A Meta-Analysis of Spearman’s Hypothesis in the United States

The present findings greatly generalise those of more restricted meta-analyses of Spearman's Hypothesis in adult US Black-White data, extending their scope with respect to moderation.

“These findings greatly generalise those of more restricted meta-analyses of SH in adult US W-B data (te Nijenhuis & van den Hoek, 2016) extending their scope with respect to moderation.”

• cites te Nijenhuis & van den Hoek, 2016 sourceSupported

Overcorrection, where the vector correlation becomes greater than 1.00, is a commonly encountered problem when disattenuation adjustments are applied.

“overcorrection (where the vector correlation becomes >1.00) is a commonly encountered problem when these sorts of adjustments are applied (e.g., Woodley of Menie et al., 2018).”

• cites Woodley of Menie et al., 2018 sourcePartly supported

  In the Analysis involving MCV section (page not specified), the paper reports one vector correlation that rose above 1.00 after measurement-error correction and calls this overcorrection. That supports the definition and an example, but not the claim that the problem is commonly encountered. (LLM, conf=0.87)

  Experimental — accuracy not yet measured

Among incarcerated and institutionalized (carceral) populations, Spearman's Hypothesis appears to be reversed.

“Of relevance are findings from incarcerated and institutionalized (carceral) populations, amongst whom SH appears to be reversed (Woodley of Menie et al., 2025).”

• cites Woodley of Menie et al., 2025 sourceSupported

Trim-and-fill imputed no missing effect sizes.

“Trim-and-fill imputed no missing effect sizes.”

• Also stated in: § Publication bias · plain

  “Trimand-fill revealed no potentially missing effect sizes.”

Trim-and-fill yielded no indications of missing effect sizes.

“Trim-and-fill yielded no indications of missing effect sizes.”

The age moderator exhibits a statistically significant effect.

“The age moderator was found to exhibit a statistically significant effect.”

• Also stated in: § Discussion · plain

  “Mean age Per year -.003 .002-.007 to -.000 .042”

The prediction interval for the mean vector correlation was .628 to .862.

“with a prediction interval of .628 to .862”

• Also stated in: § Meta-analysis · plain

  “The prediction interval ranged from .628 to .862.”

Between-study heterogeneity was I2 = 25.61%, 95% CI [0.00%, 50.5%].

“modest between-study heterogeneity, I² = 25.61%,95% CI [0.00%, 50.5%]”

• Also stated in: § Meta-analysis · plain

  “Heterogeneity fell into the moderate range based on conventional guidelines, I 2 = 25.61%,95% CI [0.00%, 50.5%]”

No quadratic effect of age was detected.

“No quadratic effect of age was detected.”

• Also stated in: § Meta-analysis · plain

  “A quadratic analysis was also conducted on age to check for non-linear moderation; however, the results were nonsignificant (F(1,41)=.002,p=.962, ΔAIC = +1.98).”

Sampling error accounts for between 46.3% and 82.7% of the variance amongst effect sizes, depending on the estimation protocol.

“Sampling error accounts for between 46.3% and 82.7% of the variance amongst effect sizes (depending on the estimation protocol), leaving some room for moderatorrelated heterogeneity.”

Sampling error accounted for 46.3% to 82.7% of between-study variance, depending on estimator.

“Sampling error accounted for 46.3% to 82.7% of between-study variance, depending on estimator”

A three-moderator meta-regression including harmonic N, sample mean age, and study year yielded evidence of negative moderation by sample age.

“A three-moderator meta-regression including harmonic N, sample mean age, and study year yielded evidence of negative moderation by sample age.”

• AssumptionRests on an assumption: The mean or midpoint sample ages sourced from studies or inferred are accurate.

Only one of the bare-bones sampling error estimates exceeds the 75% rule-of-thumb threshold.

“Only one of these estimates exceeds the 75% rule-ofthumb threshold (Schmidt et al., 1988) indicating that variability amongst the vector correlations likely reflects meaningful residual variance and is therefore more than just sampling error, consistent with the action of potential age moderation.”

• cites Schmidt et al., 1988 sourceNot checked — no full text of the source

A random-effects model using subtest number to estimate inverse-variance weights yielded a mean vector correlation of r = .745, 95% CI [.699, .792].

“A random-effects model, using subtest number to estimate inverse-variance weights, yielded a large-magnitude positive mean vector correlation, r = .745,95% CI [.699, .792]”

• Also stated in: § Meta-analysis · plain

  “The aggregate effect size is .745,95% CI [.699, .792].”

• AssumptionRests on an assumption: The included samples are representative of the US White and Black populations.
• AssumptionRests on an assumption: The subtest g-loadings used from each study are valid measures of g.

If increasing age is associated with a larger contribution of idiosyncratic, non-shared, health-related, and stochastic influences to cognitive-performance variance, then the alignment between g-loadings and between-group subtest differences should weaken.

“If increasing age is associated with a larger contribution of idiosyncratic, non-shared, healthrelated, and stochastic influences to cognitive-performance variance, then the alignment between g-loadings and between-group subtest differences should weaken.”

Age is a theoretically important moderator of Spearman's Hypothesis in the context of representative samples.

“Age is a theoretically important moderator of SH in the context of representative samples.”

Moderator collinearity was low, with variance inflation factors ranging from 1.043 to 1.079.

“Moderator collinearity was low, with variance inflation factors ranging from 1.043 to 1.079 (values <5 are considered indicative of negligible collinearity; Menard, 1995).”

• cites Menard, 1995Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Sensitivity analysis on the Fisher-z scale yielded substantively similar results to the primary raw-r model.

