*Relationship Between Creativity and Intelligence: A Multimethod Investigation of Alternative Theoretical Assumptions in Two Samples of Secondary School Students

Abstract

The threshold hypothesis and the necessary-but-not-sufficient hypothesis represent popular views on the relationship between intelligence and creativity. However, most studies investigating these hypotheses used suboptimal or even inappropriate statistical methods, calling into question the robustness of the available evidence. The ability differentiation hypothesis presents a third theoretical view on the relationship, but ability differentiation studies including creativity measures are scarce. In this study, the relationship between fluid intelligence as a core element of intelligence and divergent thinking as an important indicator of creativity was investigated in two large samples of secondary school students in Germany (N = 1,328, M_age = 14.47; N = 524, M_age = 13.77). Four different statistical approaches were applied (i.e., test for heteroscedasticity, segmented regression analysis, local structural equation modeling, and necessary-but-not-sufficient condition analysis). The results did not support the threshold hypothesis or a nonlinear relationship as predicted by ability differentiation hypothesis and only partially supported the necessary-but-not-sufficient hypothesis.

Keywords

creativity intelligence threshold hypothesis necessary-but-not-sufficient

Intelligence and creativity are important personality traits that receive much public attention. Intelligence can be defined as “the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience” (Gottfredson, 1997, p. 13). It is a powerful predictor of important outcomes such as academic achievement (Zaboski et al., 2018) and socioeconomic success (Strenze, 2007). Creativity can be defined as the ability to create something that is both novel and appropriate (Runco & Jaeger, 2012) and as “a specific capacity to not only solve problems but to solve them originally and adaptively” (Feist & Barron, 2003, p. 63). Creativity is positively associated with academic achievement (Gajda et al., 2017; Vock et al., 2011) and creative accomplishments (Kim, 2008). It is discussed as a major factor in talent development (Subotnik et al., 2011).

The nature of the relationship between intelligence and creativity remains a matter of debate (Plucker & Esping, 2015). As a modestly sized positive correlation between the two constructs has been demonstrated meta-analytically (r = .17; Kim, 2005; r = .25; Gerwig et al., 2021), the most active field of research today focuses on the question of whether the relationship remains the same over the entire ability continuum (Gerwig et al., 2021). The popular threshold hypothesis (Torrance, 1962) proposes that creativity and intelligence are positively related up to a certain intelligence level (i.e., the threshold), above which the association becomes weaker or disappears. A large number of studies have investigated the threshold hypothesis, and the findings are inconsistent (see Kim, 2005, for a meta-analysis and Weiss et al., 2020, for an overview). Theoretical support for the assumption of a threshold is weak (see below). In addition, most of the methods traditionally used to investigate the relationship between intelligence and creativity seem suboptimal to answer this question and have several important weaknesses even beyond the lack of theoretical justification (Molenaar et al., 2010; Weiss et al., 2020). The investigated samples often include only a few individuals of very high ability, which is the most relevant population for the hypothesis. The necessary-but-not-sufficient (NBNS) hypothesis (Guilford, 1967) is the second popular approach to explaining the intelligence-creativity relationship. According to this approach, high levels of creativity cannot be observed in low-intelligence individuals, whereas every level of creativity from high to low can be observed in highly intelligent individuals. Similar to the threshold hypothesis, the statistical methods applied to investigate the NBNS hypothesis have been inadequate (Ilagan & Patungan, 2018; Weiss et al., 2020). The ability differentiation hypothesis (Spearman, 1927) is a third approach that proposes a diminishing relation between general intelligence and any more specific cognitive ability with increasing ability level. Understanding creativity as a cognitive ability, this hypothesis would predict a nonlinear relationship between intelligence and creativity in which both constructs become less related the higher the level of intelligence. However, there is a lack of ability differentiation studies, including creativity measures.

In this article, we investigated the assumptions of all three approaches on the intelligence–creativity relationship with appropriate analytical methods (recently introduced by Ilagan & Patungan, 2018, and Weiss et al., 2020) in two large samples of German secondary school students with an oversampling of highly intelligent students. Despite their shaky empirical basis, the threshold and NBNS hypotheses are widely referred to by practitioners and researchers. Therefore, our aim was to test the hypotheses on the intelligence–creativity relationship in a rigorous and comprehensive manner.

The Threshold Hypothesis

Torrance (1962) was the first to propose a specific threshold in the relationship between creativity and intelligence, above which a higher level of intelligence no longer substantially affects creativity (Figure 1, left panel). He applied Anderson’s (1960) conceptualization of different ability levels as thresholds. Anderson proposed that for any task, there is a threshold of necessary cognitive ability beyond which other factors besides intelligence determine differences in performance. Torrance (1962) examined his own study results and those of others to propose a threshold of 120 IQ points for creativity without a theoretical justification. Since the earliest days of the hypothesis, most investigations have used divergent thinking measures (e.g., Guilford, 1968; Torrance, 1966; Wallach & Kogan, 1965) to represent creativity (e.g., Jauk et al., 2013; Preckel et al., 2006; Runco & Albert, 1986). Divergent thinking is defined as the ability to generate many different solutions to an open problem (Guilford, 1956). It is described as an important indicator of creative potential (e.g., Runco & Acar, 2012; Zeng et al., 2011) and an established predictor of creative achievement (see Kim, 2008, for a meta-analysis).

