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The relationship between intelligence and creativity has been subject to empirical research for decades. Nevertheless, there is yet no consensus on how these constructs are related. One of the most prominent notions concerning the interplay between intelligence and creativity is the threshold hypothesis, which assumes that above-average intelligence represents a necessary condition for high-level creativity. While earlier research mostly supported the threshold hypothesis, it has come under fire in recent investigations. The threshold hypothesis is commonly investigated by splitting a sample at a given threshold (e.g., at 120 IQ points) and estimating separate correlations for lower and upper IQ ranges. However, there is no compelling reason why the threshold should be fixed at an IQ of 120, and to date, no attempts have been made to detect the threshold empirically. Therefore, this study examined the relationship between intelligence and different indicators of creative potential and of creative achievement by means of segmented regression analysis in a sample of 297 participants. Segmented regression allows for the detection of a threshold in continuous data by means of iterative computational algorithms. We found thresholds only for measures of creative potential but not for creative achievement. For the former the thresholds varied as a function of criteria: When investigating a liberal criterion of ideational originality (i.e., two original ideas), a threshold was detected at around 100 IQ points. In contrast, a threshold of 120 IQ points emerged when the criterion was more demanding (i.e., many original ideas). Moreover, an IQ of around 85 IQ points was found to form the threshold for a purely quantitative measure of creative potential (i.e., ideational fluency). These results confirm the threshold hypothesis for qualitative indicators of creative potential and may explain some of the observed discrepancies in previous research. In addition, we obtained evidence that once the intelligence threshold is met, personality factors become more predictive for creativity. On the contrary, no threshold was found for creative achievement, i.e. creative achievement benefits from higher intelligence even at fairly high levels of intellectual ability.
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The relationship between intelligence and creativity: New
support for the threshold hypothesis by means of empirical
breakpoint detection
Emanuel Jauk
, Mathias Benedek, Beate Dunst, Aljoscha C. Neubauer
Department of Psychology, University of Graz, Austria
article info abstract
Article history:
Received 1 August 2012
Received in revised form 12 March 2013
Accepted 14 March 2013
Available online xxxx
The relationship between intelligence and creativity has been subject to empirical research for
decades. Nevertheless, there is yet no consensus on how these constructs are related. One of the
most prominent notions concerning the interplay between intelligence and creativity is the
threshold hypothesis, which assumes that above-average intelligence represents a necessary
condition for high-level creativity. While earlier research mostly supported the threshold
hypothesis, it has come under fire in recent investigations. The threshold hypothesis is commonly
investigated by splitting a sample at a given threshold (e.g., at 120 IQ points) and estimating
separate correlations for lower and upper IQ ranges. However, there is no compelling reason why
the threshold should be fixed at an IQ of 120, and to date, no attempts have been made to detect
the threshold empirically. Therefore, this study examined the relationship between intelligence
and different indicators of creative potential and of creative achievement by means of segmented
regression analysis in a sample of 297 participants. Segmented regression allows for the detection
of a threshold in continuous data by means of iterative computational algorithms. We found
thresholds only for measures of creative potential but not for creative achievement. For the former
the thresholds varied as a function of criteria: When investigating a liberal criterion of ideational
originality (i.e., two original ideas), a threshold was detected at around 100 IQ points. In contrast, a
threshold of 120 IQ points emerged when the criterion was more demanding (i.e., many original
ideas). Moreover, an IQ of around 85 IQ points was found to form the threshold for a purely
quantitative measure of creative potential (i.e., ideational fluency). These results confirm the
threshold hypothesis for qualitative indicators of creative potential and may explain some of the
observed discrepancies in previous research. In addition, we obtained evidence that once
the intelligence threshold is met, personality factors become more predictive for creativity. On the
contrary, no threshold was found for creative achievement, i.e. creative achievement benefits from
higher intelligence even at fairly high levels of intellectual ability.
© 2013 Elsevier Inc. All rights reserved.
Threshold hypothesis
Segmented regression
Breakpoint detection
1. Introduction
1.1. The relationship between intelligence and creativity
Although empirical creativity research can meanwhile look
back on a scientific tradition of over 60 years of investigation, it
is still unclear how the concepts of creativity and intelligence
relate to each other (Kaufman & Plucker, 2011). Sternberg and
O'Hara (1999) provide a general framework for researchers
encompassing five possible relationships: Intelligence and
Intelligence 41 (2013) 212221
Corresponding author at: Department of Psychology, University of Graz,
Maiffredygasse 12b, 8010 Graz, Austria. Tel.: +43 316 380 5120; fax: +43
316 380 9811.
E-mail addresses: (E. Jauk), (M. Benedek),
(B. Dunst), (A.C. Neubauer).
0160-2896/$ see front matter © 2013 Elsevier Inc. All rights reserved.
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creativity can either be seen as a subset of each other, they may
be viewed as coincident sets, they can be seen as independent
but overlapping sets, and lastly as completely disjoint sets.
Though there exists evidence in favor of each of these
perspectives (Kaufman & Plucker, 2011), several influential
models of intelligence treat creativity as a lower order factor of
intelligence (e.g., divergent production in Guilford's structure-
of-intellect model; Guilford, 1967), retrieval ability in Carrol's
three-stratum model (Carrol, 1993), or imaginativeness in the
Berlin model of intelligence structure (Bucik & Neubauer, 1996;
Jäger, 1982). These models thus assume a substantial correla-
tion between creativity and intelligence. Guilford (1967) was
one of the first to discover that this correlation may vary at
different levels of cognitive ability: He found a positive linear
relationship in the lower to average IQ range while there was
no correlation at above-average levels of intelligence. Guilford
concluded that the pattern of bivariate distribution of the cases
suggests that although high IQ is not a sufficient condition for
high DP [divergen t production] ability, it is almost a necessary
condition (p. 168). The notion that high intellectual ability is a
necessary condition for high creativity has become popular as
threshold hypothesis.
1.2. Creativity
Creativity is a concept of individual differences which is
intended to explain why some people have higher potential to
provide new solutions to old problems than others. It leads us
to change the way we think about things and is conceived as
the driving force that moves civilization forward (Hennessey &
Amabile, 2010). Creativity is usually examined at different
conceptual levels. One of the most general distinctions to be
made is the one between creative potential as opposed to
creative achievement (Eysenck, 1995). Creative potential refers
to the individual's ability to generate something novel and
useful (Sternberg & Lubart, 1999) and reflects a normally
distributed trait (Eysenck, 1995). In turn, creative achievement
refers to the actual realization of this potential in terms of
real-life accomplishments (such as having made a scientific
discovery, written a novel etc.; cf., Carson, Peterson, & Higgins,
2005). Although different authors use different terminologies
such as Little-C vs. Big-C (cf., Kaufman & Beghetto, 2009)to
describe this dichotomy, it seems that the underlying taxon-
omy is the same.
