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The Negative Religiousness-IQ Nexus is a Jensen Effect on Individual-Level Data: A Refutation of Dutton et al.’s ‘The Myth of the Stupid Believer’

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  • Ulster Institute for Social Research

Abstract and Figures

A recent study by Dutton et al. (J Relig Health 59:1567–1579. https://doi.org/10.1007/s10943-019-00926-3, 2020) found that the religiousness-IQ nexus is not on g when comparing different groups with various degrees of religiosity and the non-religious. It suggested, accordingly, that the nexus related to the relationship between specialized analytic abilities on the IQ test and autism traits, with the latter predicting atheism. The study was limited by the fact that it was on group-level data, it used only one measure of religiosity that measure may have been confounded by the social element to church membership and it involved relatively few items via which a Jensen effect could be calculated. Here, we test whether the religiousness-IQ nexus is on g with individual-level data using archival data from the Vietnam Experience Study, in which 4462 US veterans were subjected to detailed psychological tests. We used multiple measures of religiosity—which we factor-analysed to a religion-factor—and a large number of items. We found, contrary to the findings of Dutton et al. (2020), that the IQ differences with regard to whether or not subjects believed in God are indeed a Jensen effect. We also uncovered a number of anomalies, which we explore.
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Vol.:(0123456789)
Journal of Religion and Health
https://doi.org/10.1007/s10943-021-01351-1
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ORIGINAL PAPER
The Negative Religiousness‑IQ Nexus isaJensen Effect
onIndividual‑Level Data: ARefutation ofDutton etal.s ‘The
Myth oftheStupid Believer’
EdwardDutton1· EmilKirkegaard2
Accepted: 15 July 2021
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature
2021
Abstract
A recent study by Dutton etal. (J Relig Health 59:1567–1579. https:// doi. org/ 10.
1007/ s10943- 019- 00926-3, 2020) found that the religiousness-IQ nexus is not on
g when comparing different groups with various degrees of religiosity and the
non-religious. It suggested, accordingly, that the nexus related to the relationship
between specialized analytic abilities on the IQ test and autism traits, with the latter
predicting atheism. The study was limited by the fact that it was on group-level data,
it used only one measure of religiosity that measure may have been confounded by
the social element to church membership and it involved relatively few items via
which a Jensen effect could be calculated. Here, we test whether the religiousness-
IQ nexus is on g with individual-level data using archival data from the Vietnam
Experience Study, in which 4462 US veterans were subjected to detailed psycho-
logical tests. We used multiple measures of religiosity—which we factor-analysed to
a religion-factor—and a large number of items. We found, contrary to the findings
of Dutton etal. (2020), that the IQ differences with regard to whether or not subjects
believed in God are indeed a Jensen effect. We also uncovered a number of anoma-
lies, which we explore.
Keywords Religion· Intelligence· Cognitive ability· Jensen effect· Differential
item functioning· Local structural equation models· Item response theory
* Edward Dutton
e.c.dutton@dunelm.org.uk
Emil Kirkegaard
emil@emilkirkegaard.dk
1 Asbiro University, Lodz, Poland
2 Ulster Institute forSocial Research, London, UK
Journal of Religion and Health
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Introduction
Many studies have found a weak negative relationship between religiousness
and IQ. The first studies reporting this finding were published in the 1920s (e.g.
Gilkey, 1924; Howells, 1928), and it has been replicated ever since. Meta-analy-
ses have shown that this relationship is in the region of 0.2, in the general pop-
ulation, when using ‘religious belief’ as a measure, and 0.1 when employing
‘religious attendance’ (e.g. Zuckerman etal., 2013). A recent meta-analysis has,
once more, found that the relationship between religious belief and IQ is approxi-
mately − 0.2 (Zuckerman etal., 2020), and a meta-analysis of measures of reflec-
tive thinking similarly found a negative association of 0.18 (Pennycook etal.,
2016). This relationship has also been replicated using the very large OKCupid
dataset with 33–37 k subjects in the main regressions (Kirkegaard & Lasker,
2020) using a religiousness factor based on five questions. The standardized beta
in the final model (controlling for age, sex, race, sexual orientation, and coun-
try/state) was− 0.24. Similar weak negative correlations are also found between
many measures of religiousness and assorted proxies for intelligence, such as
education level and salary (Meisenberg etal., 2012). The religious groups that are
more fundamentalist (more fervent and dogmatic in their religious beliefs) tend to
have lower average IQ than do groups that are more religiously liberal (Nyborg,
2009).