Figure 1.

Illustration of Different Hypothesized Relationships Between Intelligence and Creativity.

Statistically, the threshold hypothesis has traditionally been investigated by dividing a sample at the assumed threshold and comparing the size of the intelligence–creativity correlations between the resulting groups (e.g., Preckel et al., 2006; Runco & Albert, 1986; Weinstein & Bobko, 1980). Newer studies often employ segmented regression analysis (SRA) instead (e.g., Akhtar & Kartika, 2019; Jauk et al., 2013; Shi et al., 2017). Here, the presence and location of a threshold is determined empirically by repeatedly dividing the ability continuum into two segments at different points and fitting separate regressions to the segments. A breakpoint—and therefore a threshold—is detected if the difference in slopes between two segments reaches statistical significance (Ryan & Porth, 2007). The empirical findings based on these two methods have been mixed, with contradictory and inconclusive results found even in early studies (Runco & Albert, 1986, p. 212). Weiss et al. (2020) reviewed the more recent literature and concluded that “almost as many different thresholds existed as did studies” (p. 5), and in addition, some studies failed to detect any threshold (e.g., Preckel et al., 2006; Sligh et al., 2005). Some studies found different thresholds for different divergent thinking test scores (Jauk et al., 2013; Shi et al., 2017). A meta-analysis found no significant differences in the correlation when comparing samples below IQ 120 (r = .201) and above IQ 120 (r = .235; Kim, 2005). However, Gerwig et al. (2021) argued that meta-analyses are not well suited for examining the hypothesis due to the potentially overlapping intelligence distributions of the samples included in the different IQ-level categories. Overall, the results do not convincingly support the hypothesis and do not allow any firm conclusions about the location of a threshold.

The Necessary-but-not-Sufficient Hypothesis

Guilford (1967) introduced an alternative explanation for the observed diminishing correlations between intelligence and creativity with increasing intelligence. He proposed that intelligence is an NBNS condition for creativity. According to this assumption, low-intelligence individuals can only have low creative ability, whereas high-intelligence individuals can have any level of creative ability, diminishing the correlation in this region of the intelligence distribution. This theoretical assumption can empirically be depicted in a scatterplot characterized by a triangular shape of scatter with an empty top left corner (Figure 1, center panel). Some studies have attempted to test the NBNS hypothesis by performing necessary condition analyses (NCAs; Dul, 2016), finding that intelligence is indeed a necessary condition for creativity (Karwowski et al., 2016, 2017; Shi et al., 2017). In contrast to the threshold hypothesis, the NBNS hypothesis implies a gradual and continuous decrease in the relationship (Guilford & Christensen, 1973).

The Ability Differentiation Hypothesis

A third approach to the relationship between intelligence and creativity, the ability differentiation hypothesis (Spearman, 1927), states that correlations between general intelligence and more specific cognitive abilities decrease with increasing general intelligence. Creativity or, more narrowly, divergent thinking would be expected to be affected by this phenomenon as one of the abilities included in the positive manifold (e.g., Jäger, 1984). According to this hypothesis, intelligence and creativity show a nonlinear relationship that may be best described as negatively quadratic (Tucker-Drob, 2009; in distinction from the piecewise linear relationship implied by a threshold) with higher correlations in less-intelligent persons and decreasing correlations with increasing general intelligence level (Figure 1, right panel). This nonlinear relationship may be due to some central cognitive processes constraining the expression of individual strengths and weaknesses in more specific cognitive abilities in low-intelligence individuals but not in high-intelligence individuals (Detterman, 1999; Kovacs & Conway, 2016). Evidence on the ability differentiation hypothesis comes from studies applying nonlinear or moderated factor analysis to multidimensional intelligence test data. These studies largely supported the ability differentiation hypothesis (e.g., Demetriou et al., 2017; Molenaar et al., 2017; Reynolds, 2013; Tucker-Drob, 2009). However, the analyses are usually applied to a large number of different ability tests and are not specific to the relationship between intelligence and creativity. We are aware of only one study that included measures of divergent thinking and whose results do not support the ability differentiation for measures of divergent thinking (Breit et al., 2020).

Methodological Considerations

Statistical Analyses

The statistical methods previously used to investigate the threshold hypothesis and the NBNS are problematic to the point that they do not allow drawing any robust conclusions. The issues with the methods are described in detail in the Appendix. In response to the problems of the threshold methodology, Weiss et al. (2020) introduced a more flexible approach based on three different methods that allow the investigation of the relationship between creativity and intelligence without being limited to the detection of a threshold. These methods allow for the detection of a possible threshold or a nonlinear relationship. Weiss et al. (2020) used SRA to facilitate the comparison of their results with previous research. In addition, they employed scatterplot analyses, including a test for heteroscedasticity, and local structural equation modeling (LSEM, Hildebrandt et al., 2009, 2016) to investigate the relationship continuously. To investigate the NBNS, Ilagan and Patungan (2018) proposed a new method that we will refer to as NBNSCA (necessary-but-not-sufficient condition analysis). This method solves two main problems of the previously used NCA method (see Appendix) by providing a probabilistic apparatus for statistical inference and by testing the full NBNS.