Creative potential is usually assessed by means of tests that
measure divergent thinking ability (Runco, 2010)suchasthe
Torrance Test of Creative Thinking (TTCT; Torrance, 1966), the
Guilford tests (Wilson, Guilford, & Christensen, 1953), or the
Wallach and Kogan tests (Wallach & Kogan, 1965). Divergent
thinking (DT) is hereby defined as the kind that goes off in
different directions (Guilford, 1959, p. 381). Accordingly,
divergent thinking tests involve open problems for which a
variety of possible solutions can be found. A widely used DT task
is the alternate uses task in which participants are instructed to
find creative uses for everyday objects (for example: brick
use for karate demonstration etc.) (Kaufman, Plucker, & Baer,
2008). DT tests can be scored with respect to different criteria
usually involving ideational fluency, i.e. the quantity of ideas
produced, and/or originality, i.e. the quality of ideas. However,
these scores are commonly found to be correlated to an extent
that their discriminative validity has been questioned (Hocevar,
1979; Michael & Wright, 1989; Silvia et al., 2008). This is
especially true when a summative originality scoring is em-
ployed where originality may directly increase with the num-
ber of ideas (i.e., ideational fluency). However, alternative
scorings of ideational originality, which control for fluency by
either dividing originality by fluency or by considering a
constant number of ideas, no longer show this problem
(Benedek, Mühlmann, Jauk, & Neubauer, 2013; Hocevar,
1979; Silvia et al., 2008).
Creative achievement is commonly assessed by means of
self-reports such as biographical questionnaires in which par-
ticipants indicate their achievements across diverse domains
(e.g., literature, music, or theatre). A popular example is the
Creative Achievement Questionnaire (CAQ; Carson et al., 2005).
The CAQ and related measures were found to have good
psychometric properties (Silvia, Wigert, Reiter-Pa lmon, &
Kaufman, 2012) and successfully discriminate between more
and less creative persons (Vellante et al., 2011). Moreover,
intelligence significantly predicts CAQ scores (Carson, Peterson,
& Higgins, 2003; Kéri, 2011).
Meta-analytic findings suggest that the correlation between
creative potential and intelligence generally is around r =.20
(Kim, 2005). Besides its relationship to intelligence, personality
correlates of creative potential have been extensively studied.
The most consistent and significant finding is that creative
potential is positively related to openness to experiences (cf.,
Batey & Furnham, 2006; Feist, 2010). Openness is thought to
reflect an investment trait relevant to creative potential
(Chamorro-Premuzic & Furnham, 2005). Moreover, openness
can be associated with actual creative achievement (King,
Walker, & Broyles, 1996). Open people are imaginative and
curious, which forms a good basis for creative endeavors across
all domains. On the contrary, the relationship to other per-
sonality traits such as conscientiousness or neuroticism strongly
depends on the investigated domain. While conscientiousness
may be promotive of scientific creativity, artistic creativity is
related to emotional instability (Batey & Furnham, 2006).
1.3. The threshold hypothesis
The basic idea behind the threshold hypothesis is that high
creativity requires high or at least above-average intelligence. At
this, above-average intelligence is thought to form a necessary
but not a sufficient condition for high creativity (Guilford, 1967).
More specifically, it is assumed that there exists a threshold in
intelligence which is usually set to an IQ of 120. While creativity
should be limited by intelligence below this threshold, differ-
ences in intelligence should be no longer relevant to creativity
above it. Accordingly, the threshold hypothesis predicts a cor-
relation between measures of creativity and IQ only in low to
average IQ samples, whereas there should be no correlation in
groups of higher IQ.
Studies investigating the threshold hypothesis focused pre-
dominantly on the relationship between intelligence and crea-
tive potential rather than creative achievement (for reviews
see Kaufman & Plucker, 2011; Kim, 2005). Early studies inves-
tigating the relationship between intelligence and creativity
showed that highly creative individuals are also of higher
intelligenc e (Barron, 1963, 1969; Getzels & Jackson, 1962).
Fuchs-Beauchamp, Karnes, and Johnson (1993) investigated the
threshold hypothesis in preschoolers and found correlations
213E. Jauk et al. / Intelligence 41 (2013) 212221
between intelligence and creative potential ranging from r =.19
to r = .49 for a subsample with an IQ below 120. In a subsample
above that level, none of the coefficients exceeded r = .12. In
secondary school children, a significant correlation between
intelligenc e and creative potential of r =.30wasfoundwhileno
significant correlations emerged when gifted children were
selected (Yamamoto, 1964). In a later study, correlations of r =
.50 and r = .20 were reported below and above an IQ threshold
of 120, respectively (Yamamoto, 1966). Recently, a threshold
effect was found using measures of verbal and figural creative
potential in a sample of adolescents and adults (Cho, Nijenhuis,
van Vianen, Kim, & Lee, 2010). Correlations between intelligence
and creative potential of up to r =.40 were observed in an
average IQ sample while correlations in the higher IQ sample
equaled zero. Sligh, Conners, and Roskos-Ewoldsen (2005)
reported a slight threshold effect for crystallized intelligence
while an inverse threshold effect was found for fluid intelligence.
However, other studies did not spot a threshold effect (Kim,
2005; Preckel, Holling, & Wiese, 2006; Runco & Albert, 1986;
Wallach & Kogan, 1965). Preckel et al. (2006) investigated the
threshold hypothesis in a sample of about 1300 gifted and
normal schoolchildren. They found correlations between pro-
cessing capacity and ideational fluency ranging from r =.3to
r = .4 at all levels of cognitive ability. After controlling for speed
of information processing, the correlations of intelligence and
ideational fluency were markedly reduced, but still no group
differences were found. Thus, the results did not support the
threshold hypothesis.
A meta-analysis estimated mean correlations below and
above an IQ of 120 to be r = .20 and r = .23, respectively,
and therefore rejected the threshold hypothesis (Kim, 2005).
