevant here). My village gets about 82%, the other one I mentioned gets about 78%.

I think all of this exactly matches my original description: very nice middle-class area but not “the very upper part of the upper middle class”.

I’m not sure exactly what you mean by “still pretty well correlated”; 97% on one → 90% on the other isn’t so different from what my toy model says, and 97% on one → ~80% on the other (which I think is better supported by the evidence) is pretty much exactly what my toy model says.

• That’s fair—thanks for checking, and I’d agree that that would better match “very nice middle-class area” than my assertion. (In the US, the top 2-3% is usually considered upper class, while the next 15-20% are upper middle class, and the next ~25% are “lower middle class.” This income level definitely puts your neighborhood in the middle of the upper middle class.)

• Some other relevant numbers: mean household income in my village (and the area around it that’s part of the same area, as used by that tool) is about £36k before, and about £33k after, the cost-of-living adjustment. Those are means; presumably the median is lower.

Again, that makes it a better-off-than-average area, but note that £36k is not by any reasonable standard a middle-upper-middle-class household income. So yes, this is definitely a nice area, but no, it’s not the case that everyone here is very well off or very high-status.

• Wait, the claim was never that everyone is well off—of course we expect there to be a distribution. But if a sizeable portion of the children at the school largely have very high-socioeconomic-status parents, even if it’s only 10% of the parents, that should be compared to a median of plausibly less than 1% of parents in the set of schools overall, it would be incorrect to infer that the way the school is run can be usefully compared to the “average” school.

• I said the school was “in a nice middle-class area”. You replied (way way back upthread):

Note that only around 3% of UK residents have PhDs—so I strongly suspect that what you’re calling “middle-class” is closer to the top 5% of the population, or what sociologists would say is the very upper part of the upper middle class.

Which only makes sense to me if it’s saying that what I described as middle-class is actually “the very upper part of the upper middle class”, and what I described as middle-class is not “the best-off parents of pupils at the school” but the area the school was in. (For greater precision I should really have been talking about the people at the school rather than the area as such, but I take it that was always understood, and in fact I think the school’s pupils are pretty representative of its catchment area.)

And of course I agree that the school isn’t average. That’s why I said, way back in my original comment,

It’s in a nice middle-class area with, e.g., quite a substantial fraction of parents having PhDs, and she’s one of the most able students, all of which of course makes it more likely that the school has an easier time of it and that what she sees doesn’t include the worst the school has to offer. But then you said that your school was in a nice middle-class area and you were mostly in top classes, so the two seem broadly comparable.

Emphasis added here to make it absolutely clear that right at the outset I explicitly noted the things you’re now suggesting I was somehow trying to hide or deny. Note the last sentence: I wasn’t responding to a report about the failings of an average school by saying “but my nice middle-class school is different”, I was responding to a report about the failings of a nice middle-class school by saying “but my nice middle-class school seems to be different from your nice middle-class school”.

I also want to push back a bit again about “the middle of the upper middle class” and “very high-socioeconomic-status parents”. I think it is flatly untrue that the area I’m in is “in the middle of the upper middle class” by either UK or US definitions, and I think it’s at best debatable whether “a sizeable portion of the children at the school largely have very high-socioeconomic-status parents”. Let me quote you some bits of Wikipedia, as indicative of typical usage of the term “upper middle class”.

The upper middle-class are traditionally educated at independent schools, preferably one of the “major” or “minor” “public schools” which themselves often have pedigrees going back for hundreds of years and charge fees of as much as £33,000 per year per pupil (as of 2014).

Very few people in the village where I live send their children to public schools, or even to other independent schools. (And obviously the parents of children at my daughter’s school don’t.)

Although such categorisations are not precise, popular contemporary examples of upper-middle-class people may include Boris Johnson, Catherine, Duchess of Cambridge, David Cameron, and Matthew Pinsent (athlete).

I don’t know anything much about Matthew Pinsent, but again: if there’s anyone here in the same social class as Boris Johnson, David Cameron, or the Duchess of Cambridge, it’s news to me. Maybe there are some lurking somewhere (though I doubt it), but the idea that those could be typical of the population around here is absurd.

