Inequality across prefectures in Japan: An S factor analysis

Abstract

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.

Full text

Open Quantitative Sociology & Political Science
Published 6. April 2016
Submitted 17. December 2015
Inequality across prefectures in
Japan: An S factor analysis
Emil O. W. Kirkegaard1
Abstract
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.
Key words: general socioeconomic factor, S factor, Japan, prefectures, inequality, intelligence, IQ,
cognitive ability, cognitive sociology
1. Introduction
Desirable socioeconomic outcomes for persons, and larger units such as countries, tend to correlate
positively with other desirable socioeconomic outcomes and negatively with undesirable ones, which in
turn tend to correlate positively with each other. When this is the case one can extract a general factor
1 University of Aarhus, Denmark. Email: emil@emilkirkegaard.dk

such that generally the positive outcomes have positive loadings and the negative outcomes negative
loadings. The factor has been called the general socioeconomic factor (S factor) and is similar to the g
factor of mental ability (Jensen, 1998; Kirkegaard, 2014b). The S factor has been replicated across
numerous datasets at different levels of analysis (Kirkegaard, 2014a, 2014b, 2015a, 2015e; Kirkegaard
& Fuerst, 2014; Kirkegaard & Tranberg, 2015).
Desirable (/undesirable) socioeconomic outcomes at the aggregate-level have often been found to
correlate positively (/negatively) with estimates of cognitive ability for the same regions, e.g. (Carl,
2015; Kura, 2013; Lynn, 1979, 1980; Lynn & Cheng, 2013). Because the S factor is an aggregate of
such outcomes, it is not surprising that S scores have been found to have strong positive correlations
with cognitive ability as well, e.g. (Kirkegaard, 2015b, 2015c, 2015f).
One prior study has examined socioeconomic outcomes at the aggregate-level in Japan (Kura, 2013).
However, an S factor was not extracted from the socioeconomic outcomes so it is unclear if the general
pattern of results hold in Japan as it did in the other countries.
Japan is a densely populated country2 and has a number of administrative divisions. At the highest level
there are prefectures which number 47. Below this are a variety of other administrative divisions such
as municipals (about 1700). The hierarchical structure is not simple (“Administrative divisions of
Japan,” 2015); lower level divisions sometimes contain different types of subdivisions. Aside from
administrative divisions, there are also 8 geographic regions, which are similar to those for the United
States (Northeast, Midwest, West, and South) (“List of regions of Japan,” 2015). Figure 1 shows a map
of Japan.
2 Among the top 100 most populous countries, Japan ranks 12th with a population density of about 336 per km2. For
comparison, South Korea has one of 503 (ranked 3rd), the United Kingdom one of 262 (ranked 15th), and France one of
118 (ranked 32nd) (“List of sovereign states and dependent territories by population density,” 2015).

2. Data
2.1. Data from Kenya Kura
The previous paper on Japanese prefectures analyzed 7 socioeconomic outcomes, but more data is
better, so I contacted Ken Kura, the author of the previous study who is a Japanese native, and asked
him to locate more data for me. He sent me a file with 31 variables, including those found in his
published paper. The variables from the previous paper are listed below. The first line is the variable
name, and the second line is a brief description:
1. Latitude
Latitude.
2. Height
Height at age 17.
3. IQ
IQ score. Estimated from scholastic achievement tests.
Figure 1: Map of Japanese regions (colors) and
prefectures (white borders). From Wikipedia
(“Administrative divisions of Japan,” 2015).

4. Skin.color
Skin color (brightness).
5. Income
Average per capita income.
6. Labor.participation
Labor participation rate.
7. Homicide
Homicide rate.
8. Infant.death
Infant mortality rate.
9. Divorce
Divorce rate.
10. Fertility
Total fertility rate.
11. Suicide
Suicide rate.
The explanations for these can be found in the previous paper (Kura, 2013).
The new variables from Kura are:
1. Gini.income
GINI of income (i.e. a measure of inequality, larger values mean more inequality).
2. Gini.asset
GINI of assets.
3. Unemployment
Unemployment rate.
4. Welfare.use
Welfare use rate, type 1.
5. Welfare.use2
Welfare use rate, type 2.
6. Felony
Felony rate.
7. Abortions
Abortion rate.
8. Physicians
Physicians rate.
9. Pharmacists
Pharmacists rate.

