Never march on Moscow, not in winter anyway

 

A reader requests a classic map by Minard, popularized by Tufte, depicting the overleaping ambition of a grand campaign on a continental scale, showing how the thick river of Napoleon’s soldiers set out to conquer Russia, their numbers thinning as they finally reached their prize at Moscow, and then the diminished and rapidly shrunken rivulet of survivors making their pitiful way home, gathering one bunch of auxiliary troops who had been left behind to protect their way, only to perish in a particularly badly handled Berezina river crossing. Not only is the army size shown sequentially in time and space, but the crucial impact of the falling temperatures during the retreat are coldly laid out to make their mute case.

Tufte says: “it may well be the best statistical graphic ever drawn”.  It certainly sets a benchmark for contemporary statisticians to strive to attain. Are there any current figures which match this one for economy and dramatic impact?

 

 

Visualising sex differences, Emil and Tufte

 

 

 

Edward R. Tufte’s “The Visual Display of Quantitative Information” is a well-known delight which, once read, will make you see informative displays in a new and clearer light. It was in Tufte’s book that I came across his championing of “the typographical delight of the statistician W.J. Youden whose illustration of the normal curve I reproduce above.

I had Tufte’s insights in mind when working on the original depiction of sex differences in the distribution of intelligence.

https://drjamesthompson.blogspot.co.uk/2013/09/are-girls-too-normal-sex-differences-in.htm

The Gaussian distribution, or standard normal curve, or Bell Curve, never ceases to amaze. The shape is plain to see, but the area under the normal curve is hard to estimate by  eye, hence the need for visualizers with area calculations attached.

What prompts these reflections? No sooner did I post about the visualisation of sex differences than a sharp eyed Danish commentator shot back with a good suggestion, which I have incorporated immediately.

http://emilkirkegaard.dk/understanding_statistics/?app=tail_effects

To recap: Suppose someone was to do a study on adults, not children, and test the intelligence of these adults while also having done brain scans so that we can calculate the link between the brains and mental abilities. If such a study were to show a 4 IQ point male advantage, and the sd of male intelligence is, say 15 and the female sd closer to 14, what would the distributions of male and female intelligence look like at the higher ends of the ability scale?

If we use Emil’s visualizer and put in mean=104 (sd 15) for the men in blue, and mean=100 (sd 14) for the women in red, and set the high mark cut-off as IQ 130 (corresponding to the top 2.28% of the overall population) then 4.15% of men make the cut and only 1.60% of women: the sex ratio will be 2.58 to 1. That means that 72% of bright people will be men.

Or, as has just been suggested to me from Denmark, we can use the visualizer and put in mean=102 (sd 15) for the men in blue and mean=98 (sd 14) for the women and once again set the cut-of at IQ 130. Then 3.13% of men make the cut and only 0.65% of women: the sex ratio will be 4.8 to 1. That means that 83% of bright people will be men.

In both cases there is a 4 IQ point difference, but by choosing to express this difference straddling the mean rather than above the mean, the sex ratio increases. I chose the first way because I had been triggered by the higher than average results from the Scottish National Survey. I am grateful to Emil for pointing out that I should try it closer to the mean, a more representative situation.

Using the old approach of Males 104, Females 100, moving up to IQ 140 (the top 0.38% of the overall population) then 0.82% of men make the cut and only 0.21% women: the sex ratio is 3.8 to 1. That means that 80% of these even brighter people will be men.

Using the new approach of Males 102 Females 98 then at IQ140 0.56% of men make the cut and 0.13% of women: the sex ratio is 4.18. That means that 81% of bright people will be men.

Using the old approach, moving up to IQ 145 (the top 0.13% of the population) then 0.31% of men make the cut and only 0.06% of women: the sex ratio is 4.8 to 1. That means that 82.7% of these very bright people (the three sigmas) will be men.

Using the new approach, moving up to IQ 145 (the top 0.13% of the population) then 0.21% of men make the cut and only 0.04% of women: the sex ratio is 5.3 to 1. That means that 84% of these very bright people (the three sigmas) will be men.

In the refined company of my loyal readers, you may well say that IQ 145 is no great shakes: there will be 13 three sigmas in a thousand at this level of intellect. Too common. What if we take the 1 in a thousand criterion, equivalent to an IQ of about 155 (3.7 sigma). At that refined level the sex ratio will be 7.9 to 1. Call it an 8 to 1 chance that this very bright person will be a man.

Using the Males 102 Females 98 version 0.021% of men and 0002% of women make the cut, and the sex ratio is 8.8 to 1.

So, there are slight differences in the sex ratio depending on: whether there is a mean difference of intelligence between men and women of 4 IQ points; whether the variance of male intelligence is greater than that of females; and to some extent about where one places the discrepant male/female means on the standard normal curve.

It is Bank Holiday in England, which means clouds, cold winds and no sunshine. Banks have a lot to answer for.

A mountain to climb this Sunday

 

Every now and then I buy a Sunday newspaper, supposedly for the treat of catching up with the week’s news in a more detailed manner than would have been possible on a weekday.

The Sun on Sunday and The Mail on Sunday manage 1,400,00 readers each, the more refined The Sunday Times a decent 765,000, as befits a supposed newspaper of repute. The Sunday Times aims to influence the influencers, and to be the standard bearer of accepted wisdom and genteel debate, plus cookery tips. Readers will help determine how society works by making choices and shaping opinions, not least in schools and universities. In the Culture section Siddhartha Mukherjee’s The Gene is reviewed by journalist Brian Appleyard, who inter alia says (column four):

Kinship studies around the world have repeatedly come up with percentages indicating the “heritability” of certain human traits, notably intelligence. Identical twins reared together have a much more than 50% likelihood of having similar IQs. But with non-identical siblings, the correlation plummets. And with families living apart the number drops even further. The point is that “heritability” (a genetic cause) isn’t the same as “inheritability”, the transfer of traits down the generations. Intelligence is clearly based on a vast complex of genes and their interactions that are highly unlikely to be passed on intact from parent to children. Along with now proven flaws in the whole idea of IQ, these new discoveries utterly discredit all attempts to make crude connections between race and intelligence. With the development of the theory of epigenetics, which argues that genes can be responsive to environmental factors, we now know that events in life can change the genetic destiny of future generations.

