Abstract
This study examined the relationship between the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the Reynolds Intellectual Assessment (RIAS) Verbal Scale using Principal Component Analysis (PCA). The PCA revealed a strong relationship between JCCES and the RIAS Verbal Scale, supporting the hypothesis that there is a common underlying construct representing general verbal and crystallized intelligence. Additionally, mathematical problem-solving was found to be a distinct construct from general verbal and crystallized intelligence. Despite some limitations, this study provides empirical support for the relationship between crystallized intelligence and verbal abilities, as well as the distinction between mathematical and verbal abilities, which can inform educational interventions and assessments.
Keywords: Jouve Cerebrals Crystallized Educational Scale, Reynolds Intellectual Assessment Scale, Principal Component Analysis, crystallized intelligence, mathematical problem-solving
Introduction
Psychometrics, the science of measuring psychological attributes, has a long history of developing and refining theories and instruments to assess cognitive abilities (Cattell, 1963; Carroll, 1993). The present study focuses on the relationship between the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the Reynolds Intellectual Assessment (RIAS) Verbal Scale (Reynolds & Kamphaus, 2003), two psychometric instruments designed to assess crystallized intelligence and verbal abilities, respectively. Crystallized intelligence, first proposed by Cattell (1963), refers to the ability to access and utilize accumulated knowledge and experience, which is closely related to verbal abilities (Ackerman, 1996; Kaufman & Lichtenberger, 2006). Theories of cognitive abilities, such as those proposed by Cattell (1971), Horn and Cattell (1966), and Carroll (1993), have suggested that crystallized intelligence and verbal abilities share a common underlying construct.
Previous research has supported the relationship between crystallized intelligence and verbal abilities (Cattell, 1971; Horn & Cattell, 1966; Carroll, 1993), as well as the distinction between mathematical and verbal abilities (Deary et al., 2007). However, few studies have specifically examined the relationship between the JCCES and RIAS Verbal Scale. The present study aims to address this gap by investigating the relationship between these two instruments using principal component analysis (PCA), a statistical technique commonly employed in psychometrics to reduce data complexity and identify underlying constructs (Jolliffe, 1986).
The research question guiding this study is: What is the relationship between the JCCES and RIAS Verbal Scale, as assessed by PCA? To answer this question, the study will test the hypothesis that there is a strong relationship between the JCCES and RIAS Verbal Scale, as indicated by high factor loadings on a common underlying construct, which may represent general verbal and crystallized intelligence. Additionally, the study will explore the relationship between mathematical problem-solving and the other variables, given the distinction between mathematical and verbal abilities noted in previous research (Deary et al., 2007).
This study builds on the existing literature by providing a more detailed examination of the relationship between the JCCES and RIAS Verbal Scale, which has implications for both theory and practice. Understanding the relationship between these two instruments can inform the development of educational interventions and assessments tailored to the specific needs of learners with different cognitive profiles (Kaufman & Lichtenberger, 2006; McGrew & Flanagan, 1998). Furthermore, the findings contribute to the understanding of the structure of cognitive abilities, particularly the relationship between crystallized intelligence and verbal abilities (Ackerman, 1996). This may be useful for refining theoretical models of cognitive abilities and guiding future research in this area (Carroll, 2003; Deary et al., 2007).
Method
Research Design
The current study employed a correlational research design to investigate the relationship between the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the Reynolds Intellectual Assessment (RIAS) Verbal Scale. This design allowed for the examination of associations between the variables without manipulating or controlling any of the measures (Creswell, 2009). A correlational design was chosen because it is well-suited for studying the relationships among naturally occurring variables, such as crystallized intelligence and verbal abilities (Campbell & Stanley, 1963; Kerlinger, 2000).
Participants
A total of 125 participants were recruited for this study, 81 males (64.71%) and 44 females (35.29%). The participants’ mean age was 33.82 years (SD = 12.56). In terms of education, 79.83% of the participants held at least a college degree. Participants were recruited using convenience sampling methods, such as posting advertisements on social media and online forums.
Materials
The JCCES is a measure of crystallized intelligence, consisting of three subtests: Verbal Analogies (VA), Mathematical Problems (MP), and General Knowledge (GK). The RIAS Verbal Scale (Reynolds & Kamphaus, 2003) is a measure of verbal intelligence, consisting of two subtests: Guess What? (GWH) and Verbal Reasoning (VRZ). Both the JCCES and RIAS have been validated in previous research and have demonstrated strong psychometric properties.
Procedure
Participants were provided with informed consent forms. The tasks were presented in a fixed order, starting with the JCCES (VA, MP, and GK) followed by the RIAS Verbal Scale (GWH and VRZ). Instructions for each task were provided before the commencement of each subtest. Participants were given unlimited time to complete the tasks. Upon completion of the tasks, participants were debriefed and thanked for their participation.