10. Voter.turnout.upper
Voter turnout, upper house.
11. Voter.turnout.lower
Voter turnout, lower house.
12. Marriages
Marriage rate.
13. Education.9.years
Percentage who has completed 9 years of education.
14. Education.12.years
Percentage who has completed 12 years of education.
15. Obesity
Obesity rate.
16. Smoking
Smoking rate.
17. Drinking
Drinking rate.
18. Verbal
Mean verbal test score.
19. Math
Mean math test score.
20. Science
Mean science test score.
Most of the data were averaged over a couple of recent years. Details about this can be found in the
supplementary material (S_factor_Japan_project.ods).
2.2. Data from the Japanese statistics agency
Because an initial analysis of Kura's data gave decidedly unexpected results and because of some
oddities with the data3, I decided to download additional data myself. Variables were selected and
downloaded from the English-language section of the Japanese statistics bureau's website
(http://www.stat.go.jp/english/). The selection criteria were that variables must 1) concern an important
socioeconomic outcome, and 2) not be strongly reliant on local natural environment (e.g. presence of
water for fishing).
The list of variables below were included. The first line is the variable name given by me, the second is
the description from the website:
1. Low.edu
Ratio of people having completed up to elementary or junior high school only.
3 The abortion variable has a max-min ratio of 145, meaning that the prefecture with the most abortions per capita has
145 as many of that with the fewest. For libraries (in the second dataset), the value is 100.

2. High.edu
Ratio of people having completed up to colleges and universities.
3. Foreigners
Ratio of population of foreigners (per 100,000 persons).
4. Fertility
Total fertility rate.
5. Marriages
Rate of marriages (per 1,000 persons).
6. Divorces
Rate of divorces (per 1,000 persons).
7. Income
Prefectural income per person.
8. Income.growth
Annual increase rate of prefectural income.
9. Consumer.price.index
Regional difference index of consumer prices [general: average of 51 cities = 100]
10. Financial.potential
Index of financial potential.
11. In.work.male
Labour force participation rate [male].
12. In.work.female
Labour force participation rate [female]
13. Unemployment.male
Unemployment rate [male]
14. Unemployment.female
Unemployment rate [female]
15. Tertiary.industry
Ratio of persons employed in the tertiary industry
16. Libraries
Libraries (per 1,000,000 persons)
17. Museums
Museums (per 1,000,000 persons)
18. Flush.toilet
Ratio of dwellings with flush toilet
19. Piped.water

Ratio of households covered by piped water supply system
20. Hospitals
General hospitals (per 100,000 persons)
21. Physicians
Physicians working at medical establishments (per 100,000 persons)
22. Nurses
Nurses working at medical establishments (per 100,000 persons)
23. Life.expect.male
Life expectancy [0 year old, male]
24. Life.expect.female
Life expectancy [0 year old, female]
25. Suicides
Suicides (per 100,000 persons)
26. Infant.mortality
Infant death rate (per 1,000 live births)
27. Unemployment.benefits
Ratio of recipients of benefits of employment insurance
28. Criminal.offenses
Recognitions of criminal offenses (per 1,000 persons)
29. Mean.air.temp
Yearly average of air temperature
30. Mean.humidity
Yearly average of relative humidity
31. Sunshine
Yearly sunshine hours
32. Precipitation
Yearly precipitation
33. Population
Percentage distribution by prefecture
For almost all the variables, multiple years of data were available. I downloaded only the three most
recent datapoints almost all of which were from between 2000 and 2013, and most were from 2005 and
2010. However, they were not consistently available in any particular years, so conducting a
longitudinal study akin to the study of Brazilian states (Kirkegaard, 2015f) was not easy and was not
done.
A composite dataset was created by merging the two datasets, yielding 63 variables in total. For