Correlations between the two constructs were markedly
lower when the type of creativity test was taken into account
as a moderator: Like in an early study of Wallach and Kogan
(1965), non-speeded tests were practically uncorrelated with
Turning from creative potential to creative achievement, no
evidence for an intelligence-threshold was found in recent
investigations: In a large-scale longitudinal study of intellectu-
ally gifted youth, Scholastic Aptitude Test scores of age 13 were
used to predict creative real-life outcomes in a 20 year
follow-up. Individual differences in the upper range of intellec-
tual ability predicted creative occupational accomplishments
(Wai, Lubinski, & Benbow, 2005) as well as achievement in the
arts and science (Park,Lubinski,&Benbow,2007). Moreover,
intellectual ability was found to predict scientific creativity even
within groups of equal qualification (Park, Lubinski, & Benbow,
2008). Thus, individual differences in intelligence are highly
relevant to real-life achievement not only the in general pop-
ulation (e.g., Kéri, 2011) but also within high-ability groups.
1.4. Methodological considerations for investigating the thresh-
old hypothesis
Recently, Karwowski and Gralewski (2013) tested the
threshold hypothesis in light of different methodological con-
siderations. The authors proposed three possible criteria in
order to accept or reject the threshold hypothesis by means of
the correlational approach: The most liberal criterion would be
a significant positive correlation below the threshold and an
insignificant correlation above it. As a more conservative
criterion, there should be a significant positive correlation
below the threshold that is significantly higher than the
correlation above the threshold. The most conservative test
would be to claim a significant positive correlation below, an
insignificant correlation above the threshold, and a significant
difference between both of them. The authors investigated the
threshold hypothesis at different levels of intelligence (107.5,
115, and 120 IQ points) and found a threshold effect most likely
to be observed at an IQ of 115 when considering the most
conservative criterion.
Taken together, investigations of the relationship be-
tween intelligence and creative potential provide a scattered
view: While some studies support a threshold effect, others
report low to moderate positive correlations throughout the
whole spectrum of intellectual ability. One possible reason
for the seemingly contradictory empirical findings could be
the different conceptions and measures of creative potential
employed by these studies. While some used ideational
fluency as a single quantitative indicator of creative potential,
other studies also included qualitative measures including
ideational originality. At this, recent research indicates that
ideational originality may more strongly draw on intelligence
than ideational fluency (Benedek, Franz, Heene, & Neubauer,
Moreover, Karwowski and Gralewski (2013) point out that
it is not known why the threshold is established at 120 points
rather than a few IQ points more or less (p. 25). In fact, it seems
that none of the sources that are usually quoted when the
threshold hypothesis is concerned (e.g., Guilford, 1967) explic-
itly assert that the threshold should be fixed at an IQ of 120. It
hence appears that, even in absence of any empirical evidence
for an IQ-threshold at 120, this very specific assumption of the
threshold hypothesis has hardly ever been questioned or
examined thoroughly.
1.5. The present research
This study aims at the identification of a possible threshold
in the intelligencecreativity-relationship by means of contin-
uous data analysis methods. We applied segmented linear
regression analysis which allows for an empirical test of
whether and where there is a significant shift in a correlation
pattern. Segmented hereby refers to the assumption that a
given regression function Y = f(X) has different parameters in
different segments of the independent variable X.Iterative
computational algorithms are used to estimate a breakpoint ψ
at which parameters of f are most likely to differ.
Segmented regression analysis is common in the field of
epidemiology, where doseresponse-relationships are evalu-
ated in terms of threshold models. It can for instance be
observed that a stressor X has no effect on health outcome Y up
to a certain breakpoint ψ. If the level of X, however, exceeds ψ,
the outcome of a disease has to be expected (Haybach &
Küchenhoff, 1997; Ulm, 1991). Another common application of
segmented linear regression models is the analysis of time-
series data (Wagner, Soumerai, Zhang, & Ross-Degnan, 2002).
Here, X reflects different time points before and after an
intervention and
Y represents the potential outcome. It is
examined if and how an empirically derived breakpoint ψ
corresponds to a theoretically assumed change in outcome Y at
time point X after the intervention.
214 E. Jauk et al. / Intelligence 41 (2013) 212221
In line with the threshold hypothesis, we predicted a
positive linear relationship between intelligence (X) and
creative potential (Y) up to a breakpoint ψ, which should be
followed by an insignificant relationship between X and Y
beyond this breakpoint. We further hypothesized that this
breakpoint ψ exists at an above-average level of general
intelligence (i.e., ψ > 100 IQ points). We investigated three
common indicators of creative potential: Ideational fluency,
ideational originality as measured by a constant number of
ideas (Benedek et al., in press; Silvia et al., 2008), and average
ideational originality. Additionally, we tested whether the
threshold hypothesis also applies to creative achievement. It
was predicted that the threshold hypothesis does not hold
true for creative achievement (Park et al., 2007, 2008; Wai et
al., 2005).
If a significant breakpoint is detected and intelligence does
not predict creative potential beyond it, it would be of particular
interest to further examine which other constructs can explain
variance in creative potential above the threshold. Therefore,
we also tested whether correlations of creativity and person-
ality variables are affected by potential intelligence-thresholds.
2. Method
2.1. Participants
In order to obtain a heterogeneous and not solely academic
sample, we recruited participants via a local newspaper as well
as the university's mailing lists. Inclusion criteria were an age
between 18 and 55 years, German as mother tongue, and the
absence of neurological and/or mental disorders. After exclud-
ing one person due to excessive missing data, the sample
consisted of 297 respondents (101 males) with an average age
of 30.40 years (SD = 10.68). 16% of the participants had at
least nine years of schooling, 60% had at least twelve years of
schooling, and 24% had a university degree. Participants were
paid for taking part in the study.
2.2. Assessment of intelligence
General intelligence (g) was assessed by means of four
subtests of the Intelligence Structure Battery (Intelligenz-
Struktur-Batterie, INSBAT; Arendasy et al., 2004). The four
computer based tests were selected to reflect a broad rep-
resentation of g including figural-inductive reasoning (figural
induktives Denken; FID), verbal short-term memory (verbales
Kurzzeitgedächtnis; VEK), arithmetic flexibility (arithmetische
Flexibilität; NF), and word meaning (Wortbedeutung; WB).
The FID is a 3 × 3 matrices test in which eight geometric
patterns which differ according to a set of rules are shown.