A variety of theories have been developed to explain this consistent relation-
ship such as: (1) everybody needs the certainty of a consistent worldview and
if people are insufficiently intelligent to follow a purely scientific one then they
will retreat into religion (Nyborg, 2009). (2) The arguments for God’s existence
are illogical, meaning that intelligent people would be better able to see through
them (Dutton, 2014). (3) We are adapted to the Savanna, which is ‘evolutionarily
familiar’, where we solved problems using instinct and there we developed reli-
gious belief or, at least, belief in a spiritual universe. Moving off the Savanna, we
could no longer solve problems using instinct, so had to use intelligence. Thus,
intelligent people are attracted to other ‘evolutionarily novel’ ways of thinking,
such as atheism (Kanazawa, 2012). (4). A component of problem-solving, and
thus of intelligence, involves the ability to rise above our instincts, no matter
which ecology they have derived from, and test out non-instinctive, superficially
odd possibilities in pursuit of solving a problem. Intelligent people will, there-
fore, be attracted to multiple unusual ways of thinking, including atheism (Dutton
& Van der Linden, 2017). Proponents of these models reject the idea that secular
ideologies are more logical than belief in God, arguing that both involve non-
empirical dogmas and an implicit belief in fate, and also by cautiously defending
versions of William James’ ‘pragmatic argument’ for believing in God (Dutton
& Van der Linden, 2017). But the problem with each of these explanations is
that they assume that the nexus really does relate to intelligence; that it is on the
highly heritable and core intelligence ability known as g (general intelligence;
Jensen, 1998), and not just on specialized skills. However, a recent study has
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Journal of Religion and Health
provided cautious evidence that the nexus is not on g. The relationship is not a
so-called Jensen effect.
Dutton etal. (2020) have analyzed two large data sets from the Netherlands,
allowing them to compare the IQs of groups with different levels of religious-
ness, including those who were atheists and agnostics. They found that the reli-
giousness-IQ nexus was not on g, meaning that it related to specialized abilities
rather than to general intelligence. This study can be argued to have provided
evidence that the relationship is not on g, at least when comparing religious and
non-religious samples from the same ethnic group within a particular country.
Evidently, the study’s main limitation is its use of group-level data rather than
individual data. It is also potentially limited by the nature of the data, which
involved IQ tests being administered to groups of church members, agnostics,
and atheists. This is because there is a social element to church membership and
attendance, with intelligence predicting general engagement with civic activities
(Rindermann etal., 2012). In addition, it is limited by the fact that it uses only
one method of ascertaining religious belief (church membership or otherwise),
it does not give people the chance to indicate the extent of their religious belief,
and, moreover, even if it had done, belief in God is only one aspect of religious
belief; with religions tending to involve a much more complex theology. A sec-
ond problem with the Dutton etal. study is that the power is likely to be very low.
The groups compared typically had sample sizes in the 100s, and the gaps were
very small, often about 2 IQ points.
A third problem was unearthed when we carried out a simulation study to esti-
mate the statistical precision of the Dutton etal. study. We did this by simulating
data from the hypothesized true case where g gaps entirely account for group gaps
(i.e. the true Jensen correlation is 1.0). We furthermore varied sample size and the
gap size. To maximize the comparability with the prior study, we used the same
g-loadings as reported in their tables, 10 and 9g-loadings, respectively, for the GIT
and EMS test batteries. For each simulation setting, we simulated 100 results. Fig-
ure1a, b shows the results.
It can be seen that at small sample sizes and at small gap sizes, the distribution
of correlations seen is not close to their true value of 1.0. Thus, the method has a
downwards bias as a function of gap size and sample size. This means that any study
based on small gaps or with small sample sizes or both is likely to produce at best
uninformative or at worst misleadingly negatively biased results. Most of the results
in Dutton etal.’s analysis come from a single dataset with six group comparisons.
The sample sizes in Dutton etal.’s two samples varied across the comparisons, but
they ranged from a total of 190 to 544, and with gaps of about 0.7 to 5.9 IQ, thus at
best about d = 0.40 (non-members vs. Roman Catholics, gap = 5.85 IQ, combined
n = 378, r = 0.49). The average was about 320 people, thus at best 160 peopleper
group, and a 3 IQ gap (d = 0.2). As a consequence of these values, the statistical pre-
cision of Dutton etal.’s results is likely to be very low, and the results thus mislead-
ing. The results in their final and large comparison (almost 9k cases, thus at best
about 4.5k per group) were based on a group difference of about 2 IQ points, again,
too small for useful precision. Our results are in line with prior simulation analyses
of this method, showing that it has some known biases (Sorjonen etal., 2017). Thus,
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their method suffers from a serious problem, casting doubt on whether their conclu-
sions are accurate.
