Measurement of Executive Functioning and High Intellectual Ability in Childhood: A Comparative Meta-Analysis

: From a neuroconstructivist approach and a developmental model of high intellectual ability (HIA), it is argued that the management of intellectual resources through executive functioning (EF) is one of the factors inﬂuencing the expression of high potential. The main objective is to determine the e ﬀ ectiveness of measures of executive functioning used comparing schoolchildren with HIA and those of average intelligence. A meta-analysis was carried out on a selection of 17 studies for a total sample of 1518 children with either HIA or an average level of intelligence. Pooled estimates of e ﬀ ect size revealed a signiﬁcant di ﬀ erence favoring the HIA individuals in the two components of EF related with WM verbal ( d = 1.015), and WM visual-spatial ( d = 0.709). Other components did not show signiﬁcant di ﬀ erences: inhibition ( d = − 0.014), ﬂexibility ( d = 0.068), and planiﬁcation ( d = − 0.038). The empirical heterogeneity was very high. It is concluded that these instruments show a degree of measurement impurity, which condition their validity and reliability, and that schoolchildren with HIA display better executive functioning in the components of verbal and visual-spatial working memory.


Introduction
Research advances in human intelligence in the fields of genetics, neuroscience, and psychology have redefined the concept of high intellectual ability (HIA) as a high potential for cognitive functioning resulting from a complex interplay of factors, including genetic and environmental covariates. High biological potential, expressed epigenetically throughout an individual's development, is a necessary but insufficient condition for the emergence of HIA. Each human being has a unique developmental trajectory, shaped by endogenous and exogenous modulating factors that determine how this potential is expressed in adulthood [1].
Current neurocomputational [2] and genetic [3,4] models of HIA suggest that genetics provide a biological basis, including a distinctive cytoarchitecture and differences in brain functioning. This is one predictor of HIA, but biological factors are not immutable, nor are they sufficient to guarantee that high potential will be expressed in high ability. This expression is relatively stable, because biological potential is acted upon by other factors over the course of an individual's development, depending on his or her particular traits and contextual influences [5]. In short, HIA is not a static property hardwired in the brain but the product of an ongoing interaction with modulating factors that influence how high neurobiological potential translates into complex functions and the construction of representations that allow the brain to become more efficient.

Executive Functions and High Intellectual Ability
Executive functions have an impact on whether high potential is ultimately expressed as HIA [17]. Two particularly interesting questions are their role in the achievement of excellence and the relationship between executive dysfunction and poor performance. A review of the specialized literature bears out the assumption that studying executive functioning can help us understand the trajectories in which HIA is expressed [17], lending support to the current trend to conceptualise it as a process in development [5,18]. Other studies [19] have detected variations in executive functioning between people of different intellectual profiles, where high potential is inferred from a set of constituent skills, for instance, in gifted individuals or those displaying particular talents.
Consequently, it is important to ensure that measures of executive functioning-generally, behavioural rating scales or cognitive tasks-are both valid and reliable. If this is not the case, any results or conclusions that come from these studies will only add to the conceptual haziness that inhibits our understanding of the role of executive functioning in the management of intellectual resources in those with HIA and its influence on the expression (or non-expression) of potential or competence in outstanding performance.

Measures of Executive Functions
A great many neuropsychological measures of executive functioning have been put forward, but these tend to be overly broad and vague as to which cognitive processes they are intended to capture [20,21]. The lack of construct operationalisation, the complexity of the processes involved, inconsistencies in the administration of batteries and tests, and the use of a single task to evaluate different components are some of the reasons why this kind of research is so complex [22].
Although some experts [9] seek to demonstrate how the three core components relate to cognitive assessment tasks, analysing their validity with respect to what is being measured, the reality is that both the validity (functional and ecological) and the reliability of these instruments are limited. The concept of task impurity reminds us that not all tasks measure what they claim to measure and that they all too often measure other components, too [16]. This can occur when multiple components are mobilised in completing a particular task, or because of similarities with how a task would be approached in everyday life, including the involvement of non-executive processes. Moreover, there tends to be only a modest correlation between the various ways of measuring a single EF component, and internal consistency reliability and test-retest reliability are low [23], with a handful of exceptions [24].
These difficulties suggest that measures of executive functioning are weak instruments for capturing a construct that is itself, perhaps, still poorly defined and operationalised [25].
The main objective of this study is to determine whether the use of meta-analysis might help to answer some of these questions surrounding how executive functioning is measured in schoolchildren with HIA or an average level of intelligence. Our main research questions are as follows: 1. Are all measures of executive functioning found in the literature equally effective? 2. Are there differences in executive functioning between schoolchildren with HIA and those with average intelligence.