The task is to find the correct sequel out of eight response
alternatives. In the NF test, participants are to solve equations
with missing arithmetic operators. In the VEK test, partici-
pants have to remember a bus route. The route is graphically
displayed and the name of each bus station is visible for a
short period of time. In the WB test, participants have to decide
which of four alternatives closest matches the meaning of a
target word.
The INSBAT is based on item response theory (IRT) and
allows for tailored testing. Target reliability for each scale was
set to α = .60, which results in an average of 10 items per
test, or an average duration of 10 min per test. The INSBAT is
theoretically grounded on the CattellHornCarroll model of
intelligence (for an overview see McGrew, 2009) involving a
g-factor as well as five secondary factors, including fluid (g
and crystallized (g
) intelligence (for details see Arendasy et
al., 2004). The estimate of g used in this study is based on the
factor loadings of the INSBAT subtests, which means that g is
most strongly predicted by g
. The reported intelligence
scores reflect standardized IQ scores.
2.3. Assessment of creative potential
Creative potential was measured by means of three
alternate uses (AU) tasks and three instances (IN) tasks. In
the alternate uses tasks, participants were required to find as
many novel and uncommon uses as possible for a can,aknife,
and a hairdryer. In the instances tasks, participants were
instructed to figure out many novel and uncommon solutions
to the problems What can make noise?, What can be
elastic?, and What could one use for quicker locomotion? The
tasks were administered on a PC and participants were
required to enter their ideas via a keyboard. Each task lasted
for two minutes. After completion of each task participants
were asked to rank their responses with respect to creativity.
Four students (three female) rated originality of re-
sponses (similar to the consensual assessment technique
proposed by Amabile (1982) given in both the AU and the IN
task on a four-point scale ranging from 1 not creative to 4
very creative. Mean interrater-reliabilities were ICC = .80
in the alternate uses tasks and ICC = .69 in the instances
We computed three common scores of creative potential.
Ideational fluency was defined as the number of ideas given in
the task. For the assessment of ideational originality we used
two different scores which avoid the typical confound with
ideational fluency. First, we computed a Top 2 originality score,
which reflects the creativity ratings of the two most original
responses according to the participant's ranking (cf., Silvia et
al., 2008). Second, we also computed an average originality
score, which reflects the mean creativity ratings of all ideas.
2.4. Assessment of creative achievement
We administered a newly devised measure of creative
achievement, the Inventory of Creative Activities and
Achievements (ICAA; see also Jauk, Benedek, & Neubauer,
under review). The ICAA measures everyday creative
activities as well as actual creative achievements with two
different scales. The ICAA achievements scale is similar to the
CAQ (Carson et al., 2005), but has less extreme distributional
properties (Jauk, Benedek, & Neubauer, under review) thus
making it more suitable for breakpoint detection. Across eight
domains (literature, music, arts and crafts, creative cooking,
sports, visual arts, performing arts, and science and engineer-
ing) of creative accomplishment, participants are presented
with statements ranging from I have never been engaged in
this domain (zero points) to I have already sold some of my
work in this domain (10 points). Internal consistency of the
ICAA achievements scale across domains was satisfactory
(α = .71).
215E. Jauk et al. / Intelligence 41 (2013) 212221
2.5. Assessment of personality
Personality structure was assessed by means of the Big-Five
Structure Inventory (Big-Five Struktur Inventar, BFSI; Arendasy,
Sommer, & Feldhammer, 2011). The BFSI measures the Big Five
personality dimensions with six facets each. The test is based on
IRT and could be shown to have good correlations with the
German Big Five questionnaire NEO-PI-R, while internal con-
sistency is even higher (Arendasy et al., 2011). Each of the 30
facets is assessed with ten items. The test was administered
without time restriction.
2.6. Procedure
The experiment took place in a computer laboratory
where groups of up to 10 participants performed all tests on a
standard desktop computer. Two experimenters explained
the procedure and were present during the whole session.
Since this study was part of a larger screening for further
investigations, participants also completed motivation scales
and a speed of information processing task.
The order of tasks was the same for all participants. After
completing a sociodemographic questionnaire and motiva-
tion scales, they performed the INSBAT taking about 50 min.
After a short break of 15 min, they worked on the speed of
information processing task, the tasks of creative potential,
the creative achievement questionnaire, and finally the BFSI
personality inventory (for 20 min). The total test session took
about 2.5 h. The study was approved by the Ethics Commit-
tee of the University of Graz.
2.7. Data analyses
We computed creative potential (CP) scores by averaging
over the scores of the six divergent thinking tasks. The internal
consistency was α = .88 for the fluency score, α =.63forthe
Top 2 originality score, and α = .75 for the average originality
score. The internal consistency would have been lowered by
the exclusion of any single task.
All measures of intelligence and creative potential were
normally distributed (KolmogorovSmirnov-tests: Z
CP: Fluency
CP: Top 2
CP: Average
0.76, ns). As predicted by theory (Eysenck, 1995; Simonton,
1999), creative achievement displayed positive skewness and
kurtosis (Z
=2.13,p b .01; skewness = 1.78, kur-
tosis = 4.66). Descriptive statistics and intercorrelations of all
measures are shown in Table 1.Thedatawerecheckedfor
outliers in the multivariate distribution of the IQ score with each
of the creative potential and achievement measures by means of
Mahalanobis distance as well as Cook's distance. For analyses
involving the fluency score and the Top 2 originality score, one
person was excluded due to an excess of Mahalanobis distance
from the centroid of the multivariate distribution at p b .001.
For the creative achievement score, four persons were excluded
due to an excess of Mahalanobis distance. No influential data
points were detected by means of Cook's distance (all Ds b 0.1).
Prior to applying the segmented regression analyses, the
relationships between intelligence and the measures of creative
potential as well as creative achievement were tested for
nonlinearity. To this end, we set up hierarchical multiple
regression models to examine whether a squared intelligence
variable can explain incremental variance in creative potential
or achievement over and above the linear term (cf. Coward &
Sackett, 1990; Karwowski & Gralewski, 2013). Collinearity of
the predictors was avoided by means of residual centering
(Lance, 1988). The squared predictor term was found to explain
a significant incremental amount of variance for fluency and
Top 2 originality, respectively (CP
: ΔR
= .01. p b .05;
: ΔR
= .02. p b .01), and it also tended to explain
incremental variance for the criterion of average originality
: ΔR
= .01. p = .08). In all cases, beta weights were
negative indicating a decrease in slope as predictor scores
increase. However, the squared intelligence term did not
predict incremental variance in creative achievement (ΔR
.00. p = .72). Thus, this relationship is likely to be linear.