If Dutton etal.’s findings could be replicated using individual-level data and with
a less problematic method, then this could be said to relatively conclusively prove
Fig. 1 ab Simulation results for Jensen’s method. d refers to the gap size between two equal-sized
groups. The upper plot is based on GIT g-loadings, and the bottom plot is based on EMS loadings. Val-
ues copied from Dutton etal. Blue line is the LOESS fit. LOESS locally estimated scatterplot smoothing,
a nonlinear smoothing function. (Color figure online)
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Journal of Religion and Health
that the negative religiousness-IQ nexus is not on g. This would be further strength-
ened if this was found on different aspects of religiosity—such as practice as against
belief—as well as on different elements of religious belief. Accordingly, in this
study, we set out to replicate the findings of Dutton etal. using individual-level data,
as well as using multiple means of measuring religiosity.
Method
We used archival data from the Vietnam Experience Study (VES, https:// www. cdc.
gov/ nceh/ veter ans/ defau lt1c. htm). This is a large longitudinal study of 4,462 US
veterans (3,654 whites, 200 Hispanics, 525 blacks, 49 Native Americans, and 34
Asians). In terms of race, the sample was, therefore, roughly representative of the
US population at the time: 82% white, 12% black, 4% Hispanic, 1 Native Ameri-
can, and 1% Asian. VES is a longitudinal dataset of male US military personnel
who were inducted in the period 1965 to 1971. There was an extensive follow-up in
1985–1986, approximately 18years after initial contact. The dataset was made as a
case–control study of the effects of Agent Orange (chemical warfare) in the Vietnam
War. Consequently, about 65% of the sample are Vietnam veterans and the rest were
stationed elsewhere (e.g. Germany or Japan). Details of the recruitment and find-
ings can be found in (The Centers for Disease Control Vietnam Experience Study,
1988a, 1988b, 1988c). The dataset includes data from 19 different cognitive tests.
These have been described in detail in several previous papers and include measures
of verbal reasoning, arithmetic, spatial ability, psychomotor ability, and memory
(Kirkegaard & Nyborg, 2020; Nyborg & Jensen, 2000, 2001). At the follow-up, the
mean age was 38 (SD 2.5).
Cognitive abilities were measured both in the initial wave and the follow-up
wave. Two of the tests were given twice. The tests were as follows:
1. Grooved Pegboard Test (GPT, right hand): A measure of manual dexterity and
fine motor speed (Ruff & Parker, 1993). The speed score is the reciprocal of the
number of seconds taken to place a set of pegs in a grooved hole as quickly as
possible.
2. GPT (left hand).
3. Paced Auditory Serial Addition Test (PASAT): A measure of mental control,
speed, and computational and attentional abilities (Tombaugh, 2006). The sub-
ject mentally adds a sequence of numbers in rapid succession. Score is the total
number of correct responses.
4. Rey-Osterrieth Complex Figure Drawing (CFD): A measure of visio-spatial
ability and memory (Shin etal., 2006). The direct copy score (CFDD) is given
from a subject reproducing a complex spatial figure, while the figure is in full
view.
5. CFD, copy from immediate recall. The immediate recall score (CFDI) is given
from a subject reproducing a complex spatial figure immediately after being
shown it.
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6. CFD, copy from delayed recall. The delayed recall score (CFDL) is given from
a subject being exposed to a complex spatial figure and, after 20min of other
activities, drawing it.
7. Wechsler Adult Intelligence Scale-Revised (WAIS-R), general information
(Leckliter etal., 1986). A test of general knowledge.
8. WAIS-R, block design. A test of spatial ability.
9. Word List Generation Test (WLGT). A measure of verbal fluency. The subject
generates as many words as possible which begin with the letters F, A, and S
for 60s. The score is the total number of words generated.
10. Wisconsin Card Sort Test (WCST). A measure of executive function (Greve
etal., 2005). The score is the ratio of correct responses to countable responses.
11. Wide Range Achievement Test (WRAT). Measures ability to read aloud a list
of single words (untimed) (Witt, 1986).
12. California Verbal Learning Test (CVLT). A measure of verbal learning and
memory (Elwood, 1995). The subject recalls a list of 16 words over five repeated
learning trials. The score is the total correct over five trials.
13. Army Classification Battery (ACB). A verbal test administered at induction
(ACBVE) (Bayroff & Fuchs, 1970).
14. ACB verbal. Administered at the follow-up interview (ACBVL).
15. ACB arithmetic reasoning test. An arithmetic test administered at induction
(ACBAE).
