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The S factor in the British Isles: A reanalysis of Lynn (1979)

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Abstract and Figures

I reanalyze data reported by Richard Lynn in a 1979 paper concerning IQ and socioeconomic variables in 12 regions of the United Kingdom as well as Ireland. I find a substantial S factor across regions (66% of variance with MinRes extraction). I produce a new best estimate of the G scores of regions. The correlation of this with the S scores is .79. The MCV with reversal correlation is .47.
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The Winnower
March 28, 2015
The S factor in the British Isles: A
reanalysis of Lynn (1979)
Emil O. W. Kirkegaard1
I reanalyze data reported by Richard Lynn in a 1979 paper concerning IQ and socioeconomic variables in 12
regions of the United Kingdom as well as Ireland. I find a substantial S factor across regions (66% of variance
with MinRes extraction). I produce new best estimates of the G scores of the regions. The correlation of these
with the S scores is .79. The MCV correlation with reversal is .47.
Key words: intelligence, IQ, cognitive ability, inequality, S factor, British isles, inequality, ecology of
intelligence, sociology of intelligence, cognitive sociology
1. Introduction
The interdisciplinary academic field examining the effect of general intelligence on large scale social phenomena
has been called social ecology of intelligence by Richard Lynn (Lynn, 1979, 1980) and sociology of intelligence
by Gottfredson (Gottfredson, 1998). One could also call it cognitive sociology by analogy with cognitive
epidemiology (Deary, 2009, 2010; Gottfredson, 2004). Whatever the name, it is a field that has received renewed
attention recently. Richard Lynn and co-authors reported data on Italy (Lynn, 2010a, 2010b, 2012a; Piffer &
Lynn, 2014; see also papers by critics), Spain (Lynn, 2012b), China (Lynn & Cheng, 2013) and India (Lynn &
Yadav, 2015). Two of his older studies cover the British Isles and France (Lynn, 1979, 1980).
A number of my own recent papers have reanalyzed data reported by Lynn, as well as additional data I collected.
These cover Italy, India, United States, and China (Kirkegaard, 2015c, 2015b, 2015a, 2015d). This paper
reanalyzes Lynn’s 1979 paper.
2. Cognitive data and analysis
Lynn’s paper contains 4 datasets for IQ data that covers 11 regions in Great Britain. He further summarizes some
studies that report data on Northern Ireland and the Republic of Ireland, so that his cognitive data covers the
entire British Isles. Lynn only uses the first 3 datasets to derive a best estimate of the IQs. The last dataset does
not report cognitive scores as IQs, but merely percentages of children falling into certain score intervals. Lynn
converts these to a mean (method not disclosed). However, he is unable to convert this score to the IQ scale since
1 Ulster Institute for Social Research. Email:
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the inter-personal standard deviation (SD) is not reported in the study. Lynn thus overlooks the fact that one can
use the inter-regional SD from the first 3 studies to convert the 4th study to the common scale. Furthermore,
using the intervals one could presumably estimate the inter-personal SD, altho I did not attempt this. The method
for converting the mean scores to the IQ score is as follows:
1. Standardize the values by subtracting the mean and dividing by the inter-regional SD.
2. Calculate the inter-regional SD in the other studies, and find the mean of these. Do the same for the inter-
regional means.
3. Multiple the standardized scores by the mean inter-regional SD from the other studies and add the inter-
regional mean.
However, I did not use this method. I instead factor analyzed the four 4 IQ datasets as given and extracted 1
factor (extraction method was MinRes; (Revelle, 2015)). All factor loadings were strongly positive indicating
that an aggregate general intelligence factor, G, could be reliably measured among the regions (Rindermann,
2007). The factor scores from this analysis were put on the same scale as the first 3 studies by the method above.
This is necessary because the IQs for Northern Ireland and the Republic of Ireland are given on that scale. Table
1 shows the correlations between the cognitive variables. The correlations between G and the 4 indicator
variables are their factor loadings (italic).