2.8. Segmented regression method
The segmented regression analyses were performed with
the open statistic software R (version 2.15.0) using the
segmented package (Mueggo, 2008). IQ served as the indepen-
dent variable, and each of the measures of creative potential
and achievement served as the dependent variable. The
algorithm has to be supplied with one or more initial guess
parameter(s) for the breakpoint(s). We used an initial guess
parameter of ψ
= 100 IQ points.
Empirically determined breakpoints were tested for
statistical significance by means of the Davies test (Davies,
Table 1
Descriptive statistics and intercorrelations of intelligence, creativity, and personality measures.
Min Max M (SD) 2345678910
IQ (1) 59.27 147.37 107.21 (14.63) .22
.08 .14
.06 .07
CP: Fluency (2) 4.17 27.17 12.37 (3.89) .15
.02 .28
.11 .17
.00 .08
CP: Top 2 originality (3) 1.31 2.54 2.04 (0.21) .75
.01 .10 .16
CP: Average originality (4) 1.45 2.16 1.82 (0.12) .21
.05 .08 .14
Creative achievement (5) 0 208 40.72 (35.15) .10 .22
.03 .03
Neuroticism (6) 2.30 3.20 0.04 (0.75) .48
Extraversion (7) 2.43 2.28 0.13 (0.81) .53
Openness (8) 2.07 2.03 0.16 (0.78) .31
Agreeableness (9) 2.27 2.83 0.00 (0.80)
Conscientiousness (10) 2.15 2.46 0.05 (0.89)
Note. N = 297. Big five personality measures reflect person parameters according to the IRT model. CP: creative potential.
p b .05.
p b .01.
216 E. Jauk et al. / Intelligence 41 (2013) 212221
1987). This test estimates the probability of a significant
change in slope (H
) under the assumption that the breakpoint
parameter ψ vanishes under H
. The Davies test has to be
supplied with a number of K equally spaced evaluation points
between the 5 and 95% quantiles of the independent variable.
According to common recommendations this parameter was
set to K =7 (Mueggo, 2008). Significance tests were per-
formed two-tailed at α = .05.
3. Results
3.1. Segmented regression analyses
Segmented regression analyses were computed for all three
criteria of creative potential and for creative achievement.
For the criterion of ideational fluency, a breakpoint was
detected at an IQ of 86.09 points. This breakpoint is
statistically significant according to the Davies test for a
change in the slope (p b .05; 95% CI = 75.5796.61 points).
The bivariate correlations (i.e., standardized βs) between
intelligence and ideational fluency were r = .56 (p b .01,
n = 21) below the breakpoint of 86.09 IQ points and r = .09
(ns, n = 275) above it. These correlations differed signifi-
cantly according to Steiger's z -test (z = 2.23, p b .05). The
breakpoint model is shown in Fig. 1a.
For creative potential assessed by means of the Top 2
originality score, a significant breakpoint was detected at an
IQ of 104.00 points (p b .05; 95% CI = 93.07114.90 points).
The bivariate correlations between intelligence and creative
potential were r = .38 (p b .01, n = 121) below the
breakpoint and r = .14 (ns, n = 175) above it and differed
significantly (z = 2.17, p b .05). The scatter plot with the
segmented relationship is shown in Fig. 1b.
When the average originality was considered as a
criterion, the breakpoint was estimated at an IQ of 119.60
points. This breakpoint, however, failed to reach statistical
significance in the Davies test (p = .14; 95% CI = 107.5
131.7). Nonetheless, again, a significant correlation between
intelligence and creative potential was obtained for the lower
IQ range (r = .35, p
b .01, n = 232), but not for the upper IQ
range (r = .01, ns, n = 65). These correlation coefficients
were significantly different (z = 2.62, p b .01). Fig. 1c shows
the scatterplot containing the segmented linear relationship.
Finally, segmented regression analysis was also performed
for the criterion of creative achievement (although no non-
linear relationship was observed; see above). In line with the
test of nonlinearity, no significant breakpoint was detected
(p = .64). The linear model is shown in Fig. 1d.
3.2. Multiple regression analyses
Since a statistically significant threshold for creative
potential (Top 2 originality score) could be detected at an IQ
of 104.00 points, we performed separate multiple regression
analyses for subsamples below and above this threshold.
General intelligence and the personality dimensions openness
to experiences, conscientiousness, and agreeableness were
entered as predictors since these variables showed significant
60 80 100 120 140
1.4 1.6 1.8 2.0 2.2 2.4
CP: Top 2 originality
60 80 100 120 140
1.5 1.6 1.7 1.8 1.9
CP: Average originality
60 80 100 120 140
Creative Achievement
60 80 100 120 140
10 15 20 25
CP: Fluency
Fig. 1. Breakpoint models for the fluency score (a), the Top 2 originality score (b), and the average originality score (c). Linear model for creative achievement (d).
Horizontal lines indicate 95% CI of the breakpoint. CP: creative potential.
217E. Jauk et al. / Intelligence 41 (2013) 212221
zero-order correlations with the criterion (neuroticism and
extraversion could not explain a significant increment in var-
iance: ΔR
IQ b 104
= .03, ns; ΔR
IQ > 104
= .03, ns). The enter-
method was used in regression analyses. All variables showed
normal distribution by means of the KS-test; there was no
indication of multi-collinearity (Tolerance > 0.6; VIF b 1.5) and
the residuals showed no visible heteroscedasticity.
Results for the two independent regression models are
shown in Table 2. Both models were statistically significant
(IQ b 104: F[4, 116] = 7.15, p b .01, R
[4,170] = 4.34, p b .01, R
= .07). Below the IQ-threshold,
creative potential is significantly predicted by IQ and consci-
entiousness, but not by openness. In contrast, above the
IQ-threshold intelligence and conscientiousness are significant
predictors only by trend, whereas now openness is the
strongest predictor of creative potential. Despite weak signif-
icant zero-order correlations in the total sample, agreeableness
does not significantly predict creative potential in both re-
gression analyses of IQ subsamples, which is most likely due to
the reduced sample size.