16. ACB arithmetic. Administered at the follow-up interview (ACBAL).
17. Pattern Analysis Test (PAT). A measure of pattern recognition administered at
induction.
18. General Information Test (GIT). A test of general knowledge administered at
induction.
19. Armed Forces Qualification Test (AFQT). A general aptitude battery. This
measure is the total score on four subtests (word knowledge, paragraph com-
prehension, arithmetic reasoning, and mathematics knowledge) administered at
induction.
Five of the tests (13, 15, 17–19) were given at induction and the remaining at the
follow-up interview.
In the second wave, the Minnesota Multiphasic Personality Inventory (MMPI) was
administered (1975 version; Dahlstrom etal., 1975). This is a questionnaire of 566
statements that individuals marked as either true or false. This battery was designed to
measure various aspects of mental health as well as some other traits (e.g. masculin-
ity–femininity). We searched the list of statements for items related to religiousness and
found 12 items, shown in Table1.
We then split the questions into two categories: those six that were purely related
to beliefs (58, 115, 249, 258, 373, and 483), and the rest. The remaining set of ques-
tions contain behavioural (e.g. frequency of reading the Bible), personality (e.g. lack
of patience for unbelievers), or socially comparative elements (e.g. more religious than
others).
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Journal of Religion and Health
Results
We scored intelligence using exploratory factor analysis of the 19 tests, as done
in prior studies using the same dataset (Kirkegaard & Nyborg, 2020; Nyborg
& Jensen, 2000, 2001). Before analysis, we imputed the missing data using the
IRMI algorithm in the vim package (Templ etal., 2015). The g factor accounted
for 42% of the variance (minimum residuals method, scored by the regression
method, using the psych package for R (Revelle, 2020)). Factor loadings are
given in Table2 (further down). Figure2 shows the distribution of scores, which
was roughly normal.
The religious data were based on dichotomous (binary) indicators, thus necessi-
tating a more complex method. We used item response theory-based factor analysis,
as implemented in the mirt package for R (Chalmers etal., 2020). We scored two
versions of this, one with all the 12 items, and one based only on the six items con-
cerned with beliefs (pure set). Both analyses showed a strong general factor based
on a positive manifold (full set 56% variance, and 66% for the pure set). The empiri-
cal internal reliabilities were estimated at 0.84 and 0.68 (based on mirt’s empiri-
cal_rxx() function). Figure3 shows the distributions. For the full set, the scores were
roughly normal, except there was a bump on the left tail for the non-religious. The
pure set was less normal.
Religiousness was negatively correlated with intelligence: 0.18 for the total
score and − 0.21 for the pure scale (both p < 0.001, SE = 0.0153). Figure4a, b shows
the relationships.
The relationship was mostly linear but with evidence of diminishing returns on
the left tail for the pure scale (p = 0.0006, likelihood ratio test when compared to
a natural spline model). If we take this finding seriously, it seems that IQs that are
Table 1 Items used to measure religiousness
Question Item Prevalence Missing
53 A minister can cure disease by praying and putting his hand on your
head
0.08 0.01
58 Everything is turning out just like the prophets of the Bible said it
would
0.5 0.04
95 I go to church almost every week 0.25 0.00
115 I believe in a life hereafter 0.76 0.01
206 I am very religious (more than most people) 0.17 0.00
249 I believe there is a Devil and a Hell in afterlife 0.63 0.01
258 I believe there is a God 0.92 0.01
373 I feel sure that there is only one true religion 0.37 0.01
476 I am a special agent of God 0.09 0.00
483 Christ performed miracles such as changing water into wine 0.77 0.03
490 I read in the Bible several times a week 0.13 0.00
491 I have no patience with people who believe there is only one true
religion
0.27 0.01
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over 100 are more strongly negatively related to religiousness than these below 100,
and IQs below 80 are less positively related to religiousness. This kind of finding
has a parallel using national intelligence data (Lynn etal., 2009). With regard to the
g-loading of the relationship, we used Jensen’s method, as done in the prior meta-
analysis. Figure5a, b shows the results visually, while Table2 gives the numbers.
In contrast to Dutton etal., we find very strong relationships between the g-load-
ing of an item and its negative correlation with religiousness, thus providing sound
evidence that the relationship is mainly or entirely due to the g factor and not due to
other cognitive abilities: r = 0.86 using the religiousness score from the full set,
and r = 0.91 using the pure set scores. Aside from the g-loadedness of the pattern,
one may wonder whether the pattern was due to plausible demographic confounders.
To investigate this, we ran a series of regression models with controls added. Results
are shown in Tables3 and 4.
