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Cited by 18Cognitive Abilities and TestingPsychometric Methodologies and TestingEducation, Achievement, and Giftedness

Spearman’s Hypothesis Tested on Black Adults: A Meta-Analysis

Open access
Te Nijenhuis, Jan, Van den Hoek, Michael·2016·Journal of Intelligence
DOI 10.3390/jintelligence4020006
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Abstract

Blacks generally score significantly lower on intelligence tests than Whites. Spearman’s hypothesis predicts that there will be large Black/White differences on subtests of high cognitive complexity, and smaller Black/White differences on subtests of lower cognitive complexity. Spearman’s hypothesis tested on samples of Blacks and Whites has consistently been confirmed in many studies on children and adolescents, but there are many fewer studies on adults. We carried out a meta-analysis where we collected the existing tests of Spearman’s hypothesis on adults and collected additional datasets on Black and White adults that could be used to test Spearman’s hypothesis. Our meta-analytical search resulted in a total of 10 studies with a total of 15 datapoints, with participants numbering 251,085 Whites and 22,326 Blacks in total. For all these data points, the correlation between the loadings of a general factor that is manifested in individual differences on all mental tests, regardless of content (g) and standardized group differences was computed. The analysis of all 15 data points yields a mean vector correlation of 0.57. Spearman’s hypothesis is confirmed comparing Black and White adults. The differences between Black and White adults are strongly in line with those previously found for children and adults; however, because of lack of access to the original data, we could not test for measurement invariance.

AI snapshot

Written from the paper’s full text.

TL;DR

This meta-analysis tested the weak form of Spearman’s hypothesis on Black and White adults, aggregating 10 studies and 15 datapoints. It found a mean vector correlation of 0.57 between g loadings and Black/White differences, confirming Spearman’s hypothesis for adults.

Key findings

  • Across 15 datapoints from 10 studies, the mean-weighted vector correlation between g loadings and adult Black/White differences was 0.57; participants numbered 251,085 Whites and 22,326 Blacks, with a total harmonic N = 76,884.
  • Sampling error explained only 0.6% of the variance in observed correlations, which the authors say suggests a strong moderator or several moderators.
  • The adult result was highly similar to Jensen’s earlier mean correlation of r = 0.59; prior adult Black/White datasets had correlations ranging from r = 0.30 to 0.81.
  • The correlations were positive in sign, and the large majority were substantial in magnitude.

Methods

  • Bare-bones psychometric meta-analysis using Hunter and Schmidt Meta-Analysis Programs, correcting only for sampling error. Inclusion required at least four tests/subtests for the Method of Correlated Vectors, samples not selected on a highly g-loaded variable, and average participant age of 18 or older.
  • Searches used Google Scholar, ProQuest, PsycINFO, CataloguePlus, and reference lists; the final dataset comprised 10 studies and 15 datapoints, all available only at group level.
  • The Method of Correlated Vectors correlated subtest g loadings with standardized Black/White differences (d). d was calculated as White minus Black scores divided by the best available SD, preferably from nationally representative norming samples; a harmonic N formula was used to weight datapoints with unequal group sizes.

Limitations

  • Stated: the authors lacked access to original datasets, so they could not test for measurement invariance; some datasets might have shown a lack of measurement invariance under MGCFA. They also note that some data points did not carry out Jensen’s suggested statistical analyses, making conclusions only conditionally valid.
  • Stated: they used a trade-off involving non-optimal statistical techniques to include many studies and enable meta-analysis; MGCFA was not possible because all data were group-level only.
  • Evident: the very low percentage of variance explained by sampling error (0.6%) indicates unmodeled moderators, and the group-level data mean individual-level measurement comparability and Jensen’s seven methodological requirements could not be fully tested.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3390/jintelligence4020006

Cites

46 of 46 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

2 of 38 cited sources checked · 1 supported · 0 flagged · accuracy not yet measured

  • Findingown data

    In the meta-analysis, 0.6% of the variance in the observed correlations is explained by sampling error.

    “with 0.6% of the variance in the observed correlations explained by sampling error.”
    Quote in the paperSubstantial claim
  • Findingown data

    The analysis of all 15 data points yields a mean vector correlation of 0.57.

    “The analysis of all 15 data points yields a mean vector correlation of 0.57.”
    Quote in the paperSubstantial claim
  • Findingown data

    In the data points in the current study there was often a large disparity between group sizes.