Separate regression analyses were not performed for crea-
tive potential as defined by average originality or ideational
fluency since the subsamples above 119.60 and below 86.09 IQ
points, respectively, were too small to allow for a powerful
analysis. As there was no threshold for creative achievement
we also did not compute separate regression analyses for this
4. Discussion
While it is largely acknowledged that the constructs of
intelligence and creativity are related, the exact nature of
their interplay is still under debate (Kaufman & Plucker,
2011). The prominent threshold hypothesis proposes that a
certain minimum level of intelligence is a necessary condi-
tion for creativity. However, extensive tests of this hypothesis
showed inconsistent results and the suggested threshold of
120 IQ points represents, at best, an educated guess. We
investigated the threshold hypothesis by means of segment-
ed regression analysis aiming for an empirical determination
of the potential threshold between intelligence and creativ-
ity. To our knowledge this is the first report of an application
of this method in the context of the threshold hypothesis of
4.1. The threshold effect
In line with the threshold hypothesis, we found evidence
for a segmented linear relationship between intelligence and
creative potential. Intelligence significantly predicted crea-
tive potential in a lower IQ range but not in the upper IQ
range. Hence, the correlation between intelligence and crea-
tive potential appears to be moderated by the level of
intelligence. Moreover, the actual level of the threshold was
found to depend on the applied measure of creative potential.
For the quantitative criterion of ideational fluency we ob-
tained a rather low IQ threshold of 86.09 points. In contrast,
IQ thresholds for qualitative measures of creative potential
were higher: When ideational originality was defined by the
two most creative ideas in divergent thinking tasks (cf., Silvia
et al., 2008), the relationship between intelligence and crea-
tive potential showed a threshold at 104.00 IQ points. When
the average originality of all ideas was considered, the estimate
of 119.60 points did actually perfectly match the often
mentioned threshold of 120 IQ points. The Davies test for
differences in slope was not significant but correlations still
differed significantly. The data hence still meet the most
conservative criterion as proposed by Karwowski and
Gralewski (2013): A significant positive relationship below
the threshold, no significant correlation above it, and a
significant difference between both.
How could the observed discrepancy between the IQ
thresholds of 86, 104 and 120 IQ points be explained?
Considering first the thresholds of the qualitative measures of
creative potential, the most straightforward interpretation
would be that it simply needs higher intelligence to produce
a series of original ideas than just two of them. The
observation that the IQ threshold when predicting ideational
fluency is around 85 IQ points further supports this notion:
While one has to have at least above-average intelligence to
produce original ideas, producing a higher quantity of ideas
(disregarding their quality) seems easier to manage. Given a
necessary minimum of intelligence of about 1 standard
deviation below the population mean or higher, no signifi-
cant correlation between ideational fluency and cognitive
ability can be observed anymore. This result is well in line
with the finding that intelligence is more predictive of
ideational originality than of fluency (Benedek et al., 2012).
The unusually strong correlation of r = .56 below this
threshold also indicates that the low correlation of r = .22
in the total sample may merely be caused by the high
covariance in the low ability range.
The differences in thresholds for different measures of
creative potential might also help to explain discrepant
findings of studies using only ideational fluency as a single
indicator of creative potential and thereby disregarding the
quality of ideas. When considering only fluency, the absence
of a threshold at 120 is well in line with our data. As Batey
and Furnham (2006) conclude:
Eminent samples are a
highly select population who must possess certain abilities
over and above fluent DT to achieve success. This discrepancy
may be partly resolved by looking to quality rather than
quantity of responses to traditional DT tests (p. 367). Indeed,
the threshold hypothesis does not predict that one needs
intelligence in order to produce many ideas of unknown
quality, but that one needs a certain intellectual capacity in
order to produce creative ideas.
But what are the mechanisms by which intelligence
fosters creative potential? Past research suggests that these
mechanisms include the adoption of smart strategies, high
Table 2
Multiple regression analyses predicting creative potential by IQ and
personality factors for subsamples below and above an IQ of 104.
Predictor IQ b 104 IQ > 104
β p β p
IQ .37 .00 .14 .06
Openness .12 .23 .25 .00
Agreeableness .07 .45 .12 .13
Conscientiousness .21 .04 .13 .10
Note. n
IQ b 104
= 121, n
IQ > 104
= 175.
218 E. Jauk et al. / Intelligence 41 (2013) 212221
cognitive control and broad knowledge. Creative idea generation
is a complex task which involves many different strategies for
reframing a problem (Gilhooly, Fioratou, Anthony, & Wynn,
2007). It was shown that it can depend on intelligence whether
such strategies really result in higher creative performance
(Nusbaum & Silvia, 2011). Moreover, there is increasing evi-
dence that the relationship of creative potential and intelligence
is mediated by executive processes such as cognitive inhibition
and switching (Benedek et al., 2012; Nusbaum & Silvia, 2011).
Effective executive processes may support effective retrieval
from semantic knowledge and thus help to inhibit predominant
responses and to access remote and unrelated semantic concepts
which can be combined to form creative ideas (Benedek, Könen,
& Neubauer, 2012; Benedek & Neubauer, 2013). Finally, many
creative problems strongly draw on verbal abilities and general
knowledge. Crystallized intelligence was found to show higher
correlatio ns with specific measures of creative potential than
other components of intelligence (Cho et al., 2010). It hence can
be assumed to play an important role for the elaboration of ideas
and for challengin g verbal creativ e processes such as the creation
of metaphors (Silvia & Beaty, 2012).
We found evidence for an IQ threshold with respect to
creative potential, but not for creative achievement. Our
results thus suggest that intelligence fosters creative achieve-
ment across the whole range of intellectual ability. This is in
line with previous studies reporting that IQ is predictive of
creative achievement even within high ability groups (Park
et al., 2007, 2008; Wai et al., 2005). Moreover, intelligence
and creative potential were found to be concurrently pre-
dictive of creative achievement (Plucker, 1999). It hence can
be concluded that the threshold hypothesis only holds true
for indicators of creative potential but not for creative
achievement. Finally, this result pattern provides evidence
for the sensitivity but also the specificity of the employed
analysis strategy.
4.2. Personality predictors of creative potential
When performing separate multiple regression analyses
in samples of lower and higher intelligence, we found that
openness to experiences predicts creative potential in the
subsample above the threshold whereas conscientiousness is
negatively related to creative potential in the lower IQ range.