Vernon navy Vernon army Douglas Davis G Lynn mean
Vernon navy 1 0.66 0.92 0.62 0.96 0.92
Vernon army 0.66 1 0.68 0.68 0.75 0.89
Douglas 0.92 0.68 1 0.72 0.99 0.93
Davis 0.62 0.68 0.72 1 0.76 0.74
G0.96 0.75 0.99 0.76 1 0.96
Lynn mean 0.92 0.89 0.93 0.74 0.96 1
Table 1: Correlations between cognitive datasets
It can be noted that my use of factor analysis over simply averaging the datasets had little effect. The correlation
of Lynn’s method (mean of datasets 1-3) and my G factor is .96.
3. Socioeconomic data and analysis
Lynn reports 7 socioeconomic variables. I quote his description:
1. Intellectual achievement: (a) first-class honours degrees. All first-class honours graduates of the
year 1973 were taken from all the universities in the British Isles (with the exception of graduates of
Birkbeck College, a London College for mature and part-time students whose inclusion would bias
the results in favour of London). Each graduate was allocated to the region where he lived between
the ages of 11 and 18. This information was derived from the location of the graduate’s school. Most
of the data were obtained from The Times, which publishes annually lists of students obtaining first-
class degrees and the schools they attended. Students who had been to boarding schools were written
to requesting information on their home residence. Information from the Republic of Ireland
universities was obtained from the college records.
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The total number of students obtaining first-class honours degrees was 3477, and information was
obtained on place of residence for 3340 of these, representing 96 06 per cent of the total.
There are various ways of calculating the proportions of first-class honours graduates produced by
each region. Probably the most satisfactory is to express the numbers of firsts in each region per
1000 of the total age cohorts recorded in the census of 1961. In this year the cohorts were
approximately 9 years old. The reason for going back to 1961 for a population base is that the
criterion taken for residence is the school attended and the 1961 figures reduce the distorting effects
of subsequent migration between the regions. However, the numbers in the regions have not changed
appreciably during this period, so that it does not matter greatly which year is taken for picking up
the total numbers of young people in the regions aged approximately 21 in 1973. (An alternative
method of calculating the regional output of firsts is to express the output as a percentage of those
attending university. This method yields similar figures.)
2. Intellectual achievement: (b) Fellowships of the Royal Society. A second measure of intellectual
achievement taken for the regions is Fellowships of the Royal Society. These are well-known
distinctions for scientific work in the British Isles and are open equally to citizens of both the United
Kingdom and the Republic of Ireland. The population consists of all Fellows of the Royal Society
elected during the period 1931-71 who were born after the year 1911. The number of individuals in
this population is 321 and it proved possible to ascertain the place of birth of 98 per cent of these.
The Fellows were allocated to the region in which they were born and the numbers of Fellows born
in each region were then calculated per million of the total population of the region recorded in the
census of 1911. These are the data shown in Table 2. The year 1911 was taken as the population base
because the majority of the sample was born between the years 1911-20, so that the populations in
1911 represent approximately the numbers in the regions around the time most of the Fellows were
born. (The populations of the regions relative to one another do not change greatly over the period,
so that it does not make much difference to the results which census year is taken for the population
3. Per capita income. Figures for per capita incomes for the regions of the United Kingdom are
collected by the United Kingdom Inland Revenue. These have been analysed by McCrone (1965) for
the standard regions of the UK for the year 1959/60. These results have been used and a figure for
the Republic of Ireland calculated from the United Nations Statistical Yearbook.
4. Unemployment. The data are the percentages of the labour force unemployed in the regions for the
year 1961 (Statistical Abstracts of the UK and of Ireland).
5. Infant mortality. The data are the numbers of deaths during the first year of life expressed per 1000
live births for the year 1961 (Registrar Generals’ Reports).
6. Crime. The data are offences known to the police for 1961 and expressed per 1000 population
(Statistical Abstracts of the UK and of Ireland).
7. Urbanization. The data are the percentages of the population living in county boroughs, municipal
boroughs and urban districts in 1961 (Census).
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Lynn furthermore reports historical achievement scores as well as an estimate of inter-regional migration
(actually change in population which can also be due to differential fertility). I did not use these in my analysis
but they can be found in the datafile in the supplementary material.