    “in the data points in the current study there was often a large disparity between group sizes; for instance, quite often samples report data on 100 Blacks and 1000 Whites.”
    Quote in the paperSubstantial claim
  • Premisecitation

    On average, the American Black population scores below the White population by about 1.2 standard deviations, or 18 IQ points.

    “On average, the American Black population scores below the White population by about 1.2 standard deviations (SDs), or 18 IQ points.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [1] Jensen, A.R. (1998). The g Factor: The Science of Mental Ability, Praeger.

      Not checked in the free run.

  • Interpretationown data

    The meta-analytical sample-size weighted correlation of rho = 0.57 found for adults is highly similar to the mean correlation found in Jensen [1], who reported a correlation of r = 0.59.

    “The meta-analytical sample-size weighted correlation of rho = 0.57 we found for adults is highly similar to the mean correlation found in Jensen [1], who reported a correlation of r = 0.59.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Jensen [1] Jensen, A.R. (1998). The g Factor: The Science of Mental Ability, Praeger.

      Not checked in the free run.

    • Rests on an assumption: The vector correlation method (correlating g loadings with score differences) is a valid test of Spearman's hypothesis for the included studies.
  • May combine two claims. 23
  • Classified as probably not a substantial claim. 31
  • The quote only partly states this claim. 1

  • May combine two claims.

    Study design and conductreasoning

    All data in this study are only available at the group level, so it is not possible to use MGCFA to analyze these data.

    “As noted above, Dolan [25] suggests using MGCFA to test Spearman's hypothesis, but since all data in this study are only available at the group level, it simply is not possible to use MGCFA to analyze these data.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [25] Dolan, 2000, Investigating Spearman’s hypothesis by means of multi-group confirmatory factor analysis, Multivar. Behav. Res. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Dolan's finding that small samples in some cases yield unreliable outcomes comes as no surprise.

    “Dolan's [25] finding that small samples in some cases yield unreliable outcomes comes as no surprise [26].”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites [25] Dolan, 2000, Investigating Spearman’s hypothesis by means of multi-group confirmatory factor analysis, Multivar. Behav. Res. source

      The Discussion (page unavailable) reports difficulty distinguishing between models, says unequal group sample sizes can reduce statistical power, and calls for a larger, more evenly distributed sample. This supports a sample-size-related limitation in this analysis, but not the broader claim that Dolan found small samples generally yield unreliable outcomes. (LLM, conf=0.83)

      Experimental — accuracy not yet measured
    • cites [26] Woodley, 2014, Controlling for increased guessing enhances the independence of the Flynn effect from g: The return of the Brand effect, Intelligence source

  • The quote only partly states this claim.

    Findingown data

    The bare bones meta-analysis of all 15 data points yields a mean vector correlation of 0.57.

    “The analysis of all 15 data points yields a mean vector correlation of 0.57”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Individual-level data from published studies are generally impossible to get hold of, so the authors focused on data reported at the group level.

    “However, in searching for studies for the present meta-analysis the present authors found that the individual-level data from published studies are generally impossible to get hold of, and therefore we focused on data that were reported at the group level.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    For four of the studies, the authors tested Spearman's hypothesis themselves using data reported at the group level.

    “Several of these studies focused on testing Spearman's hypothesis, but for four of the studies we tested Spearman's hypothesis ourselves using data reported at the group level.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The vector correlations between g loadings and score differences between adult Blacks and Whites are positive in sign, and the large majority are substantial in magnitude.

    “The correlations are positive in sign, and the large majority of them are substantial in magnitude.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingreasoning

    For data points with samples of 15 and 15, the total sample size using the second formula becomes 30, and for samples of 500 and 500 it becomes 1000.

    “For data points with samples of 15 and 15, the total sample size now becomes 30, and for a datapoint with samples of 500 and 500 the total sample size now becomes 1000”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The meta-analysis included 10 studies yielding 15 data correlations, with 251,085 White participants, 22,326 Black participants, and a total harmonic N of 76,884.

    “The table shows data derived from 10 studies, yielding 15 data correlations, with participants numbering a total of 251,085 Whites, 22,326 Blacks, and with a total harmonic N = 76,884.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning

    For a datapoint with samples of 100 and 900, the value of the harmonic N using the first formula is 180.

    “for a datapoint with samples of 100 and 900, the value of the harmonic N = 180”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The meta-analytical search resulted in 10 studies with 15 datapoints, with 251,085 Whites and 22,326 Blacks in total.

