JCCES and RIAS Verbal Scale: PCA Analysis

Crystallized intelligence and verbal ability are conceptually overlapping but operationally distinct constructs. The Cattell-Horn theory (Cattell, 1963; Horn & Cattell, 1966) treats crystallized intelligence as the broad ability that subsumes verbal-knowledge tasks, but a battery designed to measure crystallized intelligence directly may share so much variance with a battery designed to measure verbal ability that the two are statistically indistinguishable. This study tested whether the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the verbal-loaded subtests of the Reynolds Intellectual Assessment Scale (RIAS; Reynolds & Kamphaus, 2003) tap a common underlying factor when both are administered to the same respondents. Principal component analysis (PCA) of the combined five-subtest set on 125 adult participants returned a strong two-factor structure: a dominant verbal/crystallized factor on which both batteries’ verbal subtests load, and a smaller mathematical factor on which only the JCCES Mathematical Problems subtest loads.

Why this analysis matters

The JCCES is constructed as a measure of crystallized intelligence with three subtests: Verbal Analogies (VA), Mathematical Problems (MP), and General Knowledge (GK). The RIAS Verbal Scale is two subtests: Guess What? (GWH; an information/factual-knowledge task) and Verbal Reasoning (VRZ). Both batteries’ verbal subtests draw on accumulated knowledge, semantic structure, and language-mediated reasoning. The expected empirical pattern: the four verbal-loaded subtests (VA, GK, GWH, VRZ) should correlate strongly and load on a common factor, while MP — though designated a JCCES subtest — should load on a separate mathematical-reasoning factor.

If this pattern emerges, three substantive points follow. First, JCCES VA and GK are functionally equivalent to RIAS verbal-scale subtests as measures of the verbal/crystallized construct. Second, JCCES MP is a distinct cognitive demand that the verbal-side cluster does not capture, supporting the case that mathematical reasoning is a separable ability not fully reducible to verbal/crystallized intelligence. Third, the JCCES total composite is a heterogeneous index combining two distinct constructs (verbal + mathematical), with implications for how it should be interpreted and reported.

Method

One hundred and twenty-five adults (81 male, 44 female; mean age 33.82, SD 12.56; 79.83% with college degree or higher) completed the JCCES (VA, MP, GK) and the RIAS Verbal Scale (GWH, VRZ) in fixed order with unlimited time per subtest. Standardized administration procedures were used for both batteries. Recruitment was through convenience sampling from social media and online forums.

The five subtest scores per participant were submitted to principal component analysis using Pearson correlations as the input. Bartlett’s test of sphericity assessed whether the correlation matrix was suitable for PCA, and the Kaiser-Meyer-Olkin (KMO) measure (Kaiser, 1974) assessed sampling adequacy at the variable and overall levels. Varimax rotation was applied to facilitate interpretation of the factor structure.

Results

Inter-subtest correlations were uniformly positive, ranging from 0.471 to 0.761. Bartlett’s test rejected the sphericity null at high significance (χ² = 385.145, df = 10, p < .0001), confirming that the correlation matrix had structure suitable for PCA. The KMO measure was 0.868 overall, with subtest-level values ranging from 0.844 to 0.891 — comfortably above the 0.6 adequacy threshold and approaching the 0.9 "excellent" range.

The unrotated PCA extracted five components with eigenvalues from 0.224 to 3.574. The first component (F1) accounted for 71.472% of total variance, the second (F2) for 12.329%, and the remaining three for the residual 16.199%. Only F1 had an eigenvalue clearly above 1 (the Kaiser threshold). After Varimax rotation, the rebalanced two-component solution distributed variance more evenly: D1 captured 57.213% and D2 captured 26.588%, totaling 83.801% of cumulative variance — a high-fidelity reproduction of the original correlation structure in two dimensions.

The rotated factor loadings recovered the predicted pattern cleanly:

• Factor D1 (verbal/crystallized): VA (JCCES) loaded at the high end of the range (0.774-0.894); GK (JCCES) and GWH (RIAS) and VRZ (RIAS) all loaded similarly. The four verbal-loaded subtests merge on this factor regardless of which battery they come from.
• Factor D2 (mathematical): MP (JCCES) loaded at 0.952 with no other subtest loading substantively. The mathematical-reasoning subtest stood alone on this factor.

The factor solution captures both the within-construct equivalence of the verbal-side subtests and the between-construct distinctiveness of the mathematical subtest. This is the empirical structure that the Cattell-Horn framework (Cattell, 1963; Horn & Cattell, 1966) predicts when crystallized verbal ability and quantitative reasoning are jointly measured: substantial shared variance among verbal-side measures, and a distinct mathematical component that does not reduce to the verbal-side cluster.

What this means for JCCES interpretation

The factor structure has direct implications for how the JCCES total composite should be interpreted. The composite combines a verbal/crystallized factor (heavy weighting from VA and GK) with a mathematical factor (loading from MP). Two respondents with the same composite score can have very different cognitive profiles: one strong in verbal abilities and weak in mathematical, the other the reverse, with the composite obscuring the difference. For applications where the cognitive profile matters — clinical assessment, vocational counseling, individualized educational planning — reporting subtest-level scores or factor-derived sub-composites preserves information that the global composite collapses.