Statistical Analysis
Data were analyzed using Excel. Descriptive statistics were calculated for the demographic variables, and a Principal Component Analysis (PCA) was conducted to examine the relationships among the JCCES and RIAS Verbal Scale subtests (Jolliffe, 1986). The PCA included Bartlett’s sphericity test to assess the suitability of the data for PCA (Bartlett, 1954) and the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy to evaluate the adequacy of the sample size for each variable (Kaiser, 1974; Hutcheson & Sofroniou, 1999).
Results
The present study investigated the relationship between the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the Reynolds Intellectual Assessment (RIAS) Verbal Scale. A Principal Component Analysis (PCA) was conducted to test the research hypotheses. This analysis was performed on five variables: Verbal Analogies (VA), Mathematical Problems (MP), and General Knowledge (GK) from JCCES, and Guess What? (GWH) and Verbal Reasoning (VRZ) from RIAS. The PCA was a Pearson (n) type, with no missing data for any of the variables. The analysis included Bartlett’s sphericity test to assess the suitability of the data for PCA, and the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy to evaluate the adequacy of the sample size for each variable.
Results of the Statistical Analyses
The correlation matrix revealed significant positive correlations between all the variables, with coefficients ranging from 0.471 to 0.761. Bartlett’s sphericity test confirmed the appropriateness of the data for PCA (χ² = 385.145, df = 10, p < 0.0001, α = 0.05). The KMO measure of sampling adequacy was satisfactory for all variables (0.844 to 0.891) and the overall KMO value was 0.868, indicating an adequate sample size.
The PCA extracted five factors with eigenvalues ranging from 0.224 to 3.574. The first factor (F1) accounted for 71.472% of the total variance, the second factor (F2) for 12.329%, and the remaining factors (F3 to F5) for 16.199%. A Varimax rotation was applied to facilitate the interpretation of the factor loadings. After rotation, the percentage of variance accounted for by the first two factors (D1 and D2) was 57.213% and 26.588%, respectively, totaling 83.801% of the cumulative variance.
The rotated factor loadings revealed that VA, GK, GWH, and VRZ loaded highly on the first factor (D1), with loadings ranging from 0.774 to 0.894. MP loaded highly on the second factor (D2), with a loading of 0.952.
Interpretation of the Results
The results of the PCA support the hypothesis that there is a strong relationship between the JCCES and the RIAS Verbal Scale, as indicated by the high loadings of the VA, GK, GWH, and VRZ variables on the first factor (D1). This factor can be interpreted as a common underlying construct, which may represent general verbal and crystallized intelligence. The high loading of the MP variable on the second factor (D2) suggests that mathematical problem-solving is a distinct construct from the general verbal and crystallized intelligence measured by the other variables.
Limitations
There are some limitations to this study that may have affected the results. First, the sample size of 125 participants is relatively small, which may limit the generalizability of the findings. However, the KMO measure indicated that the sample size was adequate for the PCA. Second, the sample was not equally distributed in terms of gender, with a majority of males (64.71%) and a high percentage of participants with at least one college degree (79.83%). This may have introduced selection bias, potentially limiting the applicability of the findings to more diverse populations. Lastly, the study relied solely on PCA to analyze the relationships between the variables, and future research may benefit from using additional statistical techniques, such as confirmatory factor analysis, structural equation modeling, or multiple regression, to further validate the findings and provide a more comprehensive understanding of the relationships among the variables.
Discussion
Interpretation of the Results in the Context of the Research Hypotheses and Previous Research
The present study aimed to investigate the relationship between the JCCES and the RIAS Verbal Scale, with the results supporting a strong relationship between these two measures. This finding is consistent with previous research on the relationship between crystallized intelligence and verbal abilities (e.g., Cattell, 1971; Horn & Cattell, 1966; Carroll, 1993). The high loadings of VA, GK, GWH, and VRZ on the first factor (D1) suggest a common underlying construct, which may represent general verbal and crystallized intelligence. This is supported by the notion that crystallized intelligence involves the acquisition and application of verbal and cultural knowledge, as well as the ability to reason using previously learned information (Cattell, 1963). Studies have consistently demonstrated that crystallized intelligence is closely related to verbal abilities, reflecting an individual’s ability to access and utilize their accumulated knowledge base (Ackerman, 1996; Kaufman & Lichtenberger, 2006).
The high loading of MP on the second factor (D2) indicates that mathematical problem-solving is a distinct construct from general verbal and crystallized intelligence. This finding adds to the existing literature on the differentiation of mathematical abilities from verbal abilities (e.g., Deary et al., 2007). Moreover, the significant positive correlations between all the variables suggest that there may be some shared cognitive processes underlying performance on these tasks, consistent with the concept of a general factor of intelligence (Spearman, 1904).