    “Our meta-analytical search resulted in a total of 10 studies with a total of 15 datapoints, with participants numbering 251,085 Whites and 22,326 Blacks in total.”
    • Also stated in: § 2.3. Searching and Screening Studies · plain
      “This search resulted in a total of 10 studies that are useable for our analysis, with a total of 15 data points.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning

    For a datapoint with samples of 100 and 900, the value of the harmonic N using the second formula is 360.

    “For a datapoint with samples of 100 and 900, the value of the harmonic N then becomes 360”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data

    For a datapoint with samples of 15 and 15, the total sample size using the first formula is only 15, and for samples of 500 and 500, the total sample size is only 500.

    “for a datapoint with samples of 15 and 15, the total sample size is only 15 and that, for a datapoint with samples of 500 and 500, the total sample size is only 500”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductreasoning

    The authors continue to use the second harmonic N formula because it gives data points with widely differing Ns a substantially reduced weight and data points with highly comparable weights a weight based on the total number of participants.

    “We therefore continue to use this formula, which is based on sound reasoning, namely that data points consisting of samples with widely differing Ns receive a substantially reduced weight in a meta-analysis, and that data points based on samples with highly comparable weights receive a weight based on the total number of research participants in these samples.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Study design and conductreasoning

    The authors employed a trade-off where they collected a substantial number of studies that could only be analyzed using non-optimal statistical techniques, but which allowed the use of the powerful technique of meta-analysis.

    “we repeat that we employed a trade-off where we collected a substantial number of studies that could only be analyzed using non-optimal statistical techniques, but which allowed the use of the powerful technique of meta-analysis.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premisenone given

    A sample of 100 has quite substantial sampling error, whereas a sample of 1000 indicates a much smaller sampling error.

    “A sample of 100 has quite substantial sampling error, whereas a sample of 1000 indicates a much smaller sampling error.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    The manifold of positive correlations among measures of various mental abilities is generally considered evidence of a general factor in all measured abilities.

    “Te Nijenhuis, Al-Shahomee, van den Hoek, Allik, Grigoriev, and Dragt [3] describe how a well-established empirical finding-the manifold of positive correlations among measures of various mental abilities-is generally considered to be evidence of a general factor in all of the measured abilities.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [3] Allik, 2015, Spearman’s hypothesis tested comparing Libyan secondary school children with various other groups of secondary school children on the items of the Standard Progressive Matrices, Intelligence source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Usually individual studies did not report g loadings, so Jensen generally used g loadings from other sources such as manuals of IQ batteries based on high-quality, representative samples.

    “Usually these individual studies did not report g loadings, in which case Jensen generally used g loadings from other sources, such as manuals of IQ batteries based upon high-quality, representative samples.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [1] Jensen, A.R. (1998). The g Factor: The Science of Mental Ability, Praeger.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Ganzach replicated earlier findings that the Black/White difference is larger on Digit Span Backward than on Digit Span Forward.

    “He replicated earlier findings by showing that the difference between Blacks and Whites is larger on DSB than on DSF.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [20] Ganzach, 2016, Another look at Spearman’s hypothesis and relationship between Digit Span and General Mental Ability, Learn. Individ. Differ. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data

    Because of lack of access to the original data, the authors could not test for measurement invariance.

    “however, because of lack of access to the original data, we could not test for measurement invariance.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In the simplified procedure, significances are not computed for each individual dataset because the combined datasets become so large that the mean correlation will always or virtually always become significant.

    “Additionally, significances are not computed for each individual dataset, as the combined datasets become so large that the mean correlation will always or virtually always become significant [36].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [36] 2007, Score gains on g-loaded tests: No g, Intelligence source

  • May combine two claims.

    Study design and conductreasoning

    Because they did not have access to the original datasets, the authors could not test for measurement invariance.

    “means that we simply could not test for measurement invariance”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductcitation

    Samples in the included studies should not be selected on a highly g-loaded variable.

    “Second, the samples in the studies should not be selected on a highly g-loaded variable (e.g., referral or gifted samples [7]).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [7] Jensen, 1993, Spearman’s hypothesis tested with chronometric information-processing tasks, Intelligence source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Goldstein, Yusko, and Nicolopoulos concluded that clear group differences emerged for more cognitively-loaded managerial competencies and much smaller differences for less cognitively-loaded competencies.