Construct Operationalization

Not only may the utilized statistical methods affect the results for the relationship between intelligence and creativity but also the way both constructs are measured may. In studies on the intelligence–creativity relationship, intelligence is usually assessed with standardized tests. These differ in the specific cognitive abilities covered; however, classified in the most recent structural model of cognitive abilities (i.e., the Cattell–Horn–Carroll [CHC] model; Schneider & McGrew, 2018), the majority of tests assess general intelligence and the same six broader abilities (Caemmerer et al., 2020). For creativity, measurements are more heterogeneous and involve different cognitive and noncognitive components (Plucker & Makel, 2010). In the investigation of the threshold hypothesis and the NBNS, divergent thinking tests are by far the most commonly used instruments. Divergent thinking, also denoted as divergent production or fluency (Carroll, 1993), can most generally be described as the ability to generate diverse and numerous ideas (Runco, 1991). Divergent thinking tasks ask for generating multiple alternative solutions to open problems and require individuals to produce several responses to a specific prompt within a certain time. High divergent thinking ability cannot guarantee real-world creative achievement because this requires additional processes such as problem analysis and successful implementation of ideas (Zeng et al., 2011). However, psychometric tests of divergent thinking are useful indicators of creative potential (Plucker & Makel, 2010). When using divergent thinking tests in research on the intelligence–creativity relationship, one must be aware that creativity is not assessed comprehensively but instead one of its central cognitive components.

The Present Studies

There is a large body of contradictory and methodically questionable findings on the relationship between creativity and intelligence. Recently, more appropriate methods of analyzing this relationship have been applied to this field of research. In these studies, the analysis protocol introduced by Weiss et al. (2020) was utilized and supplemented by NBNSCA introduced by Ilagan and Patungan (2018) in two large samples of German secondary school students. SRA was used to conduct an exploratory search for a potential threshold, and heteroscedasticity tests as well as LSEM were used to investigate the relationship continuously, testing both the threshold hypothesis and the ability differentiation hypothesis. NBNSCA was used to test the NBNS hypothesis. This study thus marks the first investigation of the creativity–intelligence relationship that tested all three theoretical hypotheses with appropriate statistical methods. Divergent thinking tests were used as an indicator of creativity, fluid intelligence tests were used as an indicator of general intelligence. Fluid intelligence is very closely related to general intelligence (Caemmerer et al., 2020; Gustafsson, 1984) and has often been used to investigate the threshold hypothesis (e.g., Shi et al., 2017; Weiss et al., 2020). Study 1 analyzed a sample (N = 1328) that has previously been analyzed with the traditional sample-dividing method (Preckel et al., 2006) and in the context of ability differentiation research (Breit et al., 2020). This allows us to directly compare the results of the more sophisticated methods with those of the traditional method and differentiation analyses. Study 2 analyzed a new sample (N = 524). Both samples included a large number of intellectually gifted individuals, allowing us more power to investigate the relationship in the higher regions of the ability distribution.

Method

Samples

Study 1

The data for Study 1 were drawn from the standardization of the Berlin Structure-of-Intelligence Test (BIS-HB; Jäger et al., 2006). Test data were available for 1,328 German secondary school students within the intended age range of the BIS-HB (12.5–16.5 years). The sample was 45.03% female (54.82% male, 0.15% missing data). The students attended grades 7 to 10, and the mean age of the sample was 14.47 years (SD = 1.09). The German school system introduces achievement-based tracking in secondary school. Of the participants, 16.79% (223) attended the lower track (mean IQ = 85.51), 15.14% (201) attended the middle track (mean IQ = 95.52), 36.67% (487) attended the high track (mean IQ = 108.53), and 30.65% (407) attended specialized schools for the gifted (mean IQ = 118.04). Track information was missing for 10 participants. The mean general intelligence of the full sample was 105.6 IQ (SD = 15.93). All parents of the participants gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the principals of the participating schools. The same data set was analyzed by Preckel et al. (2006). Moreover, an expanded version of the data set was also previously used to investigate the ability differentiation hypothesis (Breit et al., 2020).

Study 2

The participants for Study 2 stem from an ongoing study with four German secondary schools from the highest school track (Gymnasium). Between 2009 and 2020, students were assessed once with the BIS-HB. The combined sample comprised 524 students (40.46% female, 58.78% male, 0.76% missing data). At the time of testing, the students attended grades 7 to 9 (11.45% grade 7, 65.27% grade 8, 23.28% grade 9). The mean age at testing was 13.77 years (SD = .68). The mean general intelligence (IQ) of the full sample was 114.10 (SD = 13.65), and 67.94% of the sample attended special classes for the gifted at the time of testing. All parents of the participants gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the principals of the participating schools and by the local supervision and services directorate.