identification, “_A” and “_B” were added to the variables names, where the first indicates that the data
is from Kura and the second that it is from myself.
3. Redundant variables
Some of the variables were clearly overlapping between the two datasets, e.g. marriage rate. However,
it is possible that data error had been introduced at some point. Thus, these pairs were left in and were
filtered out as part the regular quality control.
When one extracts a general factor from a dataset, it will be influenced to some degree by the variables
it is extracted from. If these variables are not representative of the domain, the general factor will
include some group factor variance. To avoid this, I developed an algorithm for removing duplicates
and near-duplicates from datasets before extracting a general factor (Kirkegaard, In review). Briefly
put, the algorithm removes variables until no pair correlate above a certain threshold. No study has
examined what a good threshold would be, but .90 has been used (by me) in earlier studies and was
used here for consistency.
The output of the algorithm is shown below:
The following variable pairs had stronger intercorrelations than |0.9|:
Var1 Var2 r
2207 Physicians_A Physicians_B 0.999
1395 Marriages_A Marriages_B 0.995
1480 Income_A Income_B 0.963
832 Voter.turnout.lower_A Voter.turnout.upper_A 0.942
1872 Unemployment.male_B Unemployment.female_B 0.939
1841 Unemployment_A Unemployment.female_B 0.938
1300 Low.edu_B High.edu_B -0.915
2287 Hospitals_B Nurses_B 0.901
The following variables were excluded:
Physicians_B, Marriages_B, Income_B, Voter.turnout.upper_A, Unemployment.female_B,
High.edu_B, Nurses_B
The first three pairs are variants of the same variable that are slightly different due to the data coming
from different years. There were three unemployment variables, one with both genders, and one for
each gender. However, they all correlated near unity, so only the gender-combined one was kept. In
some rare cases, variables can be drastically different by gender, so one should not average them before
checking their correlations. In the case of low and high education, we see a very strong negative
relationship as expected.
After the exclusions, there were 44 socioeconomic variables left. However, some of these were clearly
(near-)duplicates that did not reach the threshold:
●Suicide_A and Suicides_B, r = .887
●Fertility_A and Fertility_B, r = .820
●Felony_A and Criminal.offenses_B, r = .872
●Infant.death_A and Infant.mortality_B, r = .727

We see that the first three of these narrowly missed the threshold (all r's ≥ .82), while there seems to be
something wrong with the infant data.4 Upon investigating the issue, Kura and I found that the problem
is due to two things: first, that the averages are based on slightly different years.5 Second, the year-to-
year intercorrelations are near-zero, averaging only .17. Thus, it seems that Japanese health care is so
good that differences between prefectures almost only reflect unstable variation.
4. Reliability of factor extraction across methods
In most cases, different methods for factor extraction and scoring yield near-identical results. However,
sometimes they yield radically different results. For this reason, it is a good idea to examine
consistency across methods which can be a sign of data error or violated statistical assumptions.
I extracted one factor from the dataset using every combination of factor extraction and scoring
methods available in the fa() function from the psych package for R (Revelle, 2015). Factor score
reliability was strong across methods but not always near unity. The mean correlation was .96 and the
smallest was
.82.
All further extractions were done with least squares and Bartlett's scoring method (Revelle, 2015).
5. Indicator sampling reliability
Theoretically, one can think of S as being the general factor extracted from a complete collection
(population) of socioeconomic indicators (compare with (Ashton, Lee, & Vernon, 2001; Jensen, 1998,
p. 31)). If there is a general factor of such a collection, then it should not depend strongly on which
exact indicators one extracts it from. It should to a large degree be indifferent to the indicator (Jensen,
1987, 1998, p. 32). Thus, one can assess the existence and reliability of a hypothetical factor by
repeatedly sampling indicators, extracting factors and correlating them (Kirkegaard, In review). This
method was implemented by randomly splitting the dataset into two halves (i.e. each with half the
indicators), factor analyzing each half separately and then correlating the factor scores. This was done
1000 times. Figure 2 shows a density-histogram of the results.
4 An earlier version of the analysis used infant data averaged from fewer years, which produced a correlation between the
two of only about .5.
5 Kura's variable is based on the years 2005-2014 while my variable is based on the years 2005, 2010 and 2013.

