Monday 20 May 2013

Give me a child until he is seven, and I will give you the man

 (This nostrum, attributed to St. Francis Xavier, also works for girls and women, though separate equations are required, because of interrupted careers).

In popular culture, in academic debate, and in the nitty-gritty of medico-legal battles about the bright future which might otherwise have been enjoyed by a damaged child seeking compensation, there is much interest in what one can predict about a person’s future given knowledge of their social class, circumstances, school performance and intelligence at age 7. In medieval times it was only at age 7 that it seemed pragmatic to recognise that the infant had survived the very high early life death rates, and could be welcomed as a human being. In these gentler times parents have no compunction about photographing their infant, secure its survival. It is not bad luck to register, name, photograph, film, record and display the vulnerable neonate to the world.

A recent study has added some evidence to these discussions, finding that maths and reading make an additional contribution to later success in life, over and above the general factor of intelligence. Stuart Ritchie and Tim Bates have written an elegant paper in Psychological Science “Enduring Links from Childhood Mathematics and Reading Achievement to Adult Socioeconomic Status”.

Using the population born in a single week in 1958 (National Child Development Study data held by Institute of Education, and in my view “gold dust” for proper research) they got the data on social class of origin, maths, reading, intelligence, academic motivation, duration of education and attained social class.
In a nutshell, the effects of mathematics and reading achievement at age 7 have an effect on attained Socio-Economic-Status by age 42. Mathematics and reading ability both had substantial positive associations with adult SES, above and beyond the effects of SES at birth, and with other important factors, such as intelligence. Achievement in mathematics and reading was also significantly associated with intelligence scores, academic motivation, and duration of education. These findings suggest effects of improved early mathematics and reading on SES attainment across the life span.

Of course, readers of this blog will know the standard lament by now: many causes interact with each other, and teasing them apart is difficult, but not impossible.  For example, in the original study the social class of origin of the children was noted, but the intelligence of the parents was not measured. So, we cannot assume the “influence of social class” is from social class advantage per se. It will be a blend of material advantage and genetic advantage, of unknown proportions.  The explanatory model probably should say “a class and genetic mixture”.

In ancient times the data would be presented in terms of means, standard deviations, a correlation matrix, and then perhaps a multiple regression equation. A useful and familiar progression, but not without interpretive problems. Ritchie and Bates are made of brighter stuff, and use a OpenMX magic box to generate there structured equations.

Personally, I approach structured equation modelling with some trepidation, fearing a magic lantern show which will convince me of anything, but Tim Bates thunders: “SEM exposes all assumptions, claims, and lacuna ruthlessly: it should be ubiquitous.” The (complicated story) is shown in their Figure 2, which traces direct and indirect coefficients on final achieved social status. From this it is possible to argue that, although intelligence has a strong causal effect, there is an additional direct contribution from Maths, with a lower direct effect from Reading. Nonetheless, there is a case for improving the teaching of these skills so as to make an independent additional contribution to life successes. Intelligence leads to motivation, which leads to years in education, which leads to attained socio-economic status. The latter leads into log income at the very end, which may be a relief to those who value cash over social approval.

A few points: once you put in social class of origin and housing tenure, the number of rooms in the parental home has no effect. All other things being equal, the “bedroom tax” is unlikely to diminish social mobility in a generation’s time.

I should like to have been able to give you a much more detailed statistical analysis but I was not taught maths properly when I was seven. At about that age, or slightly older, I announced to my grandfather, an Edinburgh engineer: “I know my12 times table”.  He looked at me with a dour expression, and replied: “When I was a wee lad I knew my 20 times table”.

Edinburgh has much to answer for.


  1. "Lacunae" is the plural.

  2. 20 times table - pah, that's too easy; we did the fourteen and sixteen times tables, though. Not much point now that we've swapped to kilos. I wonder whether anyone ever did the 22 times table.

  3. I meant, tables up to 20 times table. They were nothing if not thorough.

  4. From John Derbyshire:
    Item: The story goes that when P.T. Barnum told his assistant that there's a sucker born every minute, the assistant responded: "OK, but where do all the others come from?"

  5. There's something about those seven year units...

  6. Aw come on, Bruce, everyone knows that the natural unit is 2*pi. Why settle for a crude approximation?