The person-level regression results show that the relationship is not plausible due
to the confounders considered, including age, race, income, or education. The weak-
est slope is seen with the full religiousness scale, where education and income are
controlled, but even here, the slope is 0.14. Since adding these controls is likely
adjusting for a mediator, this small decrease should not be interpreted strongly.
Furthermore, the standard errors are too large to have certainty that even this small
decrease in the beta is a real change. The models that add interactions between race
and intelligence find suggestive evidence that the relationship is weaker among
blacks for the pure scale [interaction p = 0.008, implied slope among blacks = − 0.08
(− 0.22 + 0.14)]. Figure6a, b shows the marginal effects. It should be noted here that
Table 2 Test-level relationships
to religiousness and factor
loadings
Test g-loading r religiousness r religiousness pure
VE time1 0.82 − 0.20 − 0.23
AR time1 0.81 − 0.14 − 0.18
PA 0.71 − 0.14 − 0.17
GIT 0.69 − 0.19 − 0.20
AFQT 0.85 − 0.18 − 0.21
VE time2 0.82 − 0.17 − 0.20
AR time2 0.82 − 0.13 − 0.17
WAIS BD 0.67 − 0.14 − 0.17
WAIS GI 0.76 − 0.15 − 0.20
WRAT 0.73 − 0.16 − 0.21
PASAT 0.57 − 0.09 − 0.11
WLGT 0.49 − 0.09 − 0.12
Copy direct 0.47 − 0.06 − 0.08
Copy immediate 0.55 − 0.05 − 0.08
Copy delayed 0.55 − 0.05 − 0.08
CVLT 0.42 − 0.04 − 0.06
WCST 0.46 − 0.08 − 0.09
GPT left 0.34 − 0.06 − 0.08
GPT right 0.33 − 0.06 − 0.08
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Journal of Religion and Health
there are also main effects of race, such that blacks are somewhat more religious
than whites at the same level of intelligence (0.29 and 0.20 in the full/pure scale
model, both p’s < 0.001). This result is in line with many previous studies on this
issue (e.g. Fitchett etal., 2007).
Fig. 2 Distribution of IQ scores in the dataset (white = 100/15)
Fig. 3 Distribution of religiousness scores. Based on 12 and 6 items, respectively
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We go further and analyze the item data as well. Item data were available for
four of the cognitive tests (23 items from WAIS-INF, 6 from WAIS-BD, 112 from
CVLT, and 52 from CFD; we excluded items with pass rates below 0.05 or above
0.95). We fit a single factor model using mirt for the items and saved the g-loadings.
Fig. 4 ab Scatterplot of intelligence (g) and religiousness as measured by 12 or 6 items. The orange line
is the linear fit, and the blue line is the LOESS fit
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Journal of Religion and Health
Figure 7a, b shows the relationship between item g-loadings and religiousness
(latent correlation, i.e. polychoric in this case; Uebersax, 2015).
The scatterplots revealed a strong outlying item from the WAIS Information
scale. Religious people perform much better on this item than expected by their level
of intelligence, suggesting that this item has some religious content. In fact, the item
Fig. 5 ab Jensen’s method of correlated vectors used on the 19 cognitive tests for the total score (12
items, top) and pure scale (6 items, bottom)
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Table 3 Regression model results for the full religiousness score (12 items)
White race is the reference group
SES socioeconomic status
*p < .01; **p < .005; ***p < .001
Predictor/model Basic Demographic controls Add interaction Add SES Basic whites Full whites
Intercept 0.01 (0.015, 0.348) − 0.38 (0.221, 0.089) − 0.39 (0.221, 0.079) − 0.51 (0.228, 0.027) 0.00 (0.016, 1) − 0.64 (0.259, 0.013)
G − 0.17
(0.014, < 0.001***)
− 0.15
(0.015, < 0.001***)
− 0.16
(0.016, < 0.001***)
− 0.14
(0.019, < 0.001***)
− 0.16
(0.016, < 0.001***)
− 0.15
(0.021, < 0.001***)
Age 0.01 (0.006, 0.088) 0.01 (0.006, 0.078) 0.01 (0.006, 0.026) 0.02 (0.007, 0.013)
Race = Black 0.15 (0.049, 0.002**) 0.29
(0.077, < 0.001***)
0.14 (0.050, 0.005**)
Race = Hispanic 0.02 (0.071, 0.736) 0.07 (0.094, 0.44) 0.02 (0.072, 0.81)