Because factors can be reversed, values that fall away from 0 are evidence of factor reliability. One can
create a numeric measure of this by choosing a threshold for an acceptable reliability correlation, e.g.
.50, and then finding the fraction of scores such that |r| > .50 In the present case, this number was .539.
This does reveal some structure. A simulation with the same number of cases and indicators but using
random, normally distributed scores, found a value of 0, that is, none of the 1000 runs produces a
correlation |r|>.5.
Still, the results are strikingly weak compared to the country-level S factor, where 100% of the
correlations were above the threshold (Kirkegaard, In review). There does not seem to be a reliable S
factor across Japanese prefectures.
6. Mixedness
When extracting a factor structure from a dataset that has a latent structure, generally cases fit the
factor structure. However, it is possible that some cases have patterns that are strongly incongruent with
the overall structure in the data. Such cases are said to be highly mixed or structural outliers
(Kirkegaard, In review, 2015d). Several methods have been developed to try to identify such cases, see
(Kirkegaard, In review) for discussion.
Each of the earlier developed methods was used to examine if any cases showed strong mixedness.
There were no cases of strong outliers. There was only moderate correlational agreement (mean r = .40;
range .19-.63) across methods indicating a lack of clear outliers aside from sampling error.
No action was taken in relation to the mixedness results.
7. Factor loadings
A general factor was extracted using both standard interval-level data and using rank-level data. The
reason to use the second is that it is thought to be robust to non-linearity and outliers in the dataset.
Figure 2: Indicator sampling reliability. 1000 runs. The red line gives
the mean correlation.

Figure 3 shows the loadings.
If there is no clear S factor, as the indicator sampling reliability analysis suggests, then we should also
fail to observe the usual pattern of loadings: that generally desirable outcomes have positive loadings
and conversely for generally undesirable outcomes. While some indicators have expected loadings, a
large number do not: 1) three crime variables have strong positive loadings, 2) two divorce indicators
have strong positive loadings, 3) unemployment has a near-zero loading, 4) Physicians and Hospitals
have negative loadings, 5) Museums and Libraries have negative loadings, 6) Life.expect.female has a
negative loading but the male version has a positive, and 7) voter turnout has the strongest negative
loading of all, which is strange because it usually has a positive loading.
The strange negative loading of Education.9.years seems to be due to a fluke from a strong ceiling
effect, as all prefectures have values very close to 100%.
In general, the picture is very muddled at best, similar to the results from the indicator sampling
reliability analysis.
8. Relationships to cognitive ability
Still, we might be curious as to whether the 'S' factor correlates with cognitive ability as found in all
previous studies. Kura's dataset contains both his estimated IQ scores from the previous study (Kura,
2013) as well as three scholastic achievement scores (math, language and science). Factor analysis of
the three achievement scores reveal a G factor (aggregate-level g factor) and each indicator loaded
Figure 3: Loadings on the first factor.

strongly on it (all loadings >.90), as one would expect (Rindermann, 2007). The scores from this factor
were used as the measure of cognitive ability. Figure 4 shows a scatterplot between cognitive ability
and 'S'.
Not only do we not find a strong positive correlation, we find a weak negative one. The relationship
also fails Jensen's method (coefficient = -.19; with reversing (Kirkegaard, In review)).6
Still, while there seems to be no S factor in this dataset, it is possible that some of the indicators have
interesting relationships to cognitive ability as found by the previous study (Kura, 2013). Table 1 shows
the correlations between cognitive ability and the other variables.
Variable Correlation with cognitive ability Variable
Correlation
with cognitive
ability
Verbal_A 0.98 S_B -0.09
Science_A 0.98 High.edu_B -0.1
IQ_A 0.96 Nurses_B -0.11
Math_A 0.92 Life.expect.female_B -0.12
Height_A 0.55 Population_B -0.16
Latitude_A 0.54 Fertility_B -0.17
Education.9.years_A 0.48 S_AB -0.17
Skin.color_A 0.48 S_A -0.17
6 Jensen's method (method of correlated vectors, named after the great psychologist Arthur Jensen) consists of correlating
the factor loadings of indicators with their relationships to some criterion variable. The reasoning is that if the
relationship between the factor scores and the criterion variable is real, then (everything else equal) the indicators that
have stronger loadings on the factor (i.e. are better measures of it) should be more strongly related to the criterion
variable than those with weaker loadings. For more details, see (Jensen, 1998; Kirkegaard, In review).
Figure 4: Scatterplot of cognitive ability and 'S' factor scores.