Measures

In both studies, fluid intelligence and divergent thinking were assessed by the Berlin Structure-of-Intelligence Test: Assessment of Giftedness and Talent (BIS-HB; Jäger et al., 2006). The BIS-HB is a paper-and-pencil intelligence test designed to capture the intelligence structure of students of all ability levels, including very-high-ability levels. The test is based on the Berlin Model of Intelligence Structure (BIS) by Jäger (1984). The BIS is a faceted model of intelligence (Figure 2). The operation facet includes processing speed, memory, creativity (i.e., divergent thinking), and fluid intelligence. The content facet includes verbal, numerical, and figural ability. On a higher hierarchical level, all abilities are integrated into general intelligence. The test comprises 45 tasks assessing the three domains and four operations. The divergent thinking score is based on verbal, numerical, and figural production tasks that are scored for idea fluency (number of answers, seven tasks) or flexibility (number of different answer categories, five tasks). Validity studies of the BIS-HB include confirmatory factor analyses using multiple group comparisons for the different age and ability groups and correlations with academic achievement and other intelligence and creativity tests (e.g., divergent thinking and a verbal creativity test [VKT, Schoppe, 1975], r = .52; fluid intelligence and a figural reasoning test [CFT-20, Weiß, 1998], r = .74). Thus, the BIS-HB provides scores with validity evidence for both divergent thinking and fluid intelligence. The divergent thinking score is based on 12 tasks (four each for verbal, numerical, and figural divergent thinking); the fluid intelligence score is based on 15 tasks (five each for verbal, numerical, and figural reasoning). The tasks used for the divergent thinking and fluid intelligence scores did not overlap.

Figure 2.

Berlin Model of Intelligence Structure (BIS).

Statistical Analyses

All analyses were conducted in R (version 4.1.3; R Core Team, 2021) using the R package segmented (Muggeo, 2008) for SRA and the packages lavaan (Rosseel, 2012) and sirt (Robitzsch, 2022) for LSEM. The SRA, heteroscedasticity, and LSEM analyses were guided by the protocol and syntax provided by Weiss et al. (2020). The NBNSCA was guided by the protocol and syntax provided by Ilagan and Patungan (2018). The full analysis code can be found in the following webpage: https://osf.io/4jvsa/. All analyses were performed in both studies.

Scatterplots and Heteroscedasticity

First, a scatterplot analysis was used to test for deviations from linearity in the relationship. This included a visual inspection of scatterplots and a statistical test for heteroscedasticity with the Breusch–Pagan test (Breusch & Pagan, 1979). Normally distributed residuals, indicated by the absence of heteroscedasticity, contravene changes in the distribution, a nonlinear relation or threshold between divergent thinking, and fluid reasoning ability (Weiss et al., 2020) as implied by an NBNS, a threshold, or a differentiation effect.

Segmented Regression Analysis

Second, SRA was applied with fluid intelligence as the predictor and divergent thinking as the outcome variable. This method specifically tests for change in slope, indicating a threshold. The Davies test (Davies, 2002) for differences in slope was used to detect a potential threshold. This method repeatedly fits regressions between two segments, divided over the continuum of the variable, to detect significant changes in slope between the segmented regressions. A nonsignificant Davies test, therefore, indicates that there is no break in the interrelationship across the fluid intelligence distribution. Using SRA allows us to compare the present results to those of previous studies using this method.

Local Structural Equation Modeling

Third, LSEM (Hildebrandt et al., 2016) was employed. LSEM can be understood as a nonparametric, continuous variant of multigroup confirmatory factor analysis. It can be used to study the factor variance of divergent thinking over the fluid intelligence continuum by fitting several structural equation models of divergent thinking along the distribution of the moderator fluid intelligence. The weight of each observation is based on the proximity of an observation to a specific value of fluid intelligence (i.e., a focal point). Significant changes in the factor variance between focal points indicate a notable change in the relationship between divergent thinking and fluid intelligence. A common factor model for divergent thinking was estimated based on the instructions in the BIS-HB manual for constructing four indicators for structural equation modeling based on BIS-HB tasks. Each indicator is a composite of one verbal, one numerical, and one figural divergent thinking task. A moderator grid with 0.5 increments from z = −2 to z = 2 was applied, resulting in nine focal points over the continuum of fluid intelligence. Deviations from linearity (as implied by threshold and differentiation) were tested for statistical significance using a permutation test (Hildebrandt et al., 2016).

Necessary-but-not-Sufficient Condition Analysis

Last, NBNSCA (Ilagan & Patungan, 2018) was applied. This method tests the assumptions of the NBNS by fitting monotonic ceiling and floor functions to the data. Unlike NCA, these functions are specified as soft bounds (i.e., probabilistic) but also require the predictor variable to be rescaled to quantile ranks to be double bounded. The ceiling slope indicates the degree of necessity of fluid intelligence for divergent thinking, with a steeper positive slope indicating a larger degree of necessity. The floor slope indicates the degree of sufficiency of fluid intelligence for divergent thinking, with a zero slope indicating no sufficiency and a steeper positive slope indicating a larger degree of sufficiency. Using a permutation test, the approach also allows for the testing of the ceiling and floor slope as well as the difference between the slopes for statistical significance.

It is not entirely clear what pattern of results would provide sufficient support for the NBNS hypothesis. Ilagan and Patungan (2018) propose two different hypotheses. The minimal hypothesis states that the ceiling slope is positive and significantly steeper than the floor slope, which is also positive, indicating a greater degree of necessity than sufficiency and resulting in a somewhat but not perfectly triangular scatterplot. Alternatively, a cutoff hypothesis can be used to define what slopes satisfy the criteria. However, it is not clear what exactly the cutoffs should be. The “not-sufficient” part of the hypothesis implies a floor slope of zero, but it is not clear what slope constitutes a substantive deviation from zero. In the analyses, the minimal hypothesis was applied to determine if the most basic criteria of the NBNS hypothesis were met. In addition, it was tested whether the floor slope was significantly different from zero. A significant floor slope indicates that fluid intelligence is strictly speaking in fact “sufficient” for divergent thinking.

