Education and Social Mobility in the UK

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The UK Times today has a report on new research into trends in social mobility and the effect of education and social class. The research finds that social mobility declined between 1958 and 1970, and has not improved since then (boo!). But the Times focuses on a peripheral part of the research, which looks at a recent cohort of young children tested on a cognitive ability scale (actually vocabulary) at age 3 and 5. According to the Times article:

The authors said: “Those from the poorest fifth of households, but in the brightest group at age 3, drop from the 88th percentile on cognitive tests at 3 to the 65th percentile at age 5. Those from the richest households who are least able at age 3 move up from the 15th percentile to the 45th percentile by age 5. If this trend continued these children from affluent backgrounds would be likely to overtake the poorer, but initially bright, children in test scores by age 7.”

The article also contains a graph to illustrate this point, which unfortunately is not included in the online version. However, it is evidently based on Figure 4 in the original research report, available as a pdf file here.

Now, take a look at Figure 4, and don’t all shout at once: regression towards the mean! The graph is almost a textbook illustration of what we would expect to find if we took test data from the extremes of two groups with different mean performance and then retested them at a later date.

This doesn’t prove that this is simply a case of regression, but it is an obvious possibility which needs to be examined. As far as I can see (correct me if I am wrong) the authors do not consider it, but it is hard to tell, as the report is written in statisticese, a language only distantly related to English.


  1. A prediction of regression to the mean is that any extremes will regress — that is, taking high-ability, high-SES kids or low-ability, low-SES kids and retesting them should show similar regression. And Fig. 4 shows that this regression does occur, but it’s less pronounced than in the high/low or low/high cases. That’s one control for regression to the mean. 
    A second check I’d like to see is for reliability. It may be that, if you are poor, when you score in the 90th percentile it’s more likely to be by good fortune than raw talent. And vice-versa, with rich kids who score in the 10th percentile being more likely to have just had a bad day. (Please don’t start screaming, this is just being careful.) Such an effect is trivially predicted if the mean test scores of the high-SES are higher than that of the low-SES group. (The reason you expect asymmetric regression is that the pressure to regress, if you want to think of it that way, grows stronger the farther you are from your group’s mean. High-mean-group kids who score low are much farther from their mean than low-mean-group kids who score low, and vice versa, ergo the expected regression depends on which group you start in.) And Figure 1 shows that, indeed, the high-SES group scores substantially higher than the low-SES group. 
    All told, regression to the mean seems a quite plausible explanation for all of Fig. 4.

  2. I wrote to the Sutton Trust, and specifically their main stats researcher, after the publication of a previous report ( 
    UniversityAdmissionsbySchool.pdf) with some significant questions about methodology. The query was neither acknowledged nor answered.  
    Consequently, I am suspicious that they are more of a propaganda outfit than a serious social science research group. At any rate, their press releases seem calculated to stimulate class resentment.

  3. This appears to be a vocabulary test. Do these tests have a lower g loading? It seems to me that young children from a higher SES would have better opportunities to develop their vocabulary.  
    Perhaps these trends might look different once these populations reached secondary school or university, and the bright, but poor individuals began teaching themselves, and the not-so-bright but wealthy were no longer under the tutelage of their parents.

  4. I imagine IQ tests are more reliable for 5-year-olds than for 3-year-olds, so regression toward the green is especially likely to happen in this case.

  5. Couldn’t one also test above-average high-SES children and see how far they regress, if at all? 
    You should also test below-average low-SES children to see if they regress (progress?) to the mean. 
    I’m sure some mathematical models will give expected regression to the mean as a function of the distance of the score from the group mean, in which case you could try to see if regression occurs to different degrees than expected from the random fluctuations in individuals scores that make scores that are far from the mean more likely to be flukes.  
    My take on this is that I don’t think wealth alters g very much. However, if a test is 80% g-loaded, I’m pretty sure the other 20% will favor the wealthy children over the poor children.  
    Having been through private school and public school, my personal experience tells me that wealthy children grow up learning to make up for any deficiencies of natural intelligence with all the fluff and the cultural learning that covers their ass and distinguishes the upper classes from the lower-classes. They tend to read better at younger ages, have larger vocabularies, and more varied life experiences which they can use to compare things and draw analogies, even if their natural intelligence is lower.

  6. Doh! Omnivore made the same point already, so the first part of my post is unnecessary. That said, someone should look up models that can quantify the amount of regression expected as a function of the difference between the mean and the observed value. I would assume their would be a different function for each type of distribution. test scores should probably be distributed normally. Just plug in the variance and the mean, and you should get some numbers.

  7. The figures in the research paper look as if they would be consistent with a test-retest correlation of about .5 
    Another indicator of regression would be to look at the children with highest or lowest performance at age 5 and then trace back their mean performance at age 3. If the trends are purely due to regression, the graphs ‘looking back’ should be roughly a mirror-image of those ‘looking forward’. 
    I may take this up with the researchers, if I can summon up the energy.

  8. It’s always the energy you have to dedicate to random stuff, the researchers should have done this themselves as they were getting paid for it… I’m living out of a hostel in Bali right now, but if I were back home, I would definitely open up a statistics text book and try and look things up. As it is, I have to go surfing and visiting monkey forests, and I’m already a huge dork for hanging out in an internet cafe and posting on gnxp.