Since there are 13 regions in total and 7 variables, I can analyze all variables at once and still almost conform to
the rule of thumb of having a case-to-variable ratio of ≥2 (Zhao, 2009). Table 2 shows the factor loadings from
this factor analysis as well as the correlation with G for each socioeconomic variable.
Variable S G
Fellows RS 0.92 0.92
First class 0.55 0.58
Income 0.99 0.72
Unemployment -0.85 -0.79
Infant mortality -0.68 -0.69
Crime 0.83 0.52
Urbanization 0.88 0.64
S1.00 0.79
Table 2: Correlations between S, S indicators, and G
The crime variable had a strong positive loading on the S factor and also a positive correlation with the G factor.
This is in contrast to the negative relationship found at the individual-level between the g factor and crime
variables at about r=-.2 (Neisser et al., 1996). The difference in mean IQ between criminal and non-criminal
samples is usually around 7-15 points depending on which criminal group (sexual, violent and chronic offenders
score lower than other offenders; (Guay, Ouimet, & Proulx, 2005)). Beaver and Wright (Beaver & Wright, 2011)
found that IQ of countries was also negatively related to crime rates, r’s range from -.29 to -.58 depending on
type of crime variable (violent crimes highest). At the level of country of origin groups, Kirkegaard and Fuerst
(2014) found that crime variables had strong negative loadings on the S factor (-.85 and -.89) and negative
correlations with country of origin IQ. Altho not reported in the paper, Kirkegaard (2014) found that the loading
of 2 crime variables on the S factor in Norway among country of origin groups was -.63 and -.86 (larceny and
violent crime; calculated using the supplementary material using the fully imputed dataset). Kirkegaard (2015c)
found S loadings of .16 and -.72 of total crime and intentional homicide variables in Italy. Among US states,
Kirkegaard (2015a) found S loadings of -.61 and -.71 for murder rate and prison rate. The most similar finding in
the published literature is that from Italy. There are various possible explanations. Lynn (1979) suggests it is due
to large differences in urbanization (which loads positively in multiple studies; .88 in this study). There may be
some effect of the type of crime measurement. Future studies could examine this question by employing many
different crime variables. My hunch is that it is a combination of differences in urbanization (which increases
crime), immigration of crime prone persons into higher S areas, and differences in the justice system between
A scatterplot of G and S is shown in Figure 1.
Page 4 of 9.
3.1. Method of correlated vectors
As done in the previous analyses of S factors, I used the method of correlated vectors (MCV) to see whether the
G factor was the reason for the association of S with the G factor scores. S factor indicators with negative
loadings were reversed to avoid inflating the result (these are marked with “_r” in the plot). The result is shown
in Figure 2.
Page 5 of 9.
Figure 1: Scatter plot of regional G and S
As in the previous analyses, the relationship was positive even after reversal.
3.2. Per capita income and the FLynn effect
An interesting quote from the paper is:
This interpretation [that the first factor of his factor analysis is intelligence] implies that the mean
population IQs should be regarded as the cause of the other variables. When causal relationships
between the variables are considered, it is obvious that some of the variables are dependent on
others. For instance, people do not become intelligent as a consequence of getting a first-class
honours degree. Rather, they get firsts because they are intelligent. The most plausible alternative
causal variable, apart from IQ, is per capita income, since the remaining four are clearly dependent
variables. The arguments against positing per capita income as the primary cause among this set of
variables are twofold. First, among individuals it is doubtful whether there is any good evidence that
differences in income in affluent nations are a major cause of differences in intelligence. This was the
conclusion reached by Burt (1943) in a discussion of this problem. On the other hand, even Jencks
(1972) admits that IQ is a determinant of income. Secondly, the very substantial increases in per
capita incomes that have taken place in advanced Western nations since 1945 do not seem to
have been accompanied by any significant increases in mean population IQ. In Britain the
longest time series is that of Burt (1969) on London schoolchildren from 1913 to 1965 which
showed that the mean IQ has remained approximately constant. Similarly in the United States
the mean IQ of large national samples tested by two subtests from the WISC has remained
virtually the same over a 16 year period from the early 1950s to the mid-1960s (Roberts, 1971).