Results

Study 1

Mean fluid intelligence was 106.10 (range = 70–145; SD = 16.39), and mean divergent thinking was 102.92 (range = 70–145; SD = 15.26; all scores on an IQ scale with M = 100 and SD = 15). Fluid intelligence skewness was −0.27, and kurtosis was −0.47. Divergent thinking skewness was −0.15, and kurtosis was −0.37. The correlation between fluid intelligence and divergent thinking was r = .54.

Scatterplots and Heteroscedasticity

Figure 3 shows the results from the scatterplot (left) and heteroscedasticity analyses (right). Visual inspection of the scatterplot and the heteroscedasticity plot indicated no threshold or any nonlinear relationship between fluid intelligence and divergent thinking. Residuals were evenly distributed across the fitted values, as evidenced by the entirely flat line based on the loess smoothing function. The Breusch–Pagan test for heteroscedasticity was nonsignificant, BP(1) = .06, p = .80, indicating homoscedasticity and supporting the impressions gained from the visual inspection.

Figure 3.

Study 1: Scatterplot for the Correlation Between Divergent Thinking and Fluid Intelligence (left) and Heteroscedasticity Plot (Right) Including Standard Errors (Gray) and Standard Deviations of the Fitted Values (Dashed Line).

Segmented Regression Analysis

Figure 4 shows the results from the SRA, displaying the largest identified change in slope at fluid intelligence IQ = 78.33. For all identified breakpoints, the change in slope was not statistically significant (p = .07), contradicting the threshold hypothesis.

Figure 4.

The Study 1 Breakpoint for the Relation Between Fluid Intelligence and Divergent Thinking (SRA).

Local Structural Equation Modeling

Figure 5 shows the LSEM results. A common factor model with four divergent thinking indicators fit the data very well (comparative fit index [CFI] = 1.000, root mean square error of approximation [RMSEA] = .000, standardized root mean squared residual [SRMR] = .009). The results of the permutation test indicated no statistically significant changes in the common factor variance across the fluid intelligence distribution (p = .81). A model that constrained the factor loadings to equality across all focal points using the joint estimation approach for LSEM did not show decreased model fit (CFI = 1.000, RMSEA = .000, SRMR = .026), contradicting the assumption of a threshold or nonlinear relationship between the variables.

Figure 5.

Study 1: Standardized Divergent Thinking Factor Variances at Each Focal Point Along the Fluid Intelligence Continuum (LSEM).

Necessary-but-not-Sufficient Condition Analysis

Figure 6 shows the ceiling and floor slopes implied by the data. Both slopes were positive. The ceiling slope (b₁−b₀ = .226) was larger than the floor slope (a₁−a₀ = .120), with an absolute difference of .106 (p < .05). This means that the conditions for the minimal hypothesis were met. The floor slope was significantly larger than zero (p < .05).

Figure 6.

Study 1: NBNSCA Results.

Study 2

The mean fluid intelligence was 114.06 (SD = 13.43), and the mean divergent thinking was 111.37 (SD = 14.04). Fluid intelligence skewness was −0.51, and kurtosis was 0.07. Divergent thinking skewness was −0.16, and kurtosis was −0.02. The correlation between fluid intelligence and divergent thinking was r = .48.

Scatterplots and Heteroscedasticity

Figure 7 shows the results from the scatterplot (left) and heteroscedasticity analyses (right) for Study 2. Again, visual inspection did not reveal any sign of a threshold or a nonlinear relationship. Residuals were evenly distributed across the fitted values, as evidenced by the relatively flat line based on the locally weighted smoothing (LOESS) smoothing function. In support of the impressions gained from visual inspection, the Breusch–Pagan test for heteroscedasticity was nonsignificant, BP(1) = .19; p = .66.

Figure 7.

Study 2: Scatterplot for the Correlation Between Divergent Thinking and Fluid Intelligence (Left) and Heteroscedasticity Plot (Right) Including Standard Errors (Gray) and Standard Deviations of the Fitted Values (Dashed Line).

Segmented Regression Analysis

Figure 8 shows the results from the SRA. For all identified breakpoints, the change in slope was not statistically significant (p = .37), contradicting the assumption of a threshold. Similar to Study 1, the largest change in slope was observed at fluid intelligence IQ = 81.89. However, the slope below the breakpoint was negative in Study 2.

Figure 8.

The Study 2 Breakpoint for the Relation Between Fluid Intelligence and Divergent Thinking (SRA).

Local Structural Equation Modeling

Figure 9 shows the LSEM results. A common factor model to the four divergent thinking indicators fit the data very well (CFI = 1.000, RMSEA = .000, SRMR = .017). The results indicated no statistically significant changes in the common factor variance across the fluid intelligence distribution (p = .25). Again, a model that constrained the factor loadings to equality across all focal points using the joint estimation approach for LSEM showed no decrease in model fit (CFI = 1.000, RMSEA = .000, SRMR = .031), contradicting a threshold or nonlinear relationship.

Figure 9.

Study 2: Standardized Divergent Thinking Factor Variances at Each Focal Point Along the Fluid Intelligence Continuum (LSEM).