    “Goldstein, Yusko, and Nicolopoulos [10] concluded that clear group differences emerged for a majority of more cognitively-loaded managerial competencies, such as judgment, whereas much smaller differences were associated with the majority of the less cognitively-loaded competencies, such as human relations.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [10] Goldstein, 2001, Exploring Black-White subgroup differences of managerial competencies, Pers. Psychol. source

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    The average age of participants had to be 18 or older for inclusion.

    “Third, the average age of the participants had to be 18 or older, which means the sample could include some participants younger than 18.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Premisenone given

    The standard deviation of a large and representative sample is closer to the population standard deviation than a small study sample, and thus helps to give a more accurate indication of the effect size.

    “the standard deviation of a large and representative sample is closer to the population standard deviation than a small study sample, and thus helps to give a more accurate indication of the effect size.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The combination of a simplified procedure and a meta-analysis has already been successfully applied in several studies.

    “This combination of a simplified procedure and a meta-analysis has already been successfully applied in several studies, some of them often cited [28][29][30][31][32][33][34][35].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [28] Armstrong, 2015, Are adoption gains on the g factor? A meta-analyis, Personal. Individ. Differ. source
    • cites [29] Kura, 2014, The correlation between g loadings and heritability in Japan: A meta-analysis, Intelligence source
    • cites [30] Woodley, 2014, Differences in cognitive abilities among primates are concentrated on G: Phenotypic and phylogenetic comparisons with two meta-analytical databases, Intelligence source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Jensen [1] reported a correlation of r = 0.59.

    “Jensen [1], who reported a correlation of r = 0.59.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Jensen [1] Jensen, A.R. (1998). The g Factor: The Science of Mental Ability, Praeger.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

    Premisenone given

    Measurement invariance is, strictly speaking, a necessary condition on a priori grounds.

    “Measurement invariance is, strictly speaking, a necessary condition on a priori grounds.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Recent studies by te Nijenhuis and co-authors generally showed clear and often strong confirmations of Spearman's hypothesis at the item level.

    “Most recently, a number of studies by te Nijenhuis and co-authors, using a large number of datasets, generally showed clear and often strong confirmations of Spearman's hypothesis at the item level [3,[17][18][19]].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [3,[17][18][19]]

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

  • May combine two claims.

    Premisecitation

    Ganzach's results were not generalizable to Hispanics, where the White/Hispanic difference was larger on Digit Span Forward than on Digit Span Backward.

    “However, the results were not generalizable to Hispanics, where the difference between Whites and Hispanics was actually larger on DSF than on DSB.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [20] Ganzach, 2016, Another look at Spearman’s hypothesis and relationship between Digit Span and General Mental Ability, Learn. Individ. Differ. source

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    The most thorough test of Spearman's hypothesis requires that data are available at the individual level.

    “The most thorough test of Spearman's hypothesis requires that data are available at the individual level.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Jensen showed many instances where g loadings and effect sizes are correlated using group-level data, so it is not possible to test whether the seven methodological requirements were met.

    “However, Jensen [1] shows many instances where g loadings and effects sizes (r or d) are correlated not using individual-level data, but group-level data reported in individual studies, so that it is not possible to test whether the seven methodological requirement were met.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [1] Jensen, A.R. (1998). The g Factor: The Science of Mental Ability, Praeger.

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    A study had to have at least four tests or subtests to which the Method of Correlated Vectors could be applied to be included in the meta-analysis.

    “The first requirement for a study to be included in the present meta-analysis was having at least four tests or subtests to which the Method of Correlated Vectors could be applied.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisereasoning

    A harmonic N takes into account the increase in precision for the larger sample and the decrease in precision for the smaller sample.

    “A harmonic N takes this into account.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Before the present study, the total literature of Spearman's hypothesis tested on Black and White adults in the US consisted of only six datasets on adults, five reported in Jensen and one in Nyborg and Jensen; the correlations ranged from r = 0.30 to 0.81.

    “Before the present study, the total literature of Spearman's hypothesis tested on Black and White adults in the US consists of only six datasets on adults, and five of these six studies are reported in Jensen [37] and one of these six is reported in Nyborg and Jensen [38]; the correlations for these studies ranged from r = 0.30 to 0.81.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [37] * Jensen A.R. The nature of Black-White differences on various psychometric tests: Spearman’s hypothesis Behav. Brain Sci. 1985 8 193 263 10.1017/S0140525X00020392 source
    • cites [38] * Nyborg H. Jensen A.R. Black-white differences on various psychometric tests: Spearman’s hypothesis tested on American armed services veterans Personