Thursday 15 December 2016


Snapshot corrected moving to unz


It’s goodbye to

After 4 years of blogging, and 1,062,720 page views, here is a “change of address” notification. I have decided to transmute into being a columnist, at the kind invitation of Ron Unz, so as to write my psychological comments as a column at:

I am happy at the prospect of more visibility, more technical backup, and a more accessible and searchable archive of work. You can search by topic and by date, and I will start adding tags so that all searches become easier and more powerful. I hope to get more readers, given that the site gets 2 million a month, shared between many writers. Whether, in this collective of authors, I will still be able to stare at a page and immediately start writing, without knowing where it is going, as I do now in the apparent wilderness and seclusion of my own blog, is an open question.

Will I experience a crushing writer’s block, the equivalent of entering a sterile business office in order to dream up, to command, a romantic novel, and find that the fluorescent lights and lunchtime canteen deadens my soul? Will I look over my shoulder at what others are writing? Or will I just close my eyes and imagine a single reader in the wilderness, and write for that one person, regardless of all else?

Perhaps I have been over-dramatic, but shifting from my familiar abode causes a certain emotional wrench. It is like walking the empty rooms of a family house while the removal van waits outside. Worse, what if you, dear reader, resolutely refuse to follow me? Will you be set in your ways, a slave to your favourite sites, unwilling to countenance a perturbation in your URLS?

I hope you can shift as I intend to shift, to a new meeting place. The medium is not the message: the medium is what carries the message, and a message only brings you news if the content is hard to guess. We need to talk of many things, of shoes and ships and sealing wax and Shannon’s Mathematical Theory of Communication. I digress, but only a bit.

Monday 12 December 2016

Africa and the cold beauty of Maths


Africa TIMMS equipercentile

Things move fast. A published paper comes to the attention of Steve Sailer and suddenly a section of a puzzle gets completed.

Better still, the boundaries of ignorance get pushed backwards, which is always a good idea, and a fine Christmas present.

From the isolation of my study, and from the depths of my ignorance, I had always bemoaned the fact that poorer countries, particularly in Africa, avoided taking part in PISA and similar international assessments. The suspicion was that they were avoiding getting bad results, which would redound on their national pride, showing them to be dull and/or incapable of organising their schools properly. PISA has the capacity to spread embarrassment far and wide, in rich as well as poor countries, and I am all in favour of that. Let the over-paid educational authorities of the rich world be confounded by the wit of poorer nations, and may their cosy empires fall. Also, may badly organized countries stop blaming poverty and make sure they pay and support their teachers.

The problem with the lack of participation of these countries was that researchers lost a possible confirmation or disconfirmation of the IQ results obtained on those countries, which in the case of Africa seem to be too low to be believed. How to sort out this problem?

Justin Sandefur, Working Paper 444, December 2016, Center for Global Development.

Internationally Comparable Mathematics Scores for Fourteen African Countries


Internationally comparable test scores play a central role in both research and policy debates on education. However, the main international testing regimes, such as PISA, TIMSS, or PIRLS, include very few low-income countries. For instance, most countries in Southern and Eastern Africa have opted instead for a regional assessment known as SACMEQ. This paper exploits an overlap between the SACMEQ and TIMSS tests—in both country coverage, and questions asked— to assesses the feasibility of constructing global learning metrics by equating regional and international scales. I compare three different equating methods and find that learning levels in this sample of African countries are consistently (a) low in absolute terms, with average pupils scoring below the fifth percentile for most developed economies; (b) significantly lower than predicted by African per capita GDP levels; and (c) converging slowly, if at all, to the rest of the world during the 2000s. While these broad patterns are robust, average performance in individual countries is quite sensitive to the method chosen to link scores. Creating test scores which are truly internationally comparable would be a global public good, requiring more concerted effort at the design stage.

This fine paper comes from the economic sphere of study, so does not reference much psychometric literature. A pity, because it contributes much to the debate on group differences. Economists often ignore the concept of intelligence. Sandefur also seems to accept African national economic statistics, though he probably realizes they are prone to wishful thinking.  The author is circumspect about the key issue of comparability of difficulty levels across tests, but seems to have made reasonable choices. I doubt that a re-working would change the picture very much.

The linkage is made possible by Botswana and South Africa having taken both the regional SACMEQ and the TIMSS international tests; and the 2000 and 2007 regional tests having used some of the TIMSS international test questions.

Whatever the linkage methods, the results are pretty grim:

Substantively, the results here are daunting for African education systems. Most of the national test-score averages I estimate for the thirteen African countries in my sample fall more than two standard deviations below the TIMSS average, which places them below the 5th percentile in most European, North American, and East Asian countries. In contrast, scores from the SACMEQ test administered to math teachers are much higher, but fall only modestly above the TIMSS sample average for seventh- and eighth-grade pupils, in line with earlier analysis by Spaull and van der Berg (2013). African test scores appear low relative to national GDP levels; in a regression of average scores on per capita GDP in PPP terms, average scores in the SACMEQ sample are significantly below the predicted value using all three linking methodologies. Furthermore, there is little sign that African scores were improving rapidly or converging to OECD levels during the 2000s.

Of course, readers of this blog will know that Richard Lynn’s personal collection of international intelligence test results, now in the Becker edition, puts Sub Saharan intelligence two standard deviations below the European mean, so it closely matches these results.

The advantage of using Maths tests as a proxy for intelligence tests is that most intelligence tests have an Arithmetic subtest and/or number series tests, so one can follow some known correlations to estimate comparability's. Better still, Maths has a logic to it, so it is valid to talk about some operations being more complex than others. The same item is very much the same item whichever test you find it in, because the same steps are required to solve it. It has the cold beauty of which Bertrand Russell spoke:

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry”.

More prosaically, maths opens the door to many other intellectual tasks, much as literacy supersedes the oral tradition.

What is to be done with African Maths teachers? Heiner Rindermann, trying to resolve the debate between Richard Lynn and Jelte Wicherts, put Sub-Saharan African IQ at 76. As to African Maths teachers’ results in this paper, he says: In some African countries teachers seem to have lower abilities than students in Europe or East-Asia!

If teachers are one standard deviation above the national mean, then they would have IQs of 91, if two standard deviations above the mean still only 106. This is not a level likely to inculcate in their students a passion for Maths, a subject which every schoolchild recognizes as being different conceptually from other language based subjects, and hard to master. What makes problems difficult? I digress. 

Convergence is a much desired trajectory where racial differences are concerned. Put in the educational resources and the slower countries will catch up with the faster ones. Makes sense. However, this sought-after outcome does not always materialize. Convergence will take place sometime between 40 years and never, according to Woodley and Meisenberg.

Turning to the pressing issue of how to raise scholastic attainments, it is unlikely to be a simple question of investing money. Saudi Arabia has had plenty of money to spend on education for almost 50 years, and just look where it languishes in the table, in the company of far less wealthy Swaziland, Tanzania, Botswana and Uganda. Of course, given Saudi Arabia’s mean IQ of 78 that would be entirely as expected. No Africanist, I have nonetheless sung the praises of Botswana, a well run country which invests heavily in education (the Diamond Generation). Despite that, Botswana is not getting much bang for its buck. If Botswana cannot converge on other nations, despite having done so many things right, that should give pause for thought. Botswana’s mean IQ 73.

A summary of investment in education suggests that the pay-off is front-end loaded: the first $5000 has a big effect, and then it tends to plateau thereafter. Another way of looking at it is to note that once countries get to $16,000 GDP per capita then schooling in those countries accounts for only 10% of the variance of student attainment. So, poor countries (most of Africa is well below this level) should have plenty of scope for educational gains.

This paper completes a jigsaw puzzle, and extends the global scholastic attainment dataset by 14 countries. It confirms the Lynn assessments as likely to be correct, within a measurement error of roughly 4 IQ points. For these countries at least, it gives no hint of exceptional talents beyond that expected on the basis of intelligence testing.

I don’t do policy, so this is said more in hope than with any expectation of a good result, but if young Europeans school-leavers with good maths qualifications intending to do good works in Africa want to be most effective, instead of digging ditches they should concentrate on teaching Maths.

Thursday 8 December 2016

Der tag


Daily total 5018

Thank you to the 5018 readers who looked in on “Psychological Comments” yesterday.


Not complaining, just curious.

For the previous highest daily total see:

Wednesday 7 December 2016

Faking good on PISA


Faking good on PISA


One of the delights of being a member of a community of researchers in the modern age is the speed with which colleagues can come together to answer a question and scope out a solution to a problem.

Steve Sailer has looked at the most recent PISA results, which he has been discussing generically for many years.

He pointed out that in some countries a large proportion of eligible children don’t show up in the statistics. Could it possibly be the case that they are discretely told to stay at home, because national pride is at stake? Perish the thought! He pointed out that Argentina had apparently made stellar gains, but a commentator on his blog pointed out later that there was so much cheating in the Argentine provinces that the results had to be discarded, and the declared results are for Buenos Aires only, so probably higher than the national figures, or so the porteños would have you believe. Incidentally, it is only recently that Argentina has had economic data, such as for inflation, that could be vaguely trusted, so they are only just in the Truth Recovery phase.