Materials and Methods
The first step in the meta-analysis was to search for comparative studies that sought to measure differences in executive functioning between individuals with HIA and those with an average level of intelligence, by querying a specific set of databases that were deemed a sufficient starting point.

Study Selection Criteria
To be included in the analysis, a study had to meet the following six criteria: (a) be empirical in nature; (b) include participants with HIA and those of average intelligence, with no developmental disorders; (c) encompass a participant age range of 6 to 12 years; (d) employ standardised instruments for measuring executive functions and intellectual competence; (e) be published in English or Spanish between 1998 and 2019; and (f) provide the means and standard variations of their results. Any studies that did not meet these criteria were discounted.

Identification of Qualifying Studies
The search was conducted between March and June 2019, based on: (a) electronic databases (Web of Science, Scopus, Google Scholar, PsycINFO, Medline, ERIC, and Dialnet); (b) journals that publish articles related to HIA and psychology (Journal for the Education of the Gifted, Gifted Child Quarterly, Roeper Review, International Journal of Psychological Research, International Journal of Neuroscience, and Revista de Psicopedagogía); (c) a review of the references given in each article, with the aim of identifying additional studies that could potentially be included; and (d) the TESEO doctoral thesis database.
The search terms used were: executive function(s), intellectual ability(s), cognitive ability(s), executive functioning, intelligence, executive control, executive dysfunction, giftedness, talent, high intellectual ability, high achievement, high IQ, superior students, advanced students, working memory, inhibition, and flexibility. These terms were combined with Boolean operators (AND, NOT, OR, XOR) in order to make the search more precise, selective, and defined.
The initial electronic search yielded a total of 8560 texts pertaining to the research questions outlined above. To avoid omitting any articles published between 1995 and 2019 that were not included in these electronic databases, a manual search of two of the selected journals specialising in HIA (Gifted Child Quarterly and Roeper Review) was also carried out. Once duplicates had been removed and the abstract of each study reviewed using inclusion and exclusion criteria, 24 texts remained.
All texts were found to contain the statistical data needed to establish effect size. An initial inspection of these 24 texts led to 7 being excluded, leaving a final set of 16 articles and 1 doctoral thesis.
As it was expected that the selected studies would employ more than one measure of executive functioning with the same participants, as well as different scoring methods for the same task, and given that including such measures would have violated the principle of sample independence [26], parallel meta-analyses were conducted for all EF components that appeared in the studies. There were only a small number of qualifying studies for each EF component, so the planned analysis of moderating variables was abandoned. Figure 1 illustrates the search, selection, and inclusion process followed. Data from each selected article were coded in accordance with the following variables: (a) authors and date; (b) number of participants (with HIA and with average intelligence); (c) age range; (d) measure used to identify participants with HIA; (e) components of executive functioning; and (f) cognitive tasks used to measure each component. To ensure acceptable data quality, interobserver reliability between two independent observers was calculated using the kappa coefficient. This produced a k of 0.89, confirming the reliability of the coding.
The statistical analysis was conducted as follows.

Effect Size Calculation
We calculated the effect size of each study on each component of executive functioning in the articles analyzed. The chosen index was the standarized mean difference, or Cohen's d [27]. This is the most suited index to measure the difference between two groups in a continuous variable. Furthermore, many studies in this area provide means and standard deviations, the statistics necessary for calculations. The difference between the group means appears in the numerator of the formula. The way which we replaced in that formula for this meta-analysis was such that positive values reflect better performance of the group with HIA over the group with an average level of intelligence.
The d values were obtained using the practical meta-analysis effect size calculator [28]. The calculated values were subsequently adjusted for bias, to correct for the well-known trend of d to overestimate the parameter [29].