What about US notions of the upper middle class? They don’t fit much better. Social class in the US is more about money than it is in the UK. Here’s Wikipedia again:

Sociologists Dennis Gilbert, William Thompson and Joseph Hickey estimate the upper middle class to constitute roughly 15% of the population. [...] In 2020, the threshold for entering the top 15% of American household incomes is \$166,000

I’m sure there are people around here whose annual household income is over \$166k, but they’re a small minority. (I think my family is one of the better-off ones around here; our household income is comfortably below \$166k.)

So: no, our neighbourhood is pretty comfortably off, but it’s not anywhere near “the middle of the upper middle class” whether you mean the British or the US upper middle class. (It would be near the bottom of the upper middle class, if you translated the “top 15%” criterion from the US to the UK, but note that that gives you a group of people markedly less elevated than either the people called “upper middle class” in the UK or the people called “upper middle class” in the US.)

As for “very high-socioeconomic-status parents”: I guess it depends on what you mean by “very high”. This is an area rich in engineers (broadly defined), who tend to be higher in income than in social status (i.e., if you pick a bunch of people earning say a very comfortable £100k/​year, there’ll be engineers and doctors and lawyers and quants and senior managers and the like, and the engineers will on the whole be the lowest-status of them). And, while I don’t know anyone’s income other than my own, my impression is that e.g. the fraction earning over ~£80k/​year, which according to the UK government’s tables is about the 95th percentile, is not much bigger than 5%. In fact, my best guess is that it’s somewhat below 5%. But let’s suppose that fully 10% of the parents at my daughter’s school are top-5% -- which, again, I bet is not true. Is that “very high”? I personally wouldn’t say so, any in any event I don’t think “maaaaybe as many as 10% of the parents are top-5%” is a stronger statement than the one I already made at the very outset about this being a nice middle-class school where quite a few parents have PhDs.

(I’m aware that the tone of this comment is a bit defensive. I’m sorry if that makes it disagreeable to read. For what it’s worth, the way it feels to me right now is that I have gone out of my way to be honest about ways in which the experience I’m reporting may not be representative, and have been met with Isolated Demands For Rigor and implications that I have a wildly inaccurate idea of my own level of privilege and that of others around me, and that even after the person making these accusations has made a concrete prediction that turned out to be wrong while mine was spot-on there’s still this constant suggestion that surely I’m trying to mislead everyone about how nice-and-middle-class my area is, and it’s a little bit tiring.)

• First, I apologize. I really didn’t intend for the tone to be attacking, and I am sorry that was how it sounded. I certainly wasn’t intentionally “suggesting [you were] somehow trying to hide or deny” any of the issues. I thought it was worth noting that the initial characterization was plausibly misleading, given that the sole indicator of being a “nice middle class area” seemed to be percentage of people with PhDs. Your defense was that it was no more than 3x the number of PhDs, but that doesn’t mean top 13, a point which you later agreed to. And after further discussion, I made and you checked an object level prediction I made, so I ceded the point.

Despite ceding the main earlier point, I continued the discussion, since I think the terms and definitions have gotten very confused by citing various incompatible sources and citing isolated sections of articles. And the same way that I have picked specific things to focus on responding to, you have picked many things I have said which you ignore. That’s fine—but my responses were not an isolated demand for rigor; I have made concrete claims and acknowledged those which were refuted, and you have raised points which I have responded to.

So again, I am not disputing your neighborhood, which I conceded I initially thought was more affluent than it is. Despite that, there is plenty you have now said characterizing classes, in responses, which I think should be clarified if you want to continue. Again, this doesn’t reflect on your earlier claim about you child’s school, but your defense of the position has been confusing to me, at least. For example, you compare \$166,000/​year in the US, which is the top 15% there, to incomes in your neighborhood—then note that £80k (i.e. \$110k) in the UK is the top 5%. You don’t say anything about the equivalent income in the UK. I again agree that your neighborhood is not in the top 15%, but the top 15% there in the UK is £46k. (not \$166k, i.e. £118k) The actual average income in your area, £36k, is in the top 25%. (I would suspect the incomes for those with children in the area is higher, but again, not near the top of upper middle class) Finally, the specific examples of upper middle class that you cite—Cameron, etc. are discussing their family backgrounds, not their current status.