Race = Asian − 0.23 (0.167, 0.165) − 0.25 (0.169, 0.136) − 0.22 (0.166, 0.186)
Race = Native 0.00 (0.139, 0.973) − 0.09 (0.150, 0.553) − 0.02 (0.140, 0.896)
g* race = Black 0.12 (0.052, 0.019)
g* race = Hispanic 0.07 (0.078, 0.375)
g * race = Asian − 0.10 (0.146, 0.503)
g* race = Native − 0.21 (0.131, 0.115)
Education 0.01 (0.019, 0.696) 0.00 (0.021, 0.928)
Income − 0.05 (0.016,
0.004**)
− 0.04 (0.018, 0.039)
R2 adj 0.034 0.036 0.037 0.038 0.026 0.027
N4462 4462 4462 4376 3654 3580
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Journal of Religion and Health
Table 4 Regression model results for the pure religiousness scale (6 items)
White race is the reference group
SES socioeconomic status
*p < .01; **p < .005; ***p < .001
Predictor/model Basic Demographic controls Add interaction Add SES Basic whites Full whites
Intercept 0.00 (0.015, 0.999) − 0.22 (0.219, 0.315) − 0.24 (0.219, 0.267) − 0.36 (0.225, 0.114) 0.00 (0.016, 0.999) − 0.45 (0.257, 0.081)
G − 0.21
(0.013, < 0.001***)
− 0.20
(0.015, < 0.001***)
− 0.22
(0.016, < 0.001***)
− 0.18
(0.018, < 0.001***)
− 0.22
(0.016, < 0.001***)
− 0.19
(0.021, < 0.001***)
Age 0.01 (0.006, 0.314) 0.01 (0.006, 0.265) 0.01 (0.006, 0.114) 0.01 (0.007, 0.081)
Race = Black 0.05 (0.048, 0.35) 0.20 (0.076, 0.009*) 0.07 (0.050, 0.176)
Race = Hispanic − 0.03 (0.070, 0.694) 0.07 (0.093, 0.454) − 0.01 (0.071, 0.868)
Race = Asian − 0.45 (0.164, 0.007*) − 0.43 (0.167, 0.01*) − 0.43 (0.165, 0.009*)
race = Native 0.00 (0.137, 0.994) − 0.09 (0.148, 0.562) − 0.03 (0.139, 0.853)
g* race = Black 0.14 (0.051, 0.008*)
g * race = Hispanic 0.13 (0.077, 0.081)
g* race = Asian 0.09 (0.144, 0.515)
g* race = Native − 0.18 (0.129, 0.163)
Education − 0.04 (0.018, 0.047) − 0.04 (0.021, 0.051)
Income − 0.02 (0.016, 0.321) − 0.01 (0.018, 0.568)
R2 adj 0.052 0.053 0.054 0.054 0.048 0.048
N4460 4460 4460 4374 3652 3578
Journal of Religion and Health
1 3
asks “What is the main theme of the book of Genesis”? (the first book of the Bible).
Aside from the outlier, the plots revealed a medium-sized negative correlation, in
line with results from the test-level analysis in Figs.5a, b. The relative weakness of
the item-level results compared to the test-level results is perhaps best interpreted as
being due to the increased sampling error in the estimates of the item statistics.
We then replicated our Jensen’s method results using standard approaches
of examining for test bias. Specifically, for the test-level data, we employed local
structural equation modelling (LSEM) to examine for measurement invariance for
a continuous variable (moderator) (Hildebrandt etal., 2016). This is the continuous
analogue of the more common multi-group confirmatory factor analysis approach
(MGCFA) (Frisby & Beaujean, 2015; Lasker etal., 2019). We developed a model
for the 19 tests in the battery. Since no prior theory existed on the topic, we used an
iterative approach using the modification indexes and our professional judgement
(Beaujean, 2014). The model was fit with the lavaan package (Rosseel etal., 2020),
and we used the sirt package for LSEM (Robitzsch, 2020). The model was complex.
We opted for a bi-factor approach with four group factors (verbal, memory, math-
ematics, and visual-spatial ability), two test occasion factors (time 1 and time 2), as
well as 2 covariances. The appendix contains the details of this model. The model
had excellent overall fit to the data RMSEA = 0.040, CFI = 0.985, TLI = 0.978,
GFI = 0.977, SRM r = 0.025. We fit LSEM to the data in the region of 1.5 to 1.5
with a bandwidth factor (h) of 5. Results revealed only minor differences in fit meas-
ures between high and low levels of religiousness, with slightly higher values for
the religious. Figure8 shows an example plot from this, and the full results can be
found in the technical output. The modelled RMSEA was about 0.044 for persons
with 1.5 religiousness and 0.038 for those with 1.5. The other fit measures showed
similar results.
