Regression to the Mean

An impressively clear explanation of an all too often misunderstood concept. Perhaps the single least appreciated aspect of this effect is that it does not imply that children are doomed to be more mediocre than their parents on any given variable: to be precise, the mean towards which regression occurs is that of the generation under measurement, not that of the parents, and it can therefore actually rise between successive generations. One would think this would be obvious to most people, but it clearly isn't, especially in the field of psychometrics.

Comments

[Frank McGahon]

"One would think this would be obvious to most people, but it clearly isn't, especially in the field of psychometrics."

Amen to that. Another problem with how regression to the mean is abused at the likes of gnxp is that it facilitates begging the question. I seem to remember David B. making a suggestion to the effect that African immigrants to the UK might be of higher IQ but their children "regressed to the lower African mean" which rather assumed that the property of "african-ness" was more relevant than the property of being-the-offspring-of-parents-X&Y or the property of growing-up-in-the-uk-in-generation-a. As you note, the statistical relationship has to be there in the first place - the group being measured. You can't just pluck a "mean" of some other group out of the air and assert that it applies.

[Abiola Lapite]

A very good point! Putting aside the question of whether the concept of an "African mean" even makes sense, there simply is no justification for assuming that the children of African immigrants will approach the performance of those growing up in Africa, despite having the benefit of a European environment themselves; the hidden assumption is that they just don't have the stuff to benefit from improved circumstances.

[Frank McGahon]

Here's another thing that bugs me about "h-bd" and regression to the mean: If their position is that groups have differing mean innate "ability" (leaving aside the questionable assumption that such a thing as innate ability actually exists) there are actually two contradictory corrollaries to this. 1) Hereditarianism - "ability" is largely inherited and groups differ as to the frequency of those with the "good genes" and 2) Non-hereditarianism - the group displays a similar range of abilities but "ability" comes from a general group gene and is shuffled randomly for each generation rather than directly inherited. Regression to the mean is consistent with non-hereditarianism rather than hereditarianism. If I inherit my "smart-guy genes" from my parents, it really doesn't matter what is the mean of any group to which I am assigned. Yet, you will find that if a hereditarian argument makes Blacks look bad and Asians good, it is evoked. If it doesn't then there's a seamless seque into regression to the mean non-hereditarianism without any apparent awareness of the contradiction.

[David B]

Perhaps before critising me people would take the precaution of checking what I actually said. I did *not* refer to the children of African immigrants in the UK "regressing to the lower African mean", and so far as I recall I have never used this term.

I did note that the children of African immigrants appeared to do less well academically, relative to other ethnic groups in the UK (such as Bangladeshis), than their parents, and speculated on three possible reasons for this, one of which was clearly 'environmental', namely that 'the younger cohort of Black Africans [may] have assimilated some of the habits and values of the White British and Black Caribbean groups in their localities (predominantly inner cities)'.

I did indeed also point out that older cohorts of African immigrants were a selected group, and that their children might show 'regression to the mean', but did not say an 'African' mean. For a variety of genetic and environmental reasons the correlation between academic performance of parents and children is far from perfect, so regression to the mean (some mean!) is to be expected.

With hindsight, I did not notice another possible explanation, namely that there have been large and rapid shifts in the composition of the African immigrant population in the UK, so that the present cohort of children may not be comparable (e.g. in country of origin) to older cohorts.

[David B]

...and I suppose before pressing the 'post' button I should check for typos! Of course I meant to say 'criticising'.

[Frank McGahon]

"that older cohorts of African immigrants were a selected group, and that their children might show 'regression to the mean'"

I grant that you didn't use the specific term "lower African mean" (I couldn't remember where the comment was and was working off memory) but this is precisely the same fallacy. The assumption is that the older cohorts were somehow exceptional freaks and heritability goes right out the window when it comes to their children - an assumption which never seems to apply to discussions* of, say, higher IQ immigrants from South Asia where regression to the mean goes out the window, in comes heritability and this IQ is assumed to be "banked" for the next generation. If you are going to posit group differences in "innate ability", either "ability" is heritable from one's parents, in which case regression to the mean makes no sense at all** or it derives from some group characteristic, you can't have it both ways.