Page 6 of 9.
Figure 2: Method of correlated vectors scatterplot.
These findings make it doubtful whether the relatively small differences in per capita incomes
between the regions of the British Isles can be responsible for the mean IQ differences. It seems
more probable that the major causal sequence is from the IQ differences to the income differences
although it may be that there is also some less important reciprocal effect of incomes on IQ. This is a
problem which could do with further analysis. [my emphasis]
Compare with Lynn’s recent overview of the history of the FLynn effect (Lynn, 2013).
Supplementary material and acknowledgments
Supplementary materials including code, high quality figures and data can be found at
This paper was updated in March 2017 to make it more readable and improve the quality of the figures. The
original code was used and the numbers were reproduced, except for the MCV analysis which for unknown
reasons changed from r = .47 to r = .49.
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... It would be worthwhile to re-do all the previous 'state'-level S factor studies with a similar control for population density and see how this affects the results. Finally, during the review, Noah Carl pointed out that Lynn (1979) employed a similar control and observed that this can have large effects (see also Kirkegaard (2015g) for a reanalysis that study). ...
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Two datasets of Japanese socioeconomic data for Japanese prefectures (N=47) were obtained and merged. After quality control, there were 44 variables for use in a factor analysis. Indicator sampling reliability analysis revealed poor reliability (54% of the correlations were |r| > .50). Inspection of the factor loadings revealed no clear S factor with many indicators loading in opposite than expected directions. A cognitive ability measure was constructed from three scholastic ability measures (all loadings > .90). On first analysis, cognitive ability was not strongly related to 'S' factor scores, r = -.19 [CI95: -.45 to .19; N=47]. Jensen's method did not support the interpretation that the relationship is between latent 'S' and cognitive ability (r = -.15; N=44). Cognitive ability was nevertheless related to some socioeconomic indicators in expected ways. A reviewer suggested controlling for population size or population density. When this was done, a relatively clear S factor emerged. Using the best control method (log population density), indicator sampling reliability was high (93% |r|>.50). The scores were strongly related to cognitive ability r = .67 [CI95: .48 to .80]. Jensen's method supported the interpretation that cognitive ability was related to the S factor (r = .78) and not just to the non-general factor variance.
... Many recent studies have examined within-country regional correlates of (general) cognitive ability (also known as (general) intelligence, general mental ability, g),. This has been done for the British Isles (Lynn, 1979;Kirkegaard, 2015g), France (Lynn, 1980), Italy (Lynn, 2010;Kirkegaard, 2015e), Spain (Lynn, 2012), Portugal (Almeida, Lemos, & Lynn, 2011), India (Kirkegaard, 2015d;Lynn & Yadav, 2015), China (Kirkegaard, 2015f;Lynn & Cheng, 2013), Japan (Kura, 2013), the US (Kirkegaard, 2015b;McDaniel, 2006;Templer & Rushton, 2011), Mexico (Kirkegaard, 2015a) and Turkey (Lynn, Sakar, & Cheng, 2015). This paper examines data for Brazil. ...
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Sizeable S factors were found across 3 different datasets (from years 1991, 2000 and 2010), which explained 56 to 71% of the variance. Correlations of extracted S factors with cognitive ability were strong ranging from .69 to .81 depending on which year, analysis and dataset is chosen. Method of correlated vectors supported the interpretation that the latent S factor was primarily responsible for the association (r’s .71 to .81).
... Crime variables (crime rate, victimization, inmates/prisoner per capita, sentencing rate) load positively whereas they should have negative. This pattern has been found before, see Kirkegaard (2015e) for a review of S factor studies and crime variables. ...
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Two datasets of socioeconomic data was obtained from different sources. Both were factor analyzed and revealed a general factor (S factor). These factors were highly correlated with each other (.79 to .95), HDI (.68 to .93) and with cognitive ability (PISA; .70 to .78). The federal district was a strong outlier and excluding it improved results. Method of correlated vectors was strongly positive for all 4 analyses (r’s .78 to .92 with reversing).