Necessary-but-not-Sufficient Condition Analysis

Figure 10 shows the ceiling and floor slopes implied by the data. Both slopes were positive. As in Study 1, the ceiling slope (b₁−b₀ = .290) was larger than the floor slope (a₁−a₀ =.120), with an absolute difference of .170 (p < .05), meaning that the conditions for the minimal hypothesis were met. The floor slope was significantly larger than zero (p < .05).

Figure 10.

Study 2 NBNSCA Results.

Discussion

Across all methods in both studies, the results showed no evidence for a threshold or a nonlinear relationship between fluid intelligence and divergent thinking. Rather, across the ability distribution, fluid intelligence and divergent thinking showed a similar and positive relationship. The findings are consistent with the results from Weiss et al. (2020) as well as earlier studies that did not find any support for a threshold (e.g., Preckel et al., 2006; Sligh et al., 2005). There was some evidence that fluid intelligence is more of a necessary than a sufficient condition for divergent thinking, but the NBNS hypothesis was not fully supported due to a nonzero floor slope.

Convergence of the Study 1 Results With Previous Analyses of the Data set

The Study 1 data set was previously analyzed by Preckel et al. (2006) with respect to the threshold hypothesis, based on the traditional method of splitting the data set at the assumed threshold of fluid intelligence of 120 IQ. They found little difference in the correlation of fluid intelligence and divergent thinking below and above the threshold (r =.42 vs. r = .38). Preckel et al. (2006) also split the sample into quartiles and compared the correlations, again finding only marginal and unsystematic differences (.42 vs. .30 vs. .38 vs. .33, from lowest to highest quartile). Therefore, the present results converge with the previous analyses while also allowing us to examine the relationship continuously and to test for the statistical significance of any deviations from linearity.

An expanded version of the Study 1 data set (N = 1506, additionally including participants who were slightly too young to receive BIS-HB norm scores) was also used to investigate the ability differentiation hypothesis using nonlinear factor analysis (Breit et al., 2020). Nonlinear factor analysis tests for linear and quadratic effects of general intelligence on specific ability scores, with a significant negative quadratic effect indicating a diminishing relationship with increasing intelligence. This is conceptually similar to the present continuous analyses of the relationship between fluid intelligence and divergent thinking but specific to quadratic effects. Breit et al. (2020) found little support for ability differentiation overall and for divergent thinking scores in particular, with nonsignificant quadratic g-loadings of −.014, .003, and −.018 for numerical, verbal, and figural divergent thinking. These findings provide some evidence for a convergence of threshold and differentiation research results.

Implications for Future Research on the Relationship Between Intelligence and Creativity

Implications for Threshold Analyses

There was no evidence for a threshold or a nonlinear relationship in the two studies using three different methods. The present findings were based on large data sets and measures of fluid intelligence and divergent thinking with strong validity evidence. Moreover, both data sets covered the ability distribution between IQ = 70 and 145, including an oversampling of high-ability and gifted individuals, providing a wide ability range and a large number of intelligence test values beyond the often assumed threshold of IQ = 120. Therefore, the findings strongly support the notion by Weiss et al. (2020) that “there is no convincing evidence—theoretically or analytically—for the existence of a threshold in the relation between creativity and intelligence” (p.17).

One may ask why many studies find evidence for a lower correlation between intelligence and divergent thinking in high-ability individuals (e.g., Jauk et al., 2013; Shi et al., 2017). Several explanations have been proposed. First, Weiss et al. (2020) suggested that such findings could be explained by the confirmation bias. Confronted with ambiguous evidence, researchers may be more likely to interpret the evidence in concordance with their previous expectations. Second, the positive findings may occur due to the many degrees of freedom in setting the threshold and deciding on criteria for accepting or rejecting a threshold (Karwowski & Gralewski, 2013; Weiss et al., 2020). Researchers might consciously or unconsciously make decisions in a way that leads to confirmation of the hypothesis. Third, due to the statistical shortcomings described in the Appendix, the previously used statistical methods are generally unreliable (Molenaar et al., 2010; Weiss et al., 2020). Spurious threshold findings might not be uncommon when using only SRA or sample separation methods. A fourth possibility is that positive findings are due to true nonlinearity in the relationship that may be mistaken for a threshold when the statistical methods are only suited for threshold detection. Evidence for such a nonlinear relationship between intelligence and more specific cognitive abilities comes from ability differentiation research (e.g., Breit et al., 2021; Molenaar et al., 2017; Reynolds, 2013; Tucker-Drob, 2009); however, most of these studies do not include divergent thinking or creativity measures.

In general, there is little reason to methodologically or theoretically separate the relationship between fluid intelligence and divergent thinking from differentiation research. Methodologically, researchers in both fields must investigate the relationship between intelligence and one or more specific abilities continuously. Although this was already recognized in differentiation research a few years ago (e.g., Molenaar et al., 2010; Tucker-Drob, 2009), this suggestion has been largely neglected in research on the intelligence–creativity relationship until Weiss et al. (2020). This is particularly perplexing because continuous analyses of the relationship have been conducted before (e.g., Guilford & Christensen, 1973). There is also little theoretical justification for treating divergent thinking differently than any other cognitive ability with regard to its relationship with general intelligence. In modern models of intelligence, divergent thinking and related constructs such as retrieval fluency are equally ranked with other specific cognitive abilities (e.g., Schneider & McGrew, 2018). In the spirit of parsimony, the nonlinearity of the relationship between divergent thinking and intelligence should be investigated within the framework of ability differentiation research. For adequate investigation of ability differentiation, the intercorrelations between multiple cognitive abilities should be investigated, as the phenomenon relates to the g-factor that emerges from this correlation matrix (Major et al., 2011; Tucker-Drob, 2009). The absence of ability differentiation in these studies may be a result of the restriction to only two abilities. The theoretical argument remains that ability differentiation should also affect the relationship between fluid intelligence and divergent thinking.

