JCCES and ACT: A Factor Analysis

The American College Test (ACT) is one of the two dominant college-admission examinations in the United States, alongside the SAT. Its four sections — English, Mathematics, Reading, and Science Reasoning — collectively claim to measure college readiness across the major academic domains. Whether the ACT also measures something like general cognitive ability — the latent g factor that Spearman (1904) identified as the common variance running through all cognitive tests — is a long-running empirical question, with subsequent work (Deary, Strand, Smith, & Fernandes, 2007; Koenig, Frey, & Detterman, 2008) showing that ACT performance correlates strongly with intelligence-test scores. This study examines that question directly by factor-analyzing the ACT’s four section scores together with the three subtests of the Jouve Cerebrals Crystallized Educational Scale (JCCES) on the same 60 respondents, asking whether a single underlying factor accounts for the bulk of variance across both batteries.

The two batteries and the hypothesis

The JCCES measures crystallized intelligence through three subtests: Verbal Analogies (VA), Mathematical Problems (MP), and General Knowledge (GK). The construct is grounded in Cattell-Horn theory: crystallized intelligence reflects acquired knowledge and skills shaped by education and experience, and the JCCES tasks index its core domains.

The ACT measures college readiness through English (ENG), Mathematics (MATH), Reading (READ), and Science Reasoning (SCIE). Each section has its own content focus, but all four are administered together as a single composite-score test, with the assumption built in that they measure related cognitive demands.

If both batteries tap a common underlying ability — Spearman’s g — then a factor analysis of the seven subtests should recover a single dominant factor on which all seven load substantially. If they measure distinct constructs, separate factors should emerge for the JCCES versus ACT subtests, similar to the two-factor structure recovered when JCCES is paired with the nonverbal-only GAMA battery. The factor-analytic test discriminates between these alternatives directly.

Method

Sixty participants — high school seniors and college students — provided their most recent ACT scores and completed the JCCES online. The JCCES was administered with standardized procedures; ACT scores were self-reported from prior test administration. No exclusion criteria were applied beyond requiring both batteries’ scores to be available.

Pearson correlations were computed for all seven subtest pairs. Principal factor analysis with Varimax rotation was conducted following Fabrigar, Wegener, MacCallum, and Strahan’s (1999) recommendations: initial communalities estimated as squared multiple correlations, convergence criterion 0.0001, maximum 50 iterations. The Kaiser-Meyer-Olkin (KMO) measure assessed sampling adequacy; Cronbach’s alpha assessed internal consistency.

Results

The KMO was 0.809, comfortably above the 0.6 adequacy threshold and approaching the 0.8 “good” range. Cronbach’s alpha for the combined seven-subtest set was 0.887, indicating strong internal consistency. The Pearson correlation matrix showed significant positive correlations across all seven subtests at α = 0.05, including substantial cross-battery correlations between JCCES and ACT subtests.

The factor analysis produced three eigenvalues, but only the first exceeded the conventional Kaiser threshold of 1.0:

• Factor 1: eigenvalue 3.759, accounting for 53.697% of total variance — the dominant factor.
• Factor 2: eigenvalue 0.437, accounting for 6.242% of variance — well below the Kaiser threshold.
• Factor 3: eigenvalue 0.251, accounting for 3.587% of variance — also below threshold.

The strict Kaiser criterion would retain only the first factor; the second and third are statistically marginal and do not represent substantive additional structure. The cumulative variance explained by all three is 63.526%, but essentially all of that is contributed by F1.

Factor 1 loadings

The single substantive factor showed uniformly high loadings across all seven subtests:

• JCCES Verbal Analogies (VA): 0.631
• JCCES Mathematical Problems (MP): 0.734
• JCCES General Knowledge (GK): 0.651
• ACT English (ENG): 0.802
• ACT Mathematics (MATH): 0.881
• ACT Reading (READ): 0.744
• ACT Science Reasoning (SCIE): 0.905

The loadings range from 0.631 (VA) to 0.905 (SCIE), with an average around 0.77. Final communalities ranged from 0.361 (VA) to 0.742 (SCIE), indicating that the single-factor model captures roughly 36-74% of the variance in each individual subtest. The four ACT sections loaded slightly higher on F1 than the three JCCES subtests, but the loading gap is modest and the substantive interpretation — all seven subtests reflect a common underlying ability — is well-supported.

What the structure implies

The single-factor recovery argues for a substantial overlap in what the JCCES and ACT measure. F1 explains 53.697% of the joint variance — more than half — and every subtest loads at 0.6 or above on it. This is the empirical pattern that Spearman’s (1904) general intelligence factor would predict, and the result aligns with prior findings that ACT performance correlates strongly with conventional intelligence measures (Koenig, Frey, & Detterman, 2008) and with broader academic-achievement-and-IQ correlations (Deary, Strand, Smith, & Fernandes, 2007).

The contrast with the JCCES + GAMA pairing, which recovered a clean two-factor structure (one crystallized-verbal, one fluid-nonverbal), is informative. The JCCES + GAMA result is what construct theory predicts when the two batteries target deliberately distinct cognitive domains. The JCCES + ACT result is what construct theory predicts when both batteries target overlapping cognitive demand — academic content that draws heavily on crystallized knowledge plus the general reasoning ability that mediates academic performance across content areas.