Cheating is the easiest way to boost results. Teachers can look at the questions some days before the test, and do a crash course in “revision” for the class. This makes teachers, children, parents and governments happy. PISA says it has methods to ensure security and detect cheating, but Heiner Rindermann also has his own ability to look carefully at PISA’s published results, and rejects some of them on the grounds of improbability.

Anatoly Karlin also had a look at the dataset and discussed the disappointing performance of China and other eastern countries, with Russia doing better. Get his full account here:

I wondered how big the effect of such selective non-attendance on the examinations might be. There is also the confounder that age at ending secondary education varies between one country and another, so that must be factored into the equation.

Emil Kirkegaard suggested an approach, and after discussions with me and Gerhard Meisenberg, sorted it out quickly. Have a look at the full process here:

Emil had also asked Heiner Rindermann to comment, and he came in a few minutes later, with a detailed publication (not yet published, so I cannot show it to you) and a rule of thumb adjustment you can apply to all the countries.

Heiner says:

School attendance rate of 15 year old youth (usually, but not always,  given in PISA reports, usually somewhere at the end).
Do not confuse with participation rate in PISA study.

Per each percent point not attending school subtract 1.5 SASQ points (equivalent 0.225 IQ points). That is a rule of thumb.

I have made a smaller correction for countries at low ability levels - in such countries pupils in school do not learn much.

Not bad for a few hours of internet time.

A few hours later, Steve Sailer had further and better particulars on the results:

So, where does this leave us with the PISA results? First, it gives me a chance to quote myself, one of the consolations of a lonely blogger: “Nobody gets round sampling theory, not even the Spanish Inquisition.” 

Second, and arising from the quote, the consequence is that the PISA results are only generalizable if the sample is a fair selection of the relevant group. In my view, to understand the abilities of a nation, the relevant group should be the entire age cohort. If many 15 year olds have already left school then a school sample will always be a partial indicator of a nation, and will very probably flatter it. This is because weaker students find school frustrating and leave, whereas the brighter ones enjoy studying, understand its long term benefits, and stay in education as long as they can. Further, if teachers ensure that even among those still staying at school the weaker students fall discretely ill on the day of testing, then the results can be massaged upwards. Spotting weaker students is easy for teachers: they can quickly determine it from student questions, and more accurately determine it by marking their class test papers.

Third, I do not want to reject PISA results, because local examination results share many of the same problems. In any nation where some teenagers leave school early the local examination results will be better than the actual national average. Equally, if within a school cohort not everyone takes the same national examination, the same flattering distortion takes place.

Fourth and finally, I think it best to study PISA results once they have been corrected to account for incomplete age cohorts in the Rindermann fashion, or in some elaboration and refinement of that technique.  Absent that, they have a large error term and present too rosy a picture of national scholastic attainments.

Thursday 1 December 2016

Does Age make us sage or sag?


If you are of sensitive disposition, and certainly if you are over 60 years of age, look away now. Age is not good news for the thinking person. The results can be summarised in one word: decline. If you protest that I have been too brief, I can triple the word count: decline and fall.

Can we find more appealing results by taking another large sample, and applying more extensive measures of mental ability?

Elise Whitley, Ian J. Deary, Stuart J.Ritchie, G. David Batty, Meena Kumari, Michaela Benzeval. Variations in cognitive abilities across the life course: Cross-sectional evidence from Understanding Society: The UK Household Longitudinal

Background: Populations worldwide are aging. Cognitive decline is an important precursor of dementia, illness and death and, even within the normal range, is associated with poorer performance on everyday tasks. However, the impact of age on cognitive function does not always receive the attention it deserves.


We have explored cross-sectional associations of age with five cognitive tests (word recall, verbal fluency, subtraction, number sequence, and numerical problem solving) in a large representative sample of over 40,000 men and women aged 16 to 100 living in the UK.


Women performed better on word recall tests and men had higher scores for subtraction, number sequence and numerical problem solving. However, age-cognition associations were generally similar in both genders. Mean word recall and number sequence scores decreased from early adulthood with steeper declines from the mid-60s onwards Verbal fluency, subtraction and numerical problem solving scores remained stable or increased from early to mid-adulthood, followed by approximately linear declines from around age 60. Performance on all tests was progressively lower in respondents with increasingly worse self-rated health and memory. Age-related declines in word recall, verbal fluency and number sequence started earlier in those with the worst self-rated health. There was no compelling evidence for age dedifferentiation (that the general factor of cognitive ability changes in strength with age).