While it is well documented that that there exists a
positive association between openness and creative potential
(Batey & Furnham, 2006; Feist, 2010; King et al., 1996), the
present result points to an interaction between intelligence
and openness: High creative potential is not possible with a
low level IQ; but once the intelligence threshold is met,
openness may explain to some extent whether the required
cognitive disposition is actually turned into high creative
potential. Past research showed that openness influences
crystallized intelligence via the path of fluid intelligence
(Ziegler, Danay, Heene, Asendorpf, & Bühner, 2012) and thus
can be viewed as an investment trait ( Chamorro-Premuzic
& Furnham, 2005). Moreover, King et al. (1996) found that a
combination of high creative potential and high openness is
predictive for creative achievement. Although further re-
search is needed to clarify the relationship between these
constructs, it could be hypothesized that high intelligence
and high openness predict creative potential, which, in turn,
predicts creative achievement.
In the below-average IQ sample, low conscientiousness
predicted creative potential in addition to general intelligence.
Batey, Chamorro-Premuzic, and Furnham (2010) also found
conscientiousness to be negatively related to self-reported
ideational behavior. Analyses of the facets of conscientiousness
showed that deliberation predicted ideational behavior nega-
tively while competence was associated positively. The authors
interpret their findings in the way that ideational behavior may
be characterized by an inability to restrain impulses. Moreover,
the relationship between conscientiousness and creativity may
depend upon the investigated sample: While artists are of
lower conscientiousness than non-artists, scientists are gener-
ally more conscientious. More creative scientists, however,
show higher levels of facets that reflect low conscientiousness
than less creative scientists (i.e., direct expression of needs and
psychopathic deviance; Feist, 1998).
Taken together, our results point to different constella-
tions of traits that are relevant to creative potential in lower
and higher IQ samples: While divergent thinking ability may
be supported by a lack of conscientiousness, i.e. impulsive
creativity, in lower intelligent persons, higher creative
potential in more intelligent individuals may stem from
higher openness to experiences. Higher openness may foster
the acquisition of a broader general knowledge and thus
support creativity (Cho et al., 2010).
4.3. Limitations and conclusions
An important point for studies investigating the threshold
hypothesis is the IQ range of the tested sample. It is usually
considered adequate to compare lower vs. higher IQ samples
for a powerful detection of an IQ threshold in creative potential
(cf., Preckel et al., 2006). In the case of creative achievement,
even highly selective groups of very intelligent individuals have
been extensively studied (cf., Park et al., 2007, 2008; Wai et al.,
2005). The present study used a naturalistic sample showing a
continuous normal distribution of intelligence. This sample still
included about twice as many participants with an IQ above 120
points (60 persons, or 20%) than would be expected when
drawing a random sample of 300 persons. While an even more
selective sample may be suitable to discriminate among the
very brightest, this study made the attempt to perform an
unbiased detection of potential thresholds within the typical
range of intelligence (cf., Karwowski & Gralewski, 2013).
Moreover, since the tests used in this study were able to detect
significant thresholds, statistical power could be considered
sufficient. Further studies are still needed to test the robustness
of the obtained threshold estimates.
Recent research points to the relevance of crystallized
intelligence with regards to the threshold hypothesis (Cho et
al., 2010; Sligh et al., 2005). Since the intelligence test battery
administered in the present study was assembled in order to
obtain a broad and reliable measure of g it is not suited to
decompose the effects of fluid and crystallized intelligence.
Future research could employ segmented regression analyses
to examine the threshold hypothesis in more detail with
respect to lower order factors of intelligence.
Summarizing, intelligence is highly relevant for creativity,
but the kind of relationship depends on the level of intelligence
219E. Jauk et al. / Intelligence 41 (2013) 212221
as well as on the actual indicator of creativity. In line with early
assumptions, intelligence may increase creative potential up to
a certain degree where it loses impact and other factors come
into play. At this, it possibly applies that the more complex the
measure of creativity that is considered, the higher the
threshold up to which intelligence may exert its influence. For
the most advanced indicator of creativity, namely creative
achievement, intelligence remains relevant even at the highest
ability range.
This research was supported by a grant from the Austrian
Science Fund (FWF): P23914. The authors wish to express
their gratitude to Michaela Lenzhofer and Martin Wammerl
as well as Maike Sitter for their help in organizing and
conducting the test sessions. Moreover, we are grateful to the
students of the University of Graz who rated the originality of
responses. The helpful comments of the journal editor and
the anonymous reviewers are gratefully acknowledged.
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... Gifted children are children with high IQs, and are superior to normal children in cognitive ability. They usually have high creative potential Angela and Caterina 2020), but some of them do not show a high creative achievement level (Jauk et al. 2013). This might be because some of them do not have enough creative self-efficacy. ...
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Creative self-efficacy is a type of individual creative self-belief, which is an important predictor of creative activities and achievements. For gifted children who have high creative potential, the influencing factors of their creative self-efficacy need to be further explored. This study aimed to explore the relationship between gender, emotional intelligence, self-esteem, and creative self-efficacy in gifted children, with special attention on the mediating role of self-esteem and the moderating role of gender in the relationship between emotional intelligence and creative self-efficacy. Participants in this study included 226 gifted students aged 10–13 (135 boys and 91 girls) from experimental classrooms designed for gifted students in North China. The creative self-efficacy scale (CSE), the emotional intelligence scale (EIS), and the self-esteem scale (SES) were tested. The statistical results indicate that: (1) emotional intelligence significantly positively predicted creative self-efficacy in gifted children; (2) self-esteem partially mediated the link between emotional intelligence and creative self-efficacy; and (3) gender acted as a moderator for the mediation model, in which self-esteem played a complete mediating role in gifted boys, while the mediating role of self-esteem in gifted girls was not significant. The results of this study reveal the influential mechanism of creative self-efficacy in gifted children of different genders and may provide further implications for promoting the creative potential of gifted children.
... Not only would the connection be original, but the inventiveness of the new connection provides a new perspective to the data, information, and/or knowledge that is being connected and (potentially) to the field of study as a whole. The other important note to this representation is that the byproduct of creativity tends to lead to more discussions about the elements that make up the connection (Jauk et al., 2013). ...
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The discipline of information studies is one of those areas that I enjoy teaching. I had the pleasure of teaching "IS 200 Information Literacy and Critical Thinking" during my post-doc at the University of Kentucky. One of the areas that I wish I could have done early in the development of this course was craft a primer on information studies terminology that helped establish what some of the baseline terms were given in the context of this course. This primer would have assisted discussions, since the primer laid out the groundwork for the direction of future readings the students would have needed to complete. The article (though almost a decade late) would have served this purpose.