The interpretation does not require that the JCCES and ACT measure exactly the same construct. The shared variance F1 captures may reflect g, or it may reflect crystallized intelligence specifically (since both batteries are heavily knowledge-loaded), or it may reflect a more general academic-readiness construct that the two distinct measurement frameworks both tap. Disambiguating among these requires additional batteries that can isolate g from crystallized-specific variance, which is beyond the scope of this two-battery analysis.

The eigenvalue pattern

The factor analysis produced one dominant eigenvalue (3.759) and two trivially small ones (0.437, 0.251). Under factor-retention methodology, only F1 should be retained on Kaiser’s criterion, and parallel analysis or fit-index difference methods would also point to a one-factor solution given the eigenvalue gap. The original analysis reports three factors but the second and third explain trivial variance and have eigenvalues an order of magnitude below F1. The substantive reading is that the JCCES + ACT data support a one-factor model, with the apparent F2 and F3 representing residual sampling noise rather than substantive additional structure.

Methodological caveats

The 60-participant sample is small for factor analysis with seven variables. The KMO of 0.809 is reassuring about sampling adequacy, but factor-loading estimates from a sample this size have wide confidence intervals, and replication in larger samples would strengthen the result. The high Cronbach’s alpha (0.887) confirms internal consistency but is partly a function of the high single-factor loadings — internal consistency assesses something close to what factor analysis is also assessing, so the two metrics are not independent evidence.

The lack of demographic data prevents analysis of how the factor structure varies across age, education, or cultural background. ACT performance is known to vary by socioeconomic background, schooling quality, and test-prep access; whether the JCCES + ACT factor structure is invariant across these moderators is an open question that the present sample cannot address.

The reliance on factor analysis alone — without complementary methods like structural equation modeling or item response theory — limits the ability to test alternative measurement models. A confirmatory factor analysis with a hypothesized one-factor structure would test whether the model adequately fits the data, including absolute-fit indices like RMSEA and CFI; the present exploratory analysis recovers the dominant factor but does not formally test the one-factor model against alternatives.

Implications for practice

For colleges using ACT scores in admissions: the result reinforces that the ACT functions as a general cognitive measure in addition to a content-area assessment. Whatever interpretation institutions place on the ACT — whether as an academic-readiness signal, a general-ability signal, or a mix — the empirical structure suggests a substantial single-dimension reduction is defensible.

For test developers: a battery whose subtests load uniformly high on a single factor is doing its job if the goal is to measure a unified construct. A battery whose subtests load on multiple distinct factors is doing its job if the goal is to measure separable constructs. The two designs serve different purposes; the JCCES-ACT pairing illustrates the first, the JCCES-GAMA pairing illustrates the second.

For research on intelligence and academic achievement: the result fits cleanly into the established literature showing strong g-loadings on standardized college-admission measures. The novel contribution is testing this directly with the JCCES + ACT pairing in the same sample, which adds a data point to the broader case that mainstream cognitive batteries and academic-readiness tests share substantial common variance.

Frequently Asked Questions

Why did F2 and F3 appear in the analysis if they’re below the Kaiser threshold?

Some factor-analysis software reports all eigenvalues above zero by default, even those below the Kaiser threshold of 1.0. The standard interpretation under Kaiser’s rule is to retain only F1 (eigenvalue 3.759); F2 (0.437) and F3 (0.251) reflect residual sampling noise and do not represent substantive additional structure. Modern factor-retention methods would also point to a one-factor solution given the eigenvalue gap.

What does it mean that all subtests load high on F1?

It means that variation across respondents on each subtest is largely accounted for by a common underlying factor. When this factor explains 53.697% of variance and every loading exceeds 0.6, the substantive interpretation is that the seven subtests reflect a single dominant cognitive ability — most plausibly general cognitive ability or g — rather than a collection of separable domain-specific abilities.

How does this compare to the JCCES + GAMA factor analysis?

The JCCES + GAMA factor analysis recovered a clean two-factor structure (crystallized-verbal vs nonverbal-fluid) on the same 63 respondents who completed both batteries. The contrast with the present one-factor JCCES + ACT result is informative: GAMA targets a deliberately distinct cognitive domain from JCCES, while ACT shares substantial cognitive demand with JCCES and produces a single-factor structure.

Does this mean the ACT measures intelligence?

It means the ACT shares substantial variance with a crystallized-intelligence battery (JCCES) on this 60-participant sample. Whether the shared variance represents g, crystallized intelligence specifically, or a broader academic-readiness construct cannot be disambiguated from a two-battery analysis alone. The factor analysis is consistent with all three interpretations.

How large does a factor-analysis sample need to be?

Conventional rules of thumb suggest 5-10 respondents per variable, with 100+ respondents for stable solutions. Sixty respondents for seven variables is on the low end; the recovered structure is plausible but should be replicated in larger samples before being treated as definitive.