* my criticisms of the (neo-)racist misuse/misunderstanding of regression to the mean at gnxp isn't really about your specific piece but more the ignorant rubbish which pops up in the comments - I remember one gobshite suggesting that it would be rational for an employer to reject a prospective Black job applicant who IQ-tested at 110 in favour of a White applicant at 90 because "regression to the mean" meant that the Black guy's "real" IQ was much closer to 85 while the White guy's "real" IQ was closer to 100. This quandary was unlikely to present itself at any stage to this not-exactly-management-material ignoramus.

** you were, after all, talking about a mean - the mean of the group of children and not individual specific cases - how can a mean regress to another mean?

[Michael Stastny]

Here is an even better explanation:

http://the-idea-shop.com/article/43/guest-post-galtons-fallacy

[David B]

First, on the subject of "Galton's Fallacy", it isn't clear what the originator of this term (Danny Quah) meant by it, but it is reasonably clear that Galton didn't commit it! See my lengthy post on the subject at www.gnxp.com/MT2/archives/003273.html

On Frank's point, there are two things wrong with the statement "The assumption is that the older cohorts were somehow exceptional freaks and heritability goes right out the window when it comes to their children".

First, the assumption is not that the older cohorts were 'exceptional freaks', but merely that they were better educated and qualified than the average of their peers (I'll come back to the question which is the relevant group for comparison).

Second, I don't claim that 'heritability goes out of the window', just that heritability is less than perfect. Children *resemble* their parents, for reasons of both nature and nurture, but they are not *identical* to them. 'Regression to the mean' in academic achievement between parents and offspring occurs because some of the factors influenceing achievement are common between them, and some are not. Those that are *not* will, on average, be closer to the mean of the relevant group. This applies to both genetic and environmental factors, since not all genetic factors 'breed true', due to dominance and epistasis.

On the question of the 'relevant group', in the present case this is a tricky point. We are concerned with immigrants to the UK from various African countries, who are probably 'selected' (in terms of IQ, SES and education) relative both to the African countries and to the UK norm. (The starting point of my original post on the subject at gnxp was to note that in UK Census data African immigrants were on average much better qualified than 'White British'.) So it could be argued that the relevant 'mean' towards which we would expect the children of African immigrants to regress is either the mean of British children or the mean of African children in the countries of origin - or possibly some subset thereof, such as 'urban middle-class African children'. (Note that in either case it is the mean of their *own* cohort towards which they regress.) I really haven't thought this issue through, and don't wish to take a position on it now.

Anyway, for the record, let me state again (as I have frequently done on gnxp), I do not claim to know whether differences in mean IQ results between different ethnic or national groups have any genetic basis. The reported differences between different nations (e.g. as claimed in Lynn and Vanhanen's book) are within the range that we know *could* be due to environmental differences. Moreover, the differences are closely correlated with indicators of economic development such as GDP per head and infant mortality. So I think it is quite plausible that the differences in IQ are largely or wholly due to environmental rather than genetic factors. Please don't assume that everyone who posts on gnxp is a strict hereditarian.

[Pearsall Helms]

With hindsight, I did not notice another possible explanation, namely that there have been large and rapid shifts in the composition of the African immigrant population in the UK, so that the present cohort of children may not be comparable (e.g. in country of origin) to older cohorts.

I meant to ask you this on your post at GNXP, but have you seen any way to break out black African school achievements in the UK by country of origin or by religion? By this, I'd guess that the black African Muslim population of the UK is heavily Somali, and as far as I've read before I get the impression that Somalis do not do as well economically or scholastically as Nigerians or Ghanaians (and their British-born children) do.

[David B]

Pearsall: I don't know of any data on the point you ask about. The data published by the Education Department don't give any breakdown finer than 'Black African', 'Black Caribbean' and 'Black Other'. Indeed, I'm surprised they go as far as this: after years of publishing nothing at all on ethnic performance, all of a sudden (since 2000) there is a plethora of information!

On Somalis, do bear in mind that most of them are *very* recent immigrants. Often the children themselves are 1st generation, so there is a language deficit to overcome. (The BBC reporter Rageh Omar is a Somali, and *he* seems to be doing OK, but I don't know his background. Not all Somalis are goatherds!)