For the items, we used differential item functioning (DIF) testing, as implemented
in the mirt package. Specifically, we tested each cognitive item for differential func-
tioning between each of the 12 religiousness items. We tested for both intercept and
slope (discrimination) differences. We estimated the effect size of the bias using the
approach advocated by (Meade, 2010) and implemented in the empirical_ES() func-
tion in mirt. Results are shown in Table5.
All the DIF analyses found some items with differential functioning, but the
directions were mixed, so the test-level effects were all near 0 (all were below 0.1
d). As a method check, we examined which item was most frequently detected as
bias and found that this was WAIS Information item 18, the same item that was an
outlier in the Jensen’s method analyses in Fig.7a, b, again showing the congruence
of results across methods.
We examined the different indicators of religiousness for differential relationships
to intelligence. Specifically, we used Jensen’s method with the factor analysis results
from the full scale. Results are shown in Fig.9.
There was no detectable association between the religiousness factor loadings
and the item’s relationship to intelligence (r = 0.07). In other words, other factors
than merely the association with overall religiousness were responsible for the asso-
ciation with intelligence at the item level. Examining the results, one can see that
the items related to pure belief matters have stronger (negative) associations, while
1 3
Journal of Religion and Health
those that involve other factors (impure) show near-zero associations, or even posi-
tive (church going). This diversity in associations was not due to demographic con-
founders that we previously examined (Tables3, 4). When we fit regression models
Fig. 6 ab Regression slopes for intelligence on religiousness full scale (12 items, top), and pure scale (6
items, bottom), by race. Adjusted for age
Journal of Religion and Health
1 3
for each of the 12 religiousness items, we find the same patterns as shown in Fig.8,
results shown in Fig.10.
Fig. 7 ab Scatterplot of item g-loadings and item correlations to religiousness total scale (12 items, top)
and pure scale (6 items, bottom)
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Journal of Religion and Health
Fig. 8 LSEM results for religiousness (total scale, 12 items) for RMSEA measure of model fit
Table 5 Results of DIF analysis.
Liberal refers to considering
items as biased when p < .05,
and conservative when this
survived the Bonferroni
correction
Effect size refers to the standardized (Cohen d) effect size at the test
level for the partial fits with the offending items
Test-level effect
size, liberal
Test-level effect
size, conservative
Bad items
liberal
Bad items
conservative
− 0.02 0.01 20 1
− 0.07 − 0.05 56 17
0.01 0.01 27 3
0.00 0.01 23 1
0.00 0.01 10 2
− 0.05 − 0.05 49 13
− 0.08 − 0.06 43 9
− 0.05 − 0.06 68 17
− 0.01 0.00 29 3
− 0.02 − 0.01 29 5
0.01 0.01 23 2
0.03 0.01 28 2
Journal of Religion and Health
1 3
Discussion
It appears, therefore, that this study refutes the findings presented in Dutton etal.
(2020). It reaches very different results due to a different, and superior, method
whereby (1) we have a large and representative individual-level data set (2) we are
not dealing simply with church membership, which is an impure measure of religi-
osity, but rather with multiple measures of religiosity which we have also been able
to factor analyse (3) we have a much larger number of intelligence tests and items
allowing us to use Jensen’s method, differential item functioning tests, and local
structural equation modelling with a greater degree accuracy. All the methods agree
on the finding that the religion-IQ nexus is principally concerned with g and thus
one or more of theories presented above for this relationship may well explain it.
It is notable here that Jensen’s method (method of correlated vectors), which has
been criticized for nonsensical results (Wicherts, 2017; Wicherts & Johnson, 2009),
was actually congruent with the item response theory-based results, even detecting
the same highly biased knowledge item. Thus, our study indirectly shows that this
method can produce sensible results with item data, as long as the analysis is done
correctly using item response theory-based metrics (for another example, see Al-
Bursan etal., 2018).1
Fig. 9 Jensen’s method applied to the 12 items from the total religiousness scale. The X axis is the item’s
factor loading on the religiousness factor. The Y axis is the IQ gap between persons who affirm and deny
a given statement. One item was reversed due to negative factor loading (no patience for true believers).
1 This approach was first tested by Kirkegaard (2016) in an unpublished note. However, the problems
with the classical test theory approach and corrections were in fact outlined by Jensen himself (Jensen
1980, p.437 and p.445; Jensen & McGurk 1987).