Implications for Theory, Practice, and Future Research
The results of this study have several important implications. First, they provide empirical support for the relationship between crystallized intelligence and verbal abilities, as well as the distinction between mathematical and verbal abilities (Cattell, 1971; Horn & Cattell, 1966; Carroll, 1993). This can inform the development of educational interventions and assessments that are tailored to the specific needs of learners with different cognitive profiles (Kaufman & Lichtenberger, 2006; McGrew & Flanagan, 1998). For example, educators can use the JCCES and RIAS Verbal Scale to identify students who may benefit from additional support in developing their verbal or mathematical skills (Fletcher et al., 2007).
Second, the findings contribute to the understanding of the structure of cognitive abilities, particularly the relationship between crystallized intelligence and verbal abilities (Ackerman, 1996). This may be useful for refining theoretical models of cognitive abilities and guiding future research in this area (Carroll, 2003; Deary et al., 2007). For instance, researchers could investigate the underlying cognitive processes that contribute to the shared variance between the JCCES and RIAS Verbal Scale, as well as the processes that differentiate mathematical problem-solving from verbal and crystallized intelligence (Geary, 1994; Hattie, 2009). This could involve examining the role of working memory, attention, and executive functions in the development of these cognitive abilities (Baddeley, 2003; Conway et al., 2002).
Limitations and Alternative Explanations
Although the present study has several strengths, there are also some limitations that warrant consideration. As noted earlier, the sample size was relatively small, and the sample was not equally distributed in terms of gender and educational attainment. This may limit the generalizability of the findings and introduce potential selection bias (Maxwell, 2004; Pedhazur & Schmelkin, 1991). Future research should aim to replicate these findings in larger and more diverse samples to increase the robustness and external validity of the results (Cook & Campbell, 1979; Shadish et al., 2002).
Additionally, the study relied solely on PCA to analyze the relationships between the variables. Future research could employ other statistical techniques, such as confirmatory factor analysis (Jöreskog, 1969; Bollen, 1989), structural equation modeling (Kline, 2005; Schumacker & Lomax, 2004), or multiple regression (Cohen et al., 2003; Tabachnick & Fidell, 2007), to further validate the findings and provide a more comprehensive understanding of the relationships among the variables. These alternative statistical approaches could help to address potential methodological issues, such as measurement error and the influence of confounding variables, and strengthen the evidence base for the observed relationships between crystallized intelligence and verbal abilities (Bryant & Yarnold, 1995; Little et al., 1999).
Directions for Future Research
Based on the findings and limitations of the present study, several directions for future research can be identified. First, researchers could investigate the underlying cognitive processes that contribute to the shared variance between the JCCES and RIAS Verbal Scale, as well as the processes that differentiate mathematical problem-solving from verbal and crystallized intelligence (Neisser et al., 1996; Stanovich & West, 2000). This could involve examining the neural substrates of these cognitive abilities (Jung & Haier, 2007), as well as the role of environmental and genetic factors in their development (Plomin & Spinath, 2004).
Second, future research could examine the predictive validity of the JCCES and RIAS Verbal Scale for various educational and occupational outcomes, such as academic achievement, job performance, and job satisfaction (Deary, 2001; Kuncel et al., 2004). This would help to establish the practical utility of these measures in real-world settings and inform the development of evidence-based interventions and policies aimed at fostering individual success and well-being (Gottfredson, 1997).
Third, researchers could explore the potential moderating role of individual differences, such as age, gender, and socioeconomic status, on the relationship between the JCCES and RIAS Verbal Scale (Deary et al., 2005; Lubinski & Benbow, 2006). This would help to identify specific subgroups of the population for whom these measures may be particularly informative or relevant and inform the development of targeted interventions and supports.
Finally, future research could investigate the longitudinal stability of the relationships between the JCCES and RIAS Verbal Scale, as well as the potential causal mechanisms underlying these relationships (McArdle et al., 2002). Longitudinal designs would allow researchers to examine the development and change of cognitive abilities over time (Baltes et al., 1980) and provide insights into the factors that contribute to the observed patterns of covariation among the variables (Salthouse, 2004).
Conclusion
In conclusion, the present study examined the relationship between the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the Reynolds Intellectual Assessment (RIAS) Verbal Scale using a Principal Component Analysis (PCA). The results of the PCA supported the hypothesis that there is a strong relationship between the JCCES and the RIAS Verbal Scale, with the first factor representing a common underlying construct of general verbal and crystallized intelligence and the second factor representing mathematical problem-solving as a distinct construct. The findings contribute to the understanding of the structure of cognitive abilities and have implications for theory, practice, and future research. The study provides empirical support for the relationship between crystallized intelligence and verbal abilities and the differentiation of mathematical abilities from verbal abilities. The results can inform the development of educational interventions and assessments that are tailored to the specific needs of learners with different cognitive profiles. The study’s limitations include a relatively small sample size and an unequal distribution of gender and educational attainment, highlighting the need for future research to replicate the findings in larger and more diverse samples. Future research could also investigate the underlying cognitive processes, predictive validity, individual differences, and longitudinal stability of the relationships among these variables.
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