... However, intelligence ceases to predict creative accomplishment above a certain point, although the precise breakpoint is unknown. Jauk et al. (2013) found that several different IQ breakpoints are reported in the literature, but that it is often unclear where these exact threshold values come from. Their own empirical estimation lands at IQ scores of 85 for fluency, 104 for originality of the top two responses, and 119 for average originality. ...
Performances on tests of creativity have been found to be in decline in the USA. Here, we explore scores on divergent thinking tests in private schools in Khartoum State in Sudan by comparing a 2005 and a 2018 administration of the Torrance Standardized Circles test to 8- to 12-year-olds of both sexes. We find a decline across the period in all three dimensions of the test (Fluency, Flexibility and Originality), as well as in the overall index of divergent thinking. In line with much previous research, females consistently outperform males. Examining previous studies that report Negative Flynn Effects on IQ in Arab countries, we conclude that our results most likely reflect highly localized and exclusively environmental causes, and caution against assuming that the same processes that underlie Negative Flynn Effects in the West, whether on IQ or any trait correlated with it, also underlie it in the Arab World.
This study aims to unearth the influence of students’ intelligence (IQ) on their academic achievement (AA) in a mediated mechanism. Following the theoretical essence, the present study analysed cross‐sectional data in Bangladesh and China using a self‐administered survey. A sample of 287 from Bangladesh (study 1) and 317 from China (study 2) showed that IQ does not influence creativity (CR) but AA. In effect, the direct and indirect (mediating) effects of CR on AA are not supported. Surprisingly, the impact of IQ on CR is significant through the mediating effect of creative self‐belief. The findings contribute to advancing and extending the knowledge gap in developing countries as these observed variables were witnessed as being Western‐biased. Furthermore, this study also contributes to formulating policies for higher educational policymakers to involve students in positive initiatives so that they can feel tempted to engage in creative practice.
Creativity is critical to economic growth and societal progress. However, assessing creativity using objective approaches remains a challenge. To address this, we employ three objective indicators based on semantic distance to quantify the originality and appropriateness of creativity by analyzing long texts in a story‐writing experiment. Global and local distances were generated separately by computing the mean distance of the whole text and the distance between adjacent sentences, and they were positively correlated with story originality in writing. Global cohesion was positively correlated with story rationality in writing, as generated by computing the semantic coherence between the text and story context. At the behavioral level, three semantic indicators were used to measure originality and appropriateness of creativity and reflected individual differences, including creative achievement and creative personality. At the neural level, global distance was best predicted by the features of the salience and default networks, whereas global cohesion corresponded to the control and salience networks. These findings point to a stable neural basis for semantic indicators and verify the idea of separating different dimensions of creativity. Taken together, our results demonstrate the significance of semantic indicators in assessing creativity and provide insights into analyzing long texts in natural paradigm. Our findings add a new perspective on semantic distance to assess creativity in story writing, by generating three semantic indicators to quantify originality and appropriateness at behavioral and neural levels. We also identify distinguishable functional connectivity patterns for objective assessments of creativity. This provides evidence that the default mode network and executive network contribute differently to creative idea generation and evaluate.
In this chapter, the first section is discussed. The overall purpose of the section is to provide information to readers regarding the evolution of mathematical creativity, to provide information regarding the arrangement of the book, and to discuss some seminal concepts relevant to the research in the book.KeywordsCreativityDevelopmentIntelligenceMathematical creativityRight brain
This chapter examines how individual creativity and teamwork impact team creativity in part through self-efficacy mechanisms. At the team level, it examines the role played by creative collective-efficacy and teamwork collective-efficacy mechanisms in a team’s creative performance. It concludes that the individual differences leading to fit with the creative task may differ from those leading to fit with teamwork. That is, individuals may prefer creative tasks due to relatively high creative self-efficacy and relatively good performance on creative tasks but may not want to work in teams because of low teamwork self-efficacy and low performance as a team player. However, while traits are stable, efficacy beliefs can be positively influenced by managers. Therefore, interventions aimed at building efficacy beliefs are useful when organizations cannot select individuals solely according to a set of desirable stable trait characteristics.
This book provides a comprehensive state-of-the-art review of personality and intelligence, as well as covering other variables underlying academic and occupational performance. Personality and Intellectual Competence is a unique attempt to develop a comprehensive model to understand individual difference by relating major personality dimensions to cognitive ability measures, academic and job performance, and self-assessed abilities, as well as other traditional constructs such as leadership and creativity. It will be essential reading for anyone interested in personality, intelligence, and the prediction of future achievement in general. Personality and Intellectual Competence is an outstanding account of the relationship between major individual differences constructs. With its informative summary of the last century of research in the field, this book provides a robust and systematic theoretical background for understanding the psychological determinants of future achievement. The authors have sought to combine technical expertise with applied interests, making this a groundbreaking theoretical tool for anyone concerned with the scientific prediction of human performance. © 2005 by Lawrence Erlbaum Associates, Inc. All rights reserved.
In this first section, an overview of the remaining seven divisions of the chapter is presented. The second section affords a brief description of categories of instrumentation to provide the reader with a foundation within which the psychometric issues in the assessment of creativity can be viewed. In the third section, psychometric concerns pertaining to construct validity, content validity, and criterion-related validity are addressed. Subsequent to an abbreviated review of the meaning of reliability, concerns regarding optimal approaches to the estimation of reliability of creativity measures are considered in the fourth section. The impact upon reliability and validity of scoring procedures is examined in the fifth section with particular emphasis on the presence of fluency as a confounding factor in the interpretation of scores of measures of divergent thinking. The sixth section provides a survey of a number of the difficulties encountered in establishing normative data for the understanding of scores on measures of creativity. A cursory exploration of a few selected issues in the administration of tests of creativity follows in the seventh section, and the eighth section contributes a concluding statement.
Suppose that the distribution of a random variable representing the outcome of an experiment depends on two parameters xi and theta and that one wishes to test the hypothesis xi = 0 against the alternative xi > 0. If the distribution does not depend on theta when xi = 0, standard asymptotic methods such as likelihood ratio testing or C(α) testing are not directly applicable. However, these methods may, under appropriate conditions, be used to reduce the problem to one involving inference from a Gaussian process. This simplified problem is examined and a test which may be derived as a likelihood ratio test or from the union-intersection principle is introduced. Approximate expressions for the significance level and power are obtained.