The substitutability of JCCES verbal subtests with RIAS verbal subtests is an additional practical finding. A researcher who has access to one battery but not the other can use the verbal-side measures as functional equivalents for many research purposes, with the caveat that the mathematical content of the JCCES is not captured by the RIAS Verbal Scale. The empirical pattern supports cross-battery research designs that previously had to assume rather than demonstrate this substitutability.

The result is consistent with the broader pattern from JCCES + RIAS / WAIS / SAT validation: the JCCES taps the same general crystallized-IQ substrate that the established batteries do, with the additional mathematical component that the JCCES uniquely contributes. The convergence across multiple validation studies — different samples, different comparison instruments, different statistical methods — is the empirical case for the JCCES as a valid member of the crystallized-IQ family.

Connection to the broader Cogn-IQ research program

The JCCES has been examined against multiple comparison batteries: against the GAMA via multidimensional scaling (clean separation between crystallized JCCES and nonverbal GAMA), against the GAMA via factor analysis (two-factor structure), against the ACT via factor analysis (single-factor structure when both batteries are jointly academic-loaded), and against multiple cognitive and academic measures via correlations. The present analysis adds another piece: when paired with a verbal-only battery (RIAS Verbal Scale), the JCCES verbal subtests merge into a common verbal/crystallized factor while the mathematical subtest separates.

The cumulative picture is that the JCCES has a hierarchical structure: at the broadest level, a crystallized-IQ composite; at the intermediate level, separable verbal and mathematical factors; at the finest level, three subtests with internal item-level structure. This hierarchy is consistent with the Carroll three-stratum framework (Carroll, 1993) applied to a smaller battery: a general factor at the apex, broad abilities below, and specific subtests at the base.

Methodological caveats

The 125-participant sample is comfortably adequate for a 5-variable PCA — well above the 5–10 respondents-per-variable rule of thumb — and the KMO of 0.868 confirms sampling adequacy directly. The substantive caveat is demographic rather than statistical: the sample skews male (64.71%) and college-educated (79.83% with degree), which may limit generalizability to non-selected populations. Cognitive-test performance is known to vary by educational background, and the factor structure could plausibly differ in samples with broader educational range.

PCA is a data-reduction technique, not a measurement-model test. The recovered structure is consistent with multiple measurement models (single general factor with two specific factors; two correlated factors; bifactor model with general + specific factors). A confirmatory factor analysis or structural equation modeling approach (Deary, Strand, Smith, & Fernandes, 2007 supplied related framing) could distinguish among these alternatives. The PCA result is suggestive of the verbal/mathematical separation but does not formally test it against more elaborate models.

The Varimax rotation enforces orthogonal factors. If the true verbal and mathematical factors are correlated — which Cattell-Horn theory predicts at higher hierarchical levels — an oblique rotation would recover a different but more interpretable structure. The orthogonal Varimax solution presented here is the standard simplification but understates whatever inter-factor correlation exists in the population.

Frequently Asked Questions

Why is the JCCES MP subtest separated from the verbal subtests?

Because the cognitive demand is different. JCCES VA, GK, and the RIAS Verbal Scale subtests all draw on accumulated linguistic and factual knowledge — the crystallized-verbal substrate. Mathematical Problems requires applied numerical reasoning, which recruits a partly separate cognitive system, including quantitative working memory and procedural mathematical knowledge. The factor analysis recovers this distinction empirically.

Are JCCES VA/GK and RIAS GWH/VRZ interchangeable?

For research purposes targeting the verbal/crystallized construct, they appear functionally substitutable in this sample. The four subtests load on the same factor with similar loading magnitudes, suggesting they tap the same underlying ability. The substitution should be empirically validated in any new sample, but the present result supports cross-battery research designs that treat verbal-side JCCES and RIAS measures as equivalent.

What does it mean that 83.801% of variance is captured by two factors?

It means the two-factor structure reproduces most of the inter-subtest correlation matrix accurately. The five subtests are not five independent dimensions; they are essentially two dimensions (verbal/crystallized + mathematical) plus residual variance. For a five-variable PCA, capturing 83% of variance in two factors is a high-fidelity reduction.

Should I use the JCCES total composite or sub-composites?

Use sub-composites or subtest scores when the cognitive profile matters. The total composite mixes verbal and mathematical contributions; respondents with very different profiles can have similar total scores. For applications where the profile information is relevant — clinical assessment, vocational guidance, educational planning — the sub-composites preserve information the total collapses.

How does this compare to the JCCES + GAMA result?

The JCCES + GAMA factor analysis recovered a clean two-factor structure with JCCES on one side (crystallized) and GAMA on the other (nonverbal/fluid). The present JCCES + RIAS result also recovers two factors, but the split is verbal/crystallized vs mathematical rather than crystallized vs fluid. The contrast illustrates that the recovered factor structure depends on which comparison battery is paired with the JCCES.