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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
Abstract
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: emil@emilkirkegaard.dk
Page 1 of 9.
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.
Page 2 of 9.
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
base.)
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).
Page 3 of 9.
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
areas.
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 https://osf.io/zc864/.
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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