In.work.male_B 0.47 Labor.participation_A -0.18
In.work.female_B 0.43 Physicians_A -0.18
Voter.turnout.lower_A 0.35 Hospitals_B -0.18
Museums_B 0.29 Consumer.price.index_B -0.19
Voter.turnout.upper_A 0.26 Physicians_B -0.19
Libraries_B 0.26 Pharmacists_A -0.2
Suicide_A 0.24 Piped.water_B -0.22
Abortions_A 0.24 Sunshine_B -0.26
Mean.humidity_B 0.24 Gini.income_A -0.29
Precipitation_B 0.21 Unemployment.benefits_B -0.29
Income_A 0.19 Criminal.offenses_B -0.3
Education.12.years_A 0.19 Marriages_A -0.39
Low.edu_B 0.19 Obesity_A -0.4
Income_B 0.18 Felony_A -0.41
Drinking_A 0.15 Marriages_B -0.43
Suicides_B 0.15 Homicide_A -0.45
Life.expect.male_B 0.11 Divorce_A -0.46
Foreigners_B 0.09 Tertiary.industry_B -0.5
Fertility_A 0.07 Mean.air.temp_B -0.51
Income.growth_B 0.07 Unemployment_A -0.54
Infant.mortality_B 0.07 Welfare.use_A -0.55
Financial.potential_B 0.01 Welfare.use2_A -0.59
Flush.toilet_B -0.01 Gini.asset_A -0.61
Infant.death_A -0.06 Unemployment.male_B -0.64
Smoking_A -0.09 Unemployment.female_B -0.65
Divorces_B -0.72
Table 1: Correlations between cognitive ability and other variables. N=47.
A comparison with the results from Kura's study (Table 2 in that paper) shows strong agreement (Kura,
2013), that is, we both find negative correlations to homicide and divorce rate, and positive correlations
to latitude, height and skin brightness.
9. Robustness check
Because the results were so at odds with prior research, the probability of data or analysis error or some
other detectable anomaly was thought to be high. For this reason, additional checks were run.

9.1. Parallel analysis of the sub-datasets
To assess the robustness of the results, I carried out all analyses in parallel on the three datasets
(combined, Kura's and mine). Results did not generally change. As might be expected due to the very
poor indicator sampling reliability, the 'S' factors from the two datasets correlated poorly, r=.18 and
neither were substantially related to cognitive ability (also shown in Table 1).
9.2. Different duplicate variable threshold
It is possible that group factor variance were strongly coloring the first factors. To see if this could be
avoided, the analyses were re-run with lower thresholds (.70 and .80) for excluding 'duplicated' or
overlapping variables, but the results were very similar.
9.3. Controlling for population density or population
During the peer review process L. J. Zigerell suggested that population density or total population
might be obscuring the results. To test this, I created parallel versions of the dataset with controls. This
was done simply by regressing (linear regression) each indicator on the control variable and saving the
residuals. Then each control variable was used with three modes: 1) untransformed, 2) log transformed
and 3) square root transformed. This was done to make the distribution more normal and suitable for
the linear model used for the control. The population data was copied from Wikipedia (“List of
Japanese prefectures by population,” 2015).
To see if an S factor could be consistently measured in the datasets, I used indicator sampling reliability
like before. Then I calculated the proportion of correlations with an absolute value above .5. Table 2
shows the results:
Control method Proportion with |r| > .50
Standard 0.526
Pop. density 0.603
Pop. density (log) 0.931
Pop. density (sqrt) 0.907
Population 0.783
Population (log) 0.793
Population (sqrt) 0.837
Table 2: Indicator sampling reliability and control methods.
Surprisingly, most of the controls worked very well. The data controlled for log population density had
the strongest indicator sampling reliability, and the scores from that were used for the following
analyses. Figure 5 shows the distribution of reliability correlations for the chosen control method.

Below, I repeat the other analyses from before on the corrected dataset. Figure 6 shows the loadings
plot.
Figure 5: Indicator sampling reliability for the dataset corrected for
log population density. 1000 runs. The red line gives the mean
correlation.
Figure 6: First factor loadings with population controls. Indicators are sorted by the loadings from the
pop. density (log) analysis.

Clearly, there were many large changes in S loadings before and after implementing the control. All the
controlled analyses had nearly identical loadings. Examining the indicators with large changes
generally shows that the indicators with loadings in unexpected directions changed after the control.
For instance, Unemployment.male_B changed from slightly positive to very negative, and Felony_A
from very positive to moderately negative. Not all changes were improvements. For instance, labor
participation_A decreased from having a strong positive loading to have a very weak positive loading.
Figure 7 shows the scatterplot of cognitive ability and the corrected S scores.
Now we see the expected pattern. Okinawa is an outlier, but it is reasonably close to the regression line.
If Okinawa is excluded, the correlation decreases to .54 [95CI: .29 to .72].
Figure 8 shows Jensen's method applied as before.
Figure 7: Scatterplot of cognitive ability and S scores from the
corrected analysis.