• I don’t actively “want to continue”, in that it seems to me that the whole content of this discussion is you saying or implying that I’ve badly misrepresented how affluent my area is, and me pointing out in various ways that that isn’t so.

However, your last paragraph seems once again like an accusation of inconsistency, so let me clarify.

“Upper middle class” means different things in different places. In the US, “class” is largely (but not wholly) about wealth. In the UK, “class” is largely (but not wholly) about social background. These are less different than that makes them sound because the relevant differences in social background are mostly driven by the wealth of one’s forebears, and in both societies there is a strong correlation between that and one’s own wealth.

The US has a more wealth-based notion of class and is also richer. So being “upper middle class” in the US means a level of wealth that would make you quite rich in the UK.

The UK has a more social-background-based notion of class, which in particular is strongly influenced by the existence of a (statistically very small) aristocratic class. So “upper class” in the UK means a smaller, more-elite fraction of the population than in the US, and “upper middle class” is pulled in the same direction. So being “upper middle class” in the UK typically (but not always, because of the wealth/​background distinction) means being at a distinctly higher percentile of wealth than it does in the US.

The combined effect of these things is to put the typical “upper middle class” person or family at something like the same level of wealth in the two countries, although there’s plenty of fuzziness and variability.

(Perhaps I have by now made it clear that I do have some idea how social class works in the UK, enough so that you might believe me if I tell you that (1) I am definitely lower-upper-middle-class and (2) my household income is somewhere around the 95th percentile.)

So, issue 1 is that you’re wanting to call my neighbourhood “upper middle class” even though the people here don’t fit either the UK or the US notion of “upper middle class”, because you think it matches the definition you’d get if you applied the US-based notion directly to the UK despite the substantial differences between the two societies.

This would be (annoying but) excusable given that your main point was to suggest that my daughter’s school may be more atypical than I was claiming. But there’s more.

That percentile-ranking tool is not ranking individuals, it is ranking areas of the country. Areas vary less than individuals do, and (e.g.) an 80th-percentile area is not composed mostly of 80th-percentile individuals. On the other hand, terms like “upper middle class” are descriptions of individuals and families, and only secondarily of areas. If calling an area “upper middle class” (or “upper class”, or whatever) means anything, it should mean an area whose people are mostly of the class in question.

Almost no areas are “upper class” or even “upper middle class”.

(Perhaps an analogy may help. Suppose you have an area where the Jewish population is at the 95th percentile of areas in the country. Would you call it “very Jewish”? You probably shouldn’t, because I bet that 95th-percentile population is still <5%. I submit that “upper middle class” is like “Jewish” in this respect.)

In a typical 80th-percentile area, most people are middle-middle-class. That’s unusual; in a more typical area a large fraction will be lower on the socioeconomic scale. How might you describe such an area? Well, maybe as a “nice middle-class area”, for instance. Which happens to be exactly the term I used.

“But £36k is distinctly higher than a typical middle-middle-class salary in the UK.” It’s not all that much higher; median UK household income is £30k. Second, the £36k figure is a mean, not a median. Mean incomes are always higher than median incomes. UK mean household income turns out to be about £37k, if I’ve done my calculations correctly. Both the area mean of ~£36k and the national mean of ~£37k are described as “equivalised” and I don’t know whether that means the same thing in both cases, but the point is that this area is in fact about as well-off as the UK as a whole. No contradiction with the 80th-percentile thing; most areas are (when you calculate in terms of means) a bit poorer than average and a few are substantially richer.

So, issue 2 is that you’re taking terms that describe individuals and applying them to areas in a profoundly misleading way. You can call an 80th-percentile individual “upper middle class” if you like, though actually most classifications wouldn’t call them that either in the UK or in the US; but an 80th-percentile area is still not an “upper middle class” area. That’s not how the words work.)

• Sorry, this is clearly much more confrontational than I intended.