This is an interesting example of contemporary received wisdom, which will be read and even possibly believed by the chattering classes, and even some of the whispering classes, to which minority category I probably belong.

So, here in a whisper is my question: how will we ever climb this mountain of misunderstanding?

The comment is confused on so many different levels, showing much confusion about genetics, but also a touching faith in the epigenetics argument. This journalist studied English at university, but has no hesitation in reviewing a book about genetics, mangling the arguments, and making full use of the megaphone placed in his hands by credulous editors.

I have at best 1200 readers per day, so I cannot compete on numbers alone, but in the interests of establishing facts I suggest some minor correctives:

a link to the latest work on the genetics of scholastic achievement by Davies et al.

https://drjamesthompson.blogspot.co.uk/2016/04/genetics-of-mental-ability-greater-power.html

a link to the paper  on the genetics of completed school years which James Lee presented at Albuquerque last year

https://drjamesthompson.blogspot.co.uk/2015/09/scholar-in-86-snps.html

and the full version of that paper now published in Nature

https://drive.google.com/file/d/0B3c4TxciNeJZMDlGUXBlWDVFZnM/view?usp=sharing

 

and a link to Davide Piffer’s work on racial group differences, updated again so as to take in the latest Okbay findings above.

https://docs.google.com/document/d/1tDw5nIOoeuiZZ0o9IV1i_uJEbwmHUECI65BfxPxe4jY/edit?ts=5738a24e

In case you know anyone who really thinks that “there are now proven flaws in the idea of IQ” , a book written for clever sillies:

https://drjamesthompson.blogspot.co.uk/2015/06/intelligence-all-that-matters-stuart.html

If you pass this post on to another colleague you will have helped put the record straight, though you may have to do so in a whisper.

London Conference on Intelligence 2016: Population Genetics

 

From the London Conference, here is a paper by David Becker and Heiner Rindermann, looking at the arguments from a hereditarian and environmentalist perspective as to why some nations are brighter than others.

It is presented as a series of slides, so you will have to imagine the associated talk, but it is a replication and extension of the approach of Becker & Rindermann (2014). You will see that the authors use Y chromosomal haplogroup frequencies.

https://drive.google.com/file/d/0B3c4TxciNeJZQmwtYV9YR3lhSXM/view?usp=sharing

In what way are Eysenck and Gottfredson alike?

 

I have very few claims to uniqueness. Casting about for a simulacrum of eminence the best I can do is to say that I was once the basis for a character in a play. But now another minor achievement comes to mind: I am among the relatively few people who have discussed psychological matters with Hans Eysenck and Linda Gottfredson, so I am uniquely placed to set readers a Similaries subtest item as to how these two intelligence researchers resemble each other. This is the sort of abstraction which should be a doddle for contemporary readers, boosted in superficial intellectual accomplishments by free milk, free education and above all freedom from the painful and demanding instances of hard labour which bedevilled our ancestors.

So, it was an unexpected pleasure to find that Linda Gottfredson had taken the trouble to go back to Eysenck’s early work on in intelligence so as to do a little conceptual archaeology.

http://www.udel.edu/educ/gottfredson/reprints/2016Eysenck(Proofs).pdf

Gottfredson, in reviewing Eysenck’s work on intelligence, has also reviewed the conceptual, cultural and political issues which have bedevilled the proper evaluation of the evidence on mental ability. She takes us, decade by decade, through the main debates, the advances and the setbacks. She sees Eysenck as someone who simply knew that intelligence was primarily about the biology of the brain, and this fundamental ability radiated into all other human behaviours.

There is a great deal of interest in this historical overview, which also serves as a summary of the main findings about intelligence, with a particular emphasis on Gottfredson’s main contribution: what intelligence means in real life. Her summaries come as a surprise even to many practising clinical psychologists.

As regards this essay, here is Gottfredson summing up on Eysenck and his contribution to intelligence research:

He (Eysenck, 1986,pp. 396) persisted despite sometimes fierce and abusive opposition, never answering in kind but always with scientific logic and evidence: “It has always seemed to me that much of what I had to say was so obvious that it should hardly have needed saying.....I feel that I have really acted the part of the child in the fairy-tale of the Emperor's new clothes.”

What Eysenck (1973a, pp. 17) said about the great early 20th-century geneticist, J. B. S. Haldane, applies to him as well: “A great scientist sniffs out the truth even from partial and often insufficient evidence.

How are Eysenck and Gottfredson alike? They do not fear being independent seekers of the truth. Eysenck did it because he was interested in cutting through the nonsense spouted by inferior intellects, whom he relished winding up. He taunted them for his amusement, and for the edification of the intelligent laymen whom they had deluded with their obfuscations. Gottfredson did it because she hated evasion and doggedly advanced the case for the explanatory power of intelligence, particularly in terms of training requirements and occupational demands.

Eysenck sought the battle, enjoying seeing his adversaries agitated and stripped of their weak arguments. Gottfredson did not seek battle, but did not run from it when it came to her.

Brave researchers.

However, although this in no part of a Similarities test, there is an important way in which they differ: in the later part of his career Eysenck became silly, advancing weak causes out of  boredom, or for research funds. Gottfredson has become even wiser, and it is a pleasure to read her thoughtful essay.