Treating creativity as a special case is only justifiable if creativity is no longer reduced to the concept of divergent thinking in threshold research. Instead, a broader conceptualization and measurement of creativity (e.g., Plucker & Makel, 2010), potentially including other relevant aspects of personality or real-world creative behavior, would be needed to warrant a separate hypothesis. However, to conduct threshold-specific analyses, there is still a need for a strong theoretical basis for the assumption of such a threshold (Weiss et al., 2020). The specific operationalization of creativity may be critical in this case. For example, when using real-world creative achievement as a measure for creativity, the relation between intelligence and creativity may differ across the ability spectrum due to differences in access to specific achievement domains. One may choose to use the number of scientific articles, literary publications, and patents as a measure of creative productivity (e.g., Lubinski et al., 2001). Most likely, more individuals from the upper regions of the intelligence continuum will make significant contributions in these areas, severely affecting the shape of the relation between this measure and intelligence.

Implications for NBNS-Analyses

The results partially confirmed the NBNS hypothesis. The statistical approach proposed by Ilagan and Patungan (2018) was used, which is currently the only available statistical method to test all parts of the NBNS hypothesis. Our findings supported the “necessary condition” part of the hypothesis. They only partially supported the “not-sufficient” part, in that there was a larger empty space in the top left corner of the scatterplots than in the bottom right corner, but there was some empty space in the bottom right corner nonetheless. However, the “necessary condition” part was analyzed and supported before (e.g., Karwowski et al., 2016), the “not-sufficient” part was previously only investigated by Ilagan and Patungan (2018) themselves, finding strong support for the full NBNS hypothesis in creative achievement but not in divergent thinking. More research is needed to allow robust conclusions about the NBNS hypothesis.

It should be noted that NBNSCA, albeit a major improvement over NCA, is not without weaknesses. In fact, Ilagan and Patungan (2018) state that their “proposal is best seen as a proof of concept rather than an authoritative prescription” (p. 195). This characterization is especially evident in the test’s usage of the beta distribution for modeling and estimating the ceiling and floor characteristics of the supplied data. Although the use of the beta distribution makes the fundamental characteristics of the NBNS distributing tractable, it comes with various limitations. Although the parameters of the distribution (i.e., the slopes) are derived using maximum likelihood estimation, regression and fitting diagnostics are not applicable due to the test’s inherent inobservance of residuals. Consequently, evaluation of the parameters deployed to permutation testing is possible only by means of visual inspection, undermining the utility for inferential statistics. Furthermore, the method is limited to double-bounded criterion variables while also excluding minimal and maximum values due to many beta distributions having zero density at those points. Taken together, as no binding cutoff criteria exist, there is a need to develop new and improved methods to enable appropriate analyses of the NBNS hypothesis in the future.

Implications for Research and Practice in Gifted Education

Intelligence and creativity often are considered in theories of giftedness (e.g., Gagné, 2005; Renzulli, 1978) and eminence (e.g., Simonton, 2018). Therefore, findings on their relationship are also important from the perspective of theory building and interpretation. Our findings indicate that both constructs are positively correlated and that intelligence is a necessary condition for creativity. Rather than understanding them as separate dimensions of giftedness, this points to functional connections in line with theories of complex problem-solving (e.g., Funke, 2012). Convergent thinking processes associated with reasoning and fluid intelligence are used to understand the problem and to find and understand the relevant information to solve it. Divergent thinking processes are used to generate different solutions, which are subsequently evaluated, again using convergent thinking processes. Within this process, there are feedback loops that involve returning from convergent to divergent thinking processes (e.g., Amabile, 1983; Zeng et al., 2011). This frequent interaction of convergent and divergent thinking processes in problem-solving makes a strict separation of intelligence and creativity implausible. Instead, it is likely that both abilities become increasingly related over the course of cognitive development due to positive beneficial interactions (van der Maas et al., 2006).

Our finding that a threshold in the relation between intelligence and creativity could not be supported also has implications for educational practice. First, among many practitioners, there is the persistent assumption of intelligence thresholds. The idea can be traced back to Anderson (1960), who proposed that there is a threshold of necessary cognitive ability beyond which other factors besides intelligence determine differences in performance for any specific task or area of achievement. Such assumptions are also found, for example, in expertise research, where it is postulated that noncognitive factors above a certain intelligence threshold explain most of the differences in performance between individuals (e.g., Schneider, 2000). Similarly, in the Piirto Pyramid of talent development, a minimum intellectual requirement is assumed for every domain (Piirto, 2004). These assumptions come with an implicit or explicit disregard for intelligence differences in the high-ability range because these could not, after all, explain further variance in performance. However, there is little evidence for the existence of such thresholds, neither in academic and vocational achievement nor in creativity (Lubinski, 2016). Even at high-ability levels, intelligence differences continue to be meaningful for explaining achievement differences in different domains.