We have confirmed previously observed patterns of cognitive aging

Age and ability


Sharp declines for word recall, verbal fluency and number sequences; declines after 60 years of age for numerical problem solving, and even some gradual decline on subtraction. Ironic, is it not, that after the subtraction of all our skills, subtraction itself should be spared?

Somewhat chastened by these findings, I turned to another paper in the hope it would cheer me up. Written by the same incredible Edinburgh gang, who have cornered the market in ageing research, they try to find what makes people age well from a cognitive point of view. Surely with a few mental exercises and a good helping of fresh vegetables all will be well with me?

Stuart J. Ritchie,, Elliot M. Tucker-Drob, Simon R. Cox, Janie Corley, Dominika Dykiert, Paul Redmond, Alison Pattie, Adele M. Taylor, RuthSibbett, John M. Starr, Ian J. Deary

Predictors of ageing-related decline across multiple cognitive functions.


Ageing hedgehog plots

I call these “the hedgehogs”. They show that if you give every ageing person the same starting point then they age at different speeds. This gives us all hope. It may be delusional hope, but it is hope nonetheless. What makes some of us age gracefully?

It is critical to discover why some people's cognitive abilities age better than others'. We applied multivariate growth curve models to data from a narrow-age cohort measured on a multi-domain IQ measure at age 11 years and a comprehensive battery of thirteen measures of visuospatial, memory, crystallized, and processing speed abilities at ages 70, 73, and 76 years (n= 1091 at age 70). We found that 48% of the variance in change in performance on the thirteen cognitive measures was shared across all measures, an additional 26% was specific to the four ability domains, and 26% was test-specific. We tested the association of a wide variety ofsociodemographic, fitness, health, and genetic variables with each of these cognitive change factors. Models that simultaneously included all covariates accounted for appreciable proportions of variance in the cognitive change factors(e.g. approximately one third of the variance in general cognitive change). However,beyond physical fitness and possession of the APOEe4 allele, very few predictors were incrementally associated with cognitive change at statistically significant levels. The results highlight a small number of factors that predict differences in cognitive ageing, and underscore that correlates of cognitive level are not necessarily predictors of decline. Even larger samples will likely be required to identify additional variables with more modest associations with normal range heterogeneity in aging related cognitive declines.

The study has three waves of testing over six years (70 to 76 years of age), and a broad range of cognitive measures. It is also informed by the original measure of intelligence at age 11, so far better grounded than most research.

Here are the key findings:

Ageing and digit symbol

If you want a really good test of decrement of ability for the over 70s, use Digit Symbol substitution. Better than a brain scan any day.

About half of the drop in function across the 13 cognitive measures is shared. “It all goes together when it goes” is at least half true.

Brighter children become brighter, healthier, and fitter older adults. This ‘preserved differentiation’ appeared to last into the eighth decade of life.

The most robust and consistent predictor of cognitive change within old age, even after control for all the other variables, was the presence of the APOEe4 allele. APOEe4 carriers showed over half a standard deviation more general cognitive decline compared to non-carriers, with particularly pronounced decline in their Speed and numerically smaller, but still significant, declines in their verbal memory.

Women had significantly less general cognitive decline than men, mainly centered on Crystallized ability.

No evidence for a relation between education (or social class) and the slope of any of the cognitive factors.

The three fitness indicators weren’t much related to the rate of cognitive decline, but taken together there was a higher correlation, but nothing in this study to test the idea that improving physical functioning would have had a cognitive sparing effect.

If you don’t like the general drift of these results you may wish to say that age is a social construct, that the definition of old age is arbitrary, that countries differ considerably in their classifications of the elderly, that there is no precise point at which a person becomes old and that the whole concept is meaningless, or indeed totally meaningless. You could also argue that people have many abilities which have not been measured by the particular tests used in these studies, and that those untested abilities probably show no decrements. For example, tuneless whistling, stirring coffee while meditating, the recollection of things past, and smiling faintly at the last but one joke in a conversation. Each person shows their genius in their own way.

Back to the results. Perhaps a younger reader would be willing to take a quick look at all of them to make sure that I have understood them properly.

On reflection, I would ask the young reader that if this complex task takes you only a moment, please delay for a while before responding to me, so as not to make the contrast in our processing speeds too evident.