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

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.

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 (1979, 1980) and sociology of intelligence by Gottfredson (1998). One could also call it cognitive sociology by analogy with cognitive epidemiology (Deary, 2010; Special issue in Intelligence Volume 37, Issue 6, November–December 2009; Gottfredson, 2004). Whatever the name, it is a field that has received renewed attention recently. Richard Lynn and co-authors report data on Italy (Lynn 2010a, 2010b, 2012a, Piffer and Lynn 2014, see also papers by critics), Spain (Lynn 2012b), China (Lynn and Cheng, 2013) and India (Lynn and Yadav, 2015). Two of his older studies cover the British Isles and France (Lynn, 1979, 1980).

A number of my recent papers have reanalyzed data reported by Lynn, as well as additional data I collected. These cover Italy, India, United States, and China (Kirkegaard 2015a, 2015b, 2015c, 2015d). This paper reanalyzes Lynn’s 1979 paper.

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 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 shall not attempt this. The method for converting the mean scores to the IQ score is this:

  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 = MinRes). All factor loadings were strongly positive indicating that G could be reliably measured among the regions. The factor score from this analysis was 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).

Table 1 – Correlations between cognitive datasets Douglas Davis G Lynn.mean 1 0.66 0.92 0.62 0.96 0.92 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
G 0.96 0.75 0.99 0.76 1 0.96
Lynn.mean 0.92 0.89 0.93 0.74 0.96 1


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.

Socioeconomic data and analysis

Lynn furthermore reports 7 socioeconomic variables. I quote his description of these:

“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.

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).”

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.

Table 2 – Correlations between S, S indicators, and G
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
S 1 0.79


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 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 et al, 2005). Beaver and 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, Fuerst and Kirkegaard (2014a) 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 (2014b) 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 (2015a) found S loadings of .16 and -.72 of total crime and intentional homicide variables in Italy. Among US states, Kirkegaard (2015c) found S loadings of -.61 and -.71 for murder rate and prison rate. The scatter plot is shown in Figure 1.

Figure 1 – Scatter plot of regional G and S












So, the most similar finding in previous research is that from Italy. There are various possible explanations. Lynn (1979) thinks 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.

Method of correlated vectors (MCV)

As done in the previous analysis of S factors, I performed MCV analysis to see whether the G factor was the reason for the association with the G factor score. 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.

Figure 2 – MCV scatter plot








As in the previous analyses, the relationship was positive even after reversal.

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). 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.

Compare with Lynn’s recent overview of the history of the FLynn effect (Lynn, 2013).


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