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Two sets of socioeconomic data for 90-96 French departements were analyzed. One dataset was found in Lynn (1980) and contained four socioeconomic variables. Mixed results were found for this dataset, both with regards to the factor structure and the relationship to cognitive ability. Another dataset with 53 variables was created by compiling variables from the official French statistics bureau (Insee). This dataset contained an impure general socioeconomic (S) factor (some undesirable variables loaded positively), but after controlling for the presence of immigrants, the S factor became purer. This was especially salient for crime, unemployment and poverty variables. The two S factors correlated at r = 0.66 [CI95:0.52-0.76; N = 88]. The IQ scores from the 1950s dataset correlated at 0.33 [CI95:0.13-0.51, N = 88] with the S factor from the 2010-2015 dataset.
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I analyze the S factor in Italian states by reanalyzing data published by Lynn (2010) as well as new data compiled from the Italian statistics agency (7 and 10 socioeconomic variables, respectively). The S factors from the datasets are highly correlated (.92) and both are strongly correlated with a G factor from PISA scores (.93 and .88).
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I analyzed the S factor in US states by compiling a dataset of 25 diverse socioeconomic indicators. Results show that Washington DC is a strong outlier, but if it is excluded, then the S factor correlated strongly with state IQ at .75. Ethnoracial demographics of the states are related to the state's IQ and S in the expected order (White>Hispanic>Black).
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I reanalyze data published by Lynn and Yadav (2015) for Indian states. I find both G and S factors which correlate at .61. The statistical language R is used thruout the paper and the code is explained. The paper thus is both an analysis as a walkthru of how to conduct this type of study.
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I present new predictive analyses for crime, income, educational attainment and employment among immigrant groups in Norway and crime in Finland. Furthermore I show that the Norwegian data contains a strong general socioeconomic factor (S) which is highly predictable from country-level variables (National IQ .59, Islam prevalence -.71, international general socioeconomic factor .72, GDP .55), and correlates highly (.78) with the analogous factor among immigrant groups in Denmark. Analyses of the prediction vectors show very high correlations (generally > ±.9) between predictors which means that the same variables are relatively well or weakly predicted no matter which predictor is used. Using the method of correlated vectors shows that it is the underlying S factor that drives the associations between predictors and socioeconomic traits, not the remaining variance (all correlations near unity).
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The north–south difference in Italy in PISA 2006 scores in reading comprehension, mathematical and science abilities of 15-year-olds has been attributed by Lynn (2010a) to a difference of approximately 10 IQ points in intelligence and by critics to differences in educational resources. New evidence for differences between north and south Italy in the PISA 2012 Creative Problem Solving test as a measure of fluid intelligence shows a 9.2 IQ point between the north–west and the south and confirms Lynn's theory. New data are presented for genetic differences between the populations of north and south Italy.
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IQs are presented for fifteen regions of Spain showing a north-south gradient with IQs highest in the north and lowest in the south. The regional differences in IQ are significantly correlated with educational attainment, per capita income, literacy, employment and life expectancy, and are associated with the percentages of Near Eastern and North African genes in the population.
This study reports the differences in intelligence across thirty-one regions of the People's Republic of China. It was found that regional IQs were significantly associated with the percentage of Han in the population (r = .59), GDP per capita (r = .42), the percentage of those with higher education (r = 38, p<.05), and non-significantly with years of education (r = .32). The results of the multiple regression showed that both the percentage of Han in the region and the GDP per capita were significant predictors of regional IQs, accounting for 39% of the total variance.
Regional differences in cognitive ability are presented for 33 states and union territories of India. Ability was positively correlated with GDP per capita, literacy and life expectancy and negatively correlated with infant and child mortality, fertility and the percentage of Muslims. Ability was higher in the south than in the north and in states with a coast line than with those that were landlocked.
Flynn has been credited with having discovered the increase in IQs that has been reported in a number of countries during most of the twentieth century and that has come to be known as “the Flynn effect”. This paper documents and discusses a number of reports of increases in IQs that were published from 1936 onwards before the phenomenon was rediscovered by and . These early reports showed that the Flynn effect is fully present in pre-school children, does not increase during the school age years, and is greater for non-verbal abilities than for verbal abilities.