Second, our investigations of the NBNS primarily supported the part of the hypothesis that intelligence is a necessary condition for creativity, which is in line with previous findings (e.g., Karwowski et al., 2016). This, in turn, means that highly creative individuals also show above-average intelligence. Identification of highly creative individuals is described as an important and difficult challenge (Kerr & Vuyk, 2013). Our results suggest that although intelligence is not sufficient for creativity, it still makes sense to look in the population of highly intelligent for people with great creative potential. Moreover, if highly creative people are to be specifically promoted, it must be borne in mind that these people are more likely to have a higher intelligence. Therefore, promoting creativity separately from intellectual promotion seems to be misplaced, especially because the creative process also requires reasoning and problem-solving (Zeng et al., 2011). There should not be a harsh contrast between nurturing creative and intellectual talents, not only for the reasons stated here but also in light of the fact that creativity can be exhibited not only in the arts but also in other fields such as mathematics and science (Kerr & Vuyk, 2013).

Strengths and Limitations

This research has several strengths. First, it examined three theoretical hypotheses in two large samples with a wide intelligence distribution. Second, four appropriate statistical methods were used that are able to detect a threshold or any other deviation from linearity in the relationship. This also included the second application of the only currently available method to fully test the NBNS hypothesis, making this the first study on the relationship between intelligence and creativity to use all available appropriate methods. Third, one of the samples had been previously investigated using traditional methods and analyzed with regard to differentiation effects, allowing us to compare the results of all these analyses.

The present research also has limitations. First, both studies focused on adolescents. The results therefore may not generalize to other age groups. However, within adolescence, a 4-year age span (12.5–16.5 years) and a wide range of ability levels were covered, which makes the results very informative for this specific age group. Moreover, similar results were reported for an adult sample using the same methodology (Weiss et al., 2020). Second, divergent thinking scores were used to operationalize creativity. It can be argued that divergent thinking only represents a portion of creativity and that the results may differ when using different measures. However, divergent thinking tests are, by far, the most commonly used creativity measures to investigate the threshold hypothesis, making these results comparable to previous research. Moreover, it can be argued that divergent thinking is the specific cognitive ability involved in the creative process that is most unique to creativity. Third, the participants in Study 1 were nested in 17 schools from different tracks of the German school system. This nested data structure may have affected significance testing (Hox, 2010), but the number of schools was too small to conduct multilevel analyses (Maas & Hox, 2005). However, for the correlation between fluid intelligence and divergent thinking and for the Breusch–Pagan test, we were able to replicate the analyses with robust standard error estimations using the “sandwich” R package (Zeileis et al., 2022). The results were unaffected by the adjusted standard errors. In addition, the significance tests of the other statistical analyses were based on permutation tests, which provide robust standard errors (Thompson et al., 2018; Wang & De Gruttola, 2017).

Conclusion

The relationship between fluid intelligence (as an indicator of general intelligence) and divergent thinking (as an indicator of creativity) was investigated in two large samples. Both constructs were positively correlated without any evidence for a threshold or a nonlinear relationship. There was some evidence that fluid intelligence is a NBNS condition for divergent thinking. Future research with appropriate statistical methods, as used in this study, is needed to corroborate this finding. Future research should further integrate the relationship between intelligence and creativity into the ability differentiation framework because there is no major methodological or theoretical distinction between the two fields of research, especially when creativity is operationalized as divergent thinking. In educational practice, it should be avoided to treat intelligence and creativity as entirely separate abilities, especially in the high-ability range.

Footnotes

Appendix

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Research support for this project was provided by the University of Trier research fund.

Open Science Disclosure Statement

The data analyzed in this study are not available for purposes of reproducing the results due to legal restrictions. The R analysis code used to generate the findings reported in the article are available at for purposes of reproducing the results or replicating the study. There are no other newly created, unique materials used to conduct the research.

ORCID iDs

Moritz Breit

Julian Preuß

Author Biographies

Moritz Breit is a postdoctoral researcher at the University of Trier in the Department of Psychology, Giftedness Research and Education. His research interests center on the nature and development of cognitive abilities. His current research focuses on ability differentiation, the relationship between creativity and cognitive ability, and the temporal stability of cognitive abilities. He obtained his PhD in Psychology at the University of Trier.

Julian Preuß is a master’s student at the University of Trier and a student research assistant in the Department of Psychology, Giftedness Research and Education. His research interests center on intelligence, creativity, and giftedness, and his current research focuses on the evaluation of statistical methods that are used in the research on the relationship between creativity and intelligence. He obtained his BA in Psychology at the University of Trier.

Vsevolod Scherrer is a postdoctoral researcher at the University of Trier in the Department of Psychology, Giftedness Research and Education. His research interests center on predictors of academic achievement. His current research focuses on the development of achievement motivation. He obtained his PhD in Psychology at the University of Trier.

Tobias Moors is a master’s student at the University of Trier and a student research assistant in the Department of Psychology, Giftedness Research and Education. His current research focuses on the relationship between creativity and intelligence. He obtained his BA in Psychology at the University of Trier.

Franzis Preckel is Full Professor for Giftedness Research and Education at the Department of Psychology of the University of Trier, Germany. Her main research interests are psychological assessment, intelligence and giftedness, and factors influencing talent development (e.g., need for cognition and self-concept). She has presented her research in more than 150 talks and is on the editorial board of Diagnostica and Gifted and Talented International.

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