Statistical Methods
Statistical analysis was performed assuming a random effects model. A random (rather than fixed) effects model was chosen because this model allows for generalizing the differences in EF beyond the specific set of studies included here. Also, this model was chosen because it is a more conservative model with respect to statistical inferences, as compared to a fixed effect model [30].
The pooled effect size was obtained by weighting the individual estimates by the inverse of variance method. Furthermore, for the between studies specific variance was estimated by the method of moments [31]. Heterogeneity was assessed using the Q [32] and I 2 statistica [33]. The Q statistic allows testing whether the observed variance exceeds what is expected from mere sampling under a fixed parametric value. The I 2 statistic describes the heterogeneity in relative terms.
Statistical analysis was done through the Lipsey and Wilson SPSS macros [34] and the figures (forest plot and funnel plot) were obtained with the R package [35]. As the number of studies is relatively small, we only analized the threat of publication bias through the visual inspection of the funnel plot.
Sensitivity analysis for outliers was done by recalculating the confidence interval of the pooled effect size after eliminating them. This analysis allows to ascertain whether the decision of including them or not could potentially compromise the results of the meta-analysis.

Results
The final set of k = 18 estimates summed a total sample of 1518 participants, of whom 591 displayed HIA and 927 displayed an average level of intelligence. The age range of participants was between 6 and 12 years. To identify participants with HIA, 78% of studies used a formal measure of intelligence, yielding a single IQ index, whereas 11% also used formal measures with a separate score for creativity. The remainder (11%) used multiple informal measures of intellectual competence, including teachers' nominations, parents' questionnaires, or participation in programs aimed at pupils with HIA.
We observed a great deal of variety in the EF components evaluated and the measurement instruments used. Eleven studies are focused exclusively on a single component, whereas 6 looked at several components. Inhibition is examined in 10 reports, verbal WM in 9, visual-spatial WM in 8, planning and flexibility in 3, and decision making in 1. The tasks presented to participants are also highly varied, comprising 21 separate measurement instruments. A total of 12 tasks were used to measure inhibition, 13 for verbal WM, 8 for visual-spatial WM, 2 for planning, 2 for flexibility, and 1 for decision making. Furthermore, there were 2 studies where the same instrument was used to measure different components (flexibility and inhibition, verbal WM and inhibition). The selected studies were carried out in Europe (6), North America (5), Asia (4), and Latin America (2). Given that this meta-analysis involves studies with distinct samples, containing participants of different ages in different countries, and took a variety of approaches and data extraction, the results may be generalized.
As we can see in Table 1, there is a great dispersion in the measurements, which suggests a high degree of impurity. Furthermore, studies using multiple measures for a single EF component reported that there was no correlation between different measures.  Figure 2 shows the forest plot with the 18 estimates. To avoid dependence problems, we have included only one estimate from each study. When the study reported more than one, we choose the most representative core components of EF. The component represented for each study is also specified in a separate column in the figure. It is obvious that there is substantial variability between the studies, with values ranging from d = 2.97 to d = −1.04. Visual inspection revealed that heterogeneity was much greater in the earlier than in more recent studies. To highlight this effect, we have ordered the studies in the figure   The heterogeneity analysis yielded a significant value [Q (17) = 193.8990, p < 0.01; I 2 = 91.23; τ 2 = 0.63374], indicating diversity across the studies. This was to be expected since dependent variables that assess the different components of EF are included in this set. We have estimated the combined effect size for each of the EF components studied. This involved 10 estimates for the component of inhibition, 9 for verbal WM, 8 for visual-spatial WM, 3 for flexibility, and 3 for planning. Decision-making was excluded, as only one study sought to measure this component. Table 2 shows the pooled estimates and the heterogeneity statistics. Table 2. Combined effects for the set of studies reporting estimates of differences in inhibition, verbal WM, visual-spatial WM, flexibility, and planning. For each case they are also included the Q statistic and the specific variance estimate (τ 2 ). The effect sizes vary widely between components. A statistically significant effect was observed in two components, verbal WM (d = 1.0149; CI: 0.6018-1.4278) and visual-spatial WM (d = 0.7085; CI: 0.2703-1.1468). Comparing the two groups, participants with HIA display better performance in verbal WM and visual-spatial WM tasks. There are no significant differences in the other components: inhibition, flexibility, and planning. The high level of heterogeneity in the inhibition and WM components suggests the need for an analysis of the moderating variables, but they were not carried out here due to the small number of studies (and the corresponding low power).