“As the primary model is presented using a raw-r scale, a sensitivity analysis was conducted in which models that were also estimated on the Fisher-z scale were back-transformed; these yielded substantively similar results.”

Heterogeneity fell into the moderate range based on conventional guidelines.

“Heterogeneity fell into the moderate range based on conventional guidelines, I 2 = 25.61%,95% CI [0.00%, 50.5%]”

The age-related attenuation of Spearman's Hypothesis is compatible with anti-Wilson-effect accounts of late-life cognition, in which the genetic structuring of g becomes increasingly disrupted by cumulative environmental insults.

“This is compatible with anti-Wilson-effect accounts of late-life cognition, in which the genetic structuring of g becomes increasingly disrupted by cumulative environmental insults (Sarraf et al., 2023(Sarraf et al., , 2025)).”

• cites Sarraf et al., 2023 sourceNot checked — no full text of the source
• cites Sarraf et al., 2025 sourceNot checked — no full text of the source

The confidence interval for heterogeneity spans values consistent with relatively low to substantial heterogeneity.

“although the confidence interval spans values consistent with relatively low to substantial heterogeneity (Deeks et al., 2024).”

• cites Deeks et al., 2024Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

There is evidence that the direction of the effect is not invariant across contexts.

“However, there is also evidence that the direction of the effect is not invariant across contexts.”

The primary limitation of the meta-analysis is that the effect sizes were not disattenuated for error.

“The primary limitation is that the effect sizes were not disattenuated for error.”

The aggregate effect size is of large magnitude (r ≥ .50).

“This is of large magnitude (r≥.50, Cohen, 1988).”

• cites Cohen, 1988Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Variation in the magnitude of the SH vector correlation across studies might, in some instances, provide limited information about causal moderation.

“Thus, variation in the magnitude of the SH vector correlation across studies might, in some instances, provide limited information about causal moderation.”

The results suggest complex environmental confounding potentiating, attenuating, or even reversing the g-dependence of W-B differences.

“The results instead suggest complex environmental confounding potentiating, attenuating, or even reversing the g-dependence of W-B differences.”

• AssumptionRests on an assumption: The included samples are representative of the US White and Black populations.
• AssumptionRests on an assumption: The subtest g-loadings used from each study are valid measures of g.

Factors such as range restriction with respect to the nomological breadth of g loadings, the reliabilities of the g and Black-White vectors, and the validity of the g vector contribute to between-study heterogeneity independently of sampling error.

“Factors such as range-restriction with respect to the nomological breadth of g loadings, in addition to the reliabilities of the g and W-B vectors, and even the validity of the g vector will contribute to betweenstudy heterogeneity independently of sampling error (Jensen, 1998).”

• cites Jensen, 1998Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Age-related attenuation of Spearman's Hypothesis implies that Black-White differences become less cleanly organized with respect to g as non-g and environmentally contingent sources of variance accumulate.

“Age-related attenuation of SH therefore implies that such differences become less cleanly organized with respect to g, as non-g and environmentally contingent sources of variance accumulate.”

Some variance in the data is potentially due to moderators rather than sampling error.

“suggesting that some variance in those data is potentially due to moderators rather than sampling error”

The finding that the magnitude and even the sign of vector correlations vary across age-related contexts is inconsistent with the idea that Spearman's Hypothesis is isomorphic to g as proposed in its strongest form by Gordon (1985).

“The finding that the magnitude, and even the sign of vector correlations vary across age-related contexts is inconsistent with the idea that SH is isomorphic to g (as proposed in its strongest form by Gordon, 1985).”

• cites Gordon, 1985 sourceNot checked — no full text of the source

Spearman's Hypothesis appears to be weaker in older samples.

“SH therefore appears to be weaker in older samples.”

• AssumptionRests on an assumption: The mean or midpoint sample ages sourced from studies or inferred are accurate.

Evidence from later life suggests that the structure of cognitive variance changes again, as health-related and idiosyncratic environmental influences become more prominent.

“evidence from later life suggests that the structure of cognitive variance changes again, as healthrelated and idiosyncratic environmental influences become more prominent.”

The presence of age-dependent moderation, including both reversals and attenuation of effect sizes in older samples, makes claimed isomorphism between g and W-B differences difficult to sustain.

“The presence of age-dependent moderation, including both reversals and attenuation of effect sizes in older samples, makes claimed isomorphism between g and W-B differences difficult to sustain.”

• AssumptionRests on an assumption: The included samples are representative of the US White and Black populations.
• AssumptionRests on an assumption: The subtest g-loadings used from each study are valid measures of g.

In Peñaherrera-Aguirre et al. (2022), the vector of gene-by-environment interaction effects clustered positively and significantly with a group-differences vector, g loadings, and a shared environmentality vector.

“In Peñaherrera-Aguirre et al. (2022) it was found specifically that the vector of these clustered positively and significantly with a group-differences vector, g loadings, and a shared environmentality vector.”

• cites Peñaherrera-Aguirre et al. (2022) sourceNot checked — no full text of the source

The straightforward interpretation of Spearman's Hypothesis as demonstrating some non-trivial degree of moderation from g on the group-difference vector is reasonable.

“which indicates that the straightforward interpretation of SH as demonstrating some non-trivial degree of moderation from g on the group-difference vector is reasonable.”

Vector correlations can be distorted by subtest sampling in such a way as to yield misleading indications of g-moderated differences.

“vector correlations can be distorted by subtest sampling in such a way as to yield misleading indications of g moderated differences (Ashton & Lee, 2005).”

• cites Ashton & Lee, 2005 sourceNot checked — no full text of the source