1 3
Journal of Religion and Health
Many studies on this nexus have looked at a small number of measures of religi-
osity. The variety of religiosity measures we have examined here present us with
a clear point of interest. Church going, in our dataset, is slightly positively asso-
ciated with IQ, though other studies have found a weak negative association. One
possible reason for this is that as religious belief and practice declines in Western
countries, including America as has been widely documented (see Bruce, 2002),
we would expect the relationship between indicators of not being religious—such
as not believing in God or not going to church—to become more weakly associ-
ated with intelligence. The fact that some dimensions of church going—such as its
civic and pro-social nature (see Jensen, 1998)—are positively correlated with intel-
ligence would mean that at some point, this measure would become non-associated
and eventually positively associated with intelligence. This would be strengthened
by extreme liberal Christians who might not really literally believe in God but
might attend church for assorted psychological reasons. In the Church of England,
for example, there are certainly worshippers, and even priests, who do not seem to
believe in God (see Freeman, 1993). On the other hands, if people live in commu-
nities in which the local church is highly influential then they may attend church
despite not believing in God in order to avoid ostracism or to ensure social approval,
something known as extrinsic religiousness (Hills etal., 2004). The other measures
of religiosity which were only very weakly negatively correlated with intelligence,
however, were all issues which would be consistent with being a liberal Christian. A
liberal Christian may well read the Bible frequently. Indeed, reading frequently at all
could be a reflection of intelligence, as smarter people read more in general (Ritchie
Fig. 10 Logistic regression results for 12 indicators of religiousness. Model 1 controlled for nothing
(baseline), model 2 controls for age and race, and model 3 controls for age, race, income, and education
Journal of Religion and Health
1 3
etal., 2015). A liberal Christian may well have vague belief in the afterlife and they
may even regard themselves as ‘very religious’, no matter what other people might
think about them, if being ‘religious’ were a significant component of their iden-
tity in a relatively secular area. By contrast, rural fundamentalist Americans might
not regard themselves as ‘very religious’ because everybody they know is, by ordi-
nary standards, ‘very religious’. Indeed, to complicate matters further, many fun-
damentalist Protestants insist that they are not ‘religious’ at all. Roman Catholics
are ‘religious’, due to their perceived focus on ritual, but fundamentalist Protestants
like themselves, by contrast, are ‘Christian’ (see Dutton, 2008). Thus, ironically,
self-describing as ‘very religious’ in a US dataset may actually indicate that you are
moderately religious.
The measures that were most strongly negatively associated with IQ were all
markers of fundamentalism, such as belief in the Devil or in there only being one
true religion. Intelligence is negatively associated with many of the markers of
fundamentalism beyond mere religiosity including dogmatism, conservatism, and
authoritarianism (Onraet et al., 2015), in that such churches promote strict obedi-
ence to authority (see Barr, 1977). In addition, belief in God among such people
will be absolute. So these relationships make sense in terms of Nyborg’s (2009)
finding that in America, extreme liberal Christian churches have the highest aver-
age IQ—even higher than atheists, as these will include some political ideologues
and extremists with these traits being negatively associated with IQ—and the most
fundamentalist churches have the lowest average IQs. So, this is congruous with
Nyborg’s model whereby, overall, we all need a way to make sense of our world and
those who lack the intelligence to be able to do so using science will turn towards
religion. Kirkegaard and Lasker (2020) replicated Nyborg’s thesis using a large sam-
ple of dating users, finding that within every religious group with sufficient sample
size, the least religious were the highest in intelligence. Consistent with Dutton and
Van der Linden, they may also be less instinctive, due to their intelligence, meaning
that their cognitive bias towards religiosity is lower. More research into the causes
of this relationship would be fruitful, but we hope we have contributed here by com-
prehensively demonstrating that is really a matter of general intelligence.
Study Limitations
The study had a variety of limitations. First, perhaps most notably, all subjects were
male. It is possible that intelligence may relate differently to religiousness in women.
In the meta-analysis by Zuckerman etal. (2020), this was tested and found not to be
the case in several large datasets. As such, this limitation is not a significant concern.
Second, the measures of religiousness were self-reported in a psychiatric ques-
tionnaire. It is conceivable that this might distort the results, depending on any self-
report biases involved in filling this out. We are not aware of this evidence this may
be the case, however. We are also not aware of any study that used other-reported
religiousness and intelligence, to see if the mode of reporting may affect the patterns.
Third, the study was carried out many years ago, with the second wave being
collected in 1985–1986. The USA has then seen a large increase in atheism rates,
1 3
Journal of Religion and Health
whereas it has historically ‘halted behind’ other European-descended countries (Pew
Research Center, 2019). Possibly this change in the distribution of religiousness has
affected the associations with intelligence.
Funding No funding was supplied for this research.
Declarations
Conflict of interest The authors declare no conflict of interest.
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