Component
Visual inspection of the funnel plots of the WM components (as shown in Figure 3) suggest that certain results are at odds with the majority and so can be considered as potential outliers (2 in the verbal set and 1 in the visual-spatial set). They are the points lying beyond the right tail of each plot. As the inclusion of a small number of outlying studies could produce an artificial effect in the results, a sensitivity analysis was carried out in order to evaluate their potential distortive effect. After eliminating the two outlying studies on verbal WM, the estimated value d = 1.0149 (CI 95%: 0.6018-1.4278) became d = 0.6790 (CI 95%: 0.5139-0.8442), indicating a smaller but statistically significant effect.
After eliminating the only outlying study on visual-spatial WM, the estimated value d = 0.7085 (CI 95%: 0.2703-1.1467) became d = 0.4917 (CI 95%: 0.2164-0.7670); again, the effect is smaller but still statistically significant. As a result, the sensitivity analysis done after visual inspection of the funnel plots reinforce the conclusions. The existence of robust differences in the WM components does not depend on the inclusion of studies with rare results.

Discussion
Executive functioning is linked to the management of intellectual resources in HIA, in keeping with its current definition as a process in development [5]. Executive dysfunctions may explain the substantial variability in the expression of high potential, as other authors have suggested [53]. This may be one of the factors that can lead to a gap between high potential and performance. It is important to have access to pure, valid, and reliable measures of executive functions in order to understand their role in the management of extensive intellectual resources and in the wide variability in the expression of high potential, so that the appropriate educational approach can be adopted.
This analysis sought to generate new insights into this question. The meta-analysis described above met the overall objective and provided answers to the main research questions. In terms of the effectiveness of the measures used in this set of specialist studies, the findings reported here corroborate those of other authors who have raised the problem of measurement impurity [6,9,16]. The effect size values obtained indicate a certain level of dispersion in the measures, both among schoolchildren with HIA and those with an average level of intelligence. The high values yielded by the heterogeneity analysis cast doubt on whether these tests are truly measuring the aspect they were designed to measure. This heterogeneity, although significant, has decreased in recent years. However, this does not necessarily mean that the reliability of EF measures can now be taken for granted.
A qualitative analysis of the selected studies shows that heterogeneity can refer to: (a) the use of different tasks to measure the same component, (b) the use of a single task to measure different components, and (c) the use of different tasks to measure the same component without correlation between the scores for each task. These points call into question the validity of the construct, as well as the reliability and validity of the measures used, as other researchers have concluded [9,16,20,21,54].
The EF components evaluated in the selected studies can be understood to comprise the three core components [8,9], plus planning and, in one study, decision making. In other words, there is also dispersion in terms of the construct measured.
This heterogeneity raises serious concerns about the effectiveness of current measures of executive functions, and it introduces some doubt as to whether they can be used reliably as an indicator of resource management in individuals with HIA. It is not clear precisely what they are measuring or if there are other non-executive components also captured by the same instrument.
These results must be born in mind when considering whether the two populations do indeed display differences in executive functioning. Based on this study, it can be cautiously concluded that there are statistically significant differences in the verbal WM component and the visual-spatial WM component between participants with HIA and those with an average level of intelligence, but not in the other EF components studied.
In interpreting these results, one should be mindful that, in most cases (89%), HIA is identified using tests that return an IQ index or using informal instruments. Only 11% of studies adopted a formal multidimensional measure, as current thinking recommends [18]. Again, this may affect the validity of conclusions about the link between EF and HIA.
This meta-analysis has a number of limitations, one of them being the small number of comparative studies included, which ruled out any analysis of moderating variables, of the power of the contrast, or the power of publication bias. Even so, results obtained suggest that further research is required to develop pure measures of executive functioning that can improve our understanding of the role of executive management in the optimal expression of high potential. In this way, both individuals and societies can avoid the losses represented by unrealised potential.