And again, we see familiar results. Cognitive ability is more strongly related to the socioeconomic
variables that are more strongly related to other socioeconomic variables (=higher S loading).
Additionally, I tried the same analyses as above with ranked data. This produced similar but slightly
weaker results (cognitive ability x S = .56, Jensen's coef. = .70). This could but does not necessarily
mean that non-linearity or outliers were inflating the results; it may be that transforming the data to a
lower level of measurement (ordinal from interval) obscures important patterns.
10. Discussion and conclusion
The results from Japanese prefectures are markedly different from those from other studies in that from
the uncorrected data, no clear S could be extracted, the loadings did not generally fit the S factor
pattern (good outcomes with positive loadings, bad outcomes with negative loadings) and if one tried
extracting factor scores anyway, they did not correlate substantially with cognitive ability.
However, in an exploratory (unplanned) analysis, it was found that if one removes the effect of (the log
of) population density, the usual S factor study pattern emerges: the loadings go in expected directions,
S can be reliably extracted from different samples of indicators, S correlates strongly with cognitive
ability, and Jensen's method indicates that the relationship is due mostly to S, not other variance.
Thus it would seem that Japan is odd in that the large differences in population density between the
prefectures almost totally obscure the S pattern (Tokyo has a population density 92 times that of
Hokkaido). Previous S factor studies did not correct for population density even when marked
differences were present7 and still found relatively pure S factors that correlated strongly with cognitive
7 For instance, for the United States, New Jersey has a population density 931 times larger than that of Alaska and 202
times larger than that of Wyoming. Numbers from Wikipedia (“List of U.S. states by population density,” 2015).
Figure 8: Jensen's method with reversing for the corrected S factor. The suffix
“_r” means that the variable was reversed.

ability, so it is somewhat of a mystery why the control would be needed for Japanese prefectures. 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).
Strengths of the study include the relatively large number of cases (N=47), large number of indicators
(N=44) and the good quality of the cognitive ability estimates. With the caveat that the control for
population density was unplanned, the results conform to the pattern found in previous studies.
Supplementary material and acknowledgments
Open peer review thread: http://openpsych.net/forum/showthread.php?tid=260
Supplementary material including datasets and R code: https://osf.io/4bw8u/files/
Thanks to Kenya Kura for obtaining data from Japanese-language sources for the present study.
Thanks to John Fuerst for proofreading.
Thanks to LJ Zigerell, Bryan Pesta and Noah Carl for reviewing the paper.
References
Administrative divisions of Japan. (2015, October 18). In Wikipedia, the free encyclopedia. Retrieved
from https://en.wikipedia.org/w/index.php?
title=Administrative_divisions_of_Japan&oldid=686389982
Ashton, M. C., Lee, K., & Vernon, P. A. (2001). Which is the real intelligence? A reply to Robinson
(1999). Personality and Individual Differences, 30(8), 1353–1359.
http://doi.org/10.1016/S0191-8869(00)00117-3
Carl, N. (2015). IQ and socioeconomic development across Regions of the UK. Journal of Biosocial
Science, 1–12. http://doi.org/10.1017/S002193201500019X
Jensen, A. R. (1987). The g beyond factor analysis. In R. R. Ronning, J. A. Glover, J. C. Conoley, & J.
C. Witt (Eds.), The influence of cognitive psychology on testing. Hillsdale, NJ: Erlbaum.
Jensen, A. R. (1998). The g factor: the science of mental ability. Westport, Conn.: Praeger.
Kirkegaard, E. O. W. (In review). Some new methods for exploratory factor analysis of socioeconomic
data. Open Quantitative Sociology & Political Science.
Kirkegaard, E. O. W. (2014a). Crime, income, educational attainment and employment among
immigrant groups in Norway and Finland. Open Differential Psychology. Retrieved from

