Wednesday 16 October 2013

Heritability estimates and the analysis of variance


This is a note about heritability estimates and the analysis of variance, but if you want the inessential background, Dominic Cummings has published a book in The Guardian  newspaper in which, among many things, he mentions the work of Robert Plomin showing a heritability estimate of 70% for scholastic attainment.

You can read about Plomin’s most recent work on this very blog:

Steve Jones then wrote about heritability estimates in The Daily Telegraph newspaper:

Dominic Cummings then replied:

Triggered by this current debate, I am writing a very short note to cover matters partly raised by Steve Jones which I think need some amplification. The analysis of variance depends upon the setting. If we look at scholastic achievement in present-day Britain, then Plomin’s paper shows that heritability estimates run as high as 68% of the variance. However, if on that basis we were to close all publicly funded schools, in the next decades it is likely (though not certain) that heritability estimates for scholastic attainment would decrease, because there would be an increase in the deleterious effects of the environment. It would move from being almost uniformly good or good enough, to being very heterogenous: some kids would get superb schooling and many would get none at all. In terms that R.A.Fisher might have used, if you plant different strains of wheat in uniformly well ploughed, well mixed, well fertilised soil, then the differences between the different strains will be due to their inherent qualities, and not the vagaries of the soil. On the other hand, if the soil varies considerably then the yields will vary partly because of seed quality, and partly because of soil quality. The experimental method allows us to tease out these possible sources of difference by comparing the variance between strains with the variance within strains. The results will depend on the strains tested, the soils planted, and crucially whether we look at one harvest or a whole series of harvests. Long series data are generally the most informative.

If we look at the variance between one decade and another, say the 1950s versus present time Britain we would begin to capture some of the cultural and educational changes over those sixty years. (It would depend on our having historically sound measures of attainment, not always easy to obtain). That might show great historical improvements in scholastic attainment, which would count as an environmental effect. For example, increasing access to tertiary education should have a positive effect on student knowledge and abilities. It may also be subject to the laws of diminishing returns.

A further complication is that the analysis of variance does not immediately pick up and display comparative means. It is just a ratio, after all. For example, if British school children have really become much more accomplished than their grandparents one needs to look at the means over that time period in order to determine that. (The OECD study suggests no difference, see previous post).

It might help if I were to draw all this in a diagram but for the time being I will stick to the medium of words. Earl Hunt goes into the statistics of this matter in his book “Human Intelligence” showing that in the nature/nurture debates about adoption studies some writers look at the gains in the means of intelligence (which do exist), and others look at the correlations between parental and child intelligence (which are substantial). Properly, we should look at both. We need to be scholars, not lawyers, as Hunt tartly observes.

To take another example, height is heritable and also influenced by diet in the longer term. Heights have increased in wealthy Europe over the last 60 years, and it is also still true that some European people are taller than others despite diets now being good throughout Europe. We have to be able to think about two things at once. The Dutch are the tallest nation, which is just as well, poor things. Their heads are at sea level, their feet on vulnerable reclaimed soil.

The analysis of variance depends on the context and historical setting. For example, the Dutch famine in 1944/5 had health effects on children born at the time, but not on their intelligence. It may not have lasted for long enough (for experimental purposes, that is, it was certainly too long for the victims). So, the longer term picture does not always show the environmental effects one expects, but one should always look for them. Usually, bad environments have big effects, but once the environment is OK if not spectacular, heredity estimates tend to be high. Contrariwise, Flynn effects are continuing in some rich countries in the present day, so if they are due to nutrition then that is a bit odd, because nutrition was at a good standard within a few years of the end of the war. The special issue of Intelligence on the Flynn Effect will be available in December.

I am still reading Dominic Cummings’s book (which is full of lots of interesting stuff) but I doubt he really thinks that heritability estimates imply that we can ignore schools. What I have read so far is to the contrary: he wants to improve schools by making them use better techniques and stay open for more of the year. It doesn’t sound like he is ignoring the environment at all. He wants to improve public education and encourage excellence in teaching.

Looking ahead, if we manage to build a culture which provides uniformly excellent public education, with good nutrition and good standards of living for all, then heritability estimates might be even higher than 68%. Environmental variance will be reduced, and as long as the benign provision of excellent eduation lasts it will fall out of the equation, only to come back again when the supply of social support fails. On the bright side, while the Nirvana lasts, students may even learn the analysis of variance.


  1. I remember that I used to be able to do an ANOVA but I couldn't do one now without opening a book (or mindlessly using a program). There must be the possibility of a recursive study of intelligence here.

  2. good points, all around. if we could make environment uniform (!) then the only reason for people to differ would be due to genes.

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