http://openpsych.net/ODP/2014/10/crime-income-educational-attainment-and-employment-
among-immigrant-groups-in-norway-and-finland/
Kirkegaard, E. O. W. (2014b). The international general socioeconomic factor: Factor analyzing
international rankings. Open Differential Psychology. Retrieved from
http://openpsych.net/ODP/2014/09/the-international-general-socioeconomic-factor-factor-
analyzing-international-rankings/
Kirkegaard, E. O. W. (2015a). An S factor among census tracts of Boston. The Winnower. Retrieved
from https://thewinnower.com/papers/an-s-factor-among-census-tracts-of-boston
Kirkegaard, E. O. W. (2015b). Examining the S factor in Mexican states. The Winnower. Retrieved
from https://thewinnower.com/papers/examining-the-s-factor-in-mexican-states
Kirkegaard, E. O. W. (2015c). Examining the S factor in US states. The Winnower. Retrieved from
https://thewinnower.com/papers/examining-the-s-factor-in-us-states
Kirkegaard, E. O. W. (2015d). Finding mixed cases in exploratory factor analysis. The Winnower.
Retrieved from https://thewinnower.com/papers/finding-mixed-cases-in-exploratory-factor-
analysis
Kirkegaard, E. O. W. (2015e). IQ and socioeconomic development across Regions of the UK: a
reanalysis. The Winnower. Retrieved from https://thewinnower.com/papers/1419-iq-and-
socioeconomic-development-across-regions-of-the-uk-a-reanalysis
Kirkegaard, E. O. W. (2015f). The S factor in Brazilian states. The Winnower. Retrieved from
https://thewinnower.com/papers/the-s-factor-in-brazilian-states
Kirkegaard, E. O. W. (2015g). The S factor in the British Isles: A reanalysis of Lynn (1979). The
Winnower. Retrieved from https://thewinnower.com/papers/the-s-factor-in-the-british-isles-a-
reanalysis-of-lynn-1979
Kirkegaard, E. O. W., & Fuerst, J. (2014). Educational attainment, income, use of social benefits, crime
rate and the general socioeconomic factor among 71 immigrant groups in Denmark. Open
Differential Psychology. Retrieved from http://openpsych.net/ODP/2014/05/educational-
attainment-income-use-of-social-benefits-crime-rate-and-the-general-socioeconomic-factor-
among-71-immmigrant-groups-in-denmark/

Kirkegaard, E. O. W., & Tranberg, B. (2015). What is a good name? The S factor in Denmark at the
name-level. The Winnower. Retrieved from https://thewinnower.com/papers/what-is-a-good-
name-the-s-factor-in-denmark-at-the-name-level
Kura, K. (2013). Japanese north–south gradient in IQ predicts differences in stature, skin color, income,
and homicide rate. Intelligence, 41(5), 512–516. http://doi.org/10.1016/j.intell.2013.07.001
List of Japanese prefectures by population. (2015, October 5). In Wikipedia, the free encyclopedia.
Retrieved from https://en.wikipedia.org/w/index.php?
title=List_of_Japanese_prefectures_by_population&oldid=684253537
List of regions of Japan. (2015, October 14). In Wikipedia, the free encyclopedia. Retrieved from
https://en.wikipedia.org/w/index.php?title=List_of_regions_of_Japan&oldid=685759253
List of sovereign states and dependent territories by population density. (2015, December 6). In
Wikipedia, the free encyclopedia. Retrieved from https://en.wikipedia.org/w/index.php?
title=List_of_sovereign_states_and_dependent_territories_by_population_density&oldid=6940
70862
List of U.S. states by population density. (2015, December 4). In Wikipedia, the free encyclopedia.
Retrieved from https://en.wikipedia.org/w/index.php?
title=List_of_U.S._states_by_population_density&oldid=693714204
Lynn, R. (1979). The social ecology of intelligence in the British Isles. British Journal of Social and
Clinical Psychology, 18(1), 1–12. http://doi.org/10.1111/j.2044-8260.1979.tb00297.x
Lynn, R. (1980). The social ecology of intelligence in France. British Journal of Social and Clinical
Psychology, 19(4), 325–331. http://doi.org/10.1111/j.2044-8260.1980.tb00360.x
Lynn, R., & Cheng, H. (2013). Differences in intelligence across thirty-one regions of China and their
economic and demographic correlates. Intelligence, 41(5), 553–559.
http://doi.org/10.1016/j.intell.2013.07.009
Revelle, W. (2015). psych: Procedures for Psychological, Psychometric, and Personality Research
(Version 1.5.4). Retrieved from http://cran.r-project.org/web/packages/psych/index.html
Rindermann, H. (2007). The g-factor of international cognitive ability comparisons: the homogeneity
of results in PISA, TIMSS, PIRLS and IQ-tests across nations. European Journal of

Personality, 21(5), 667–706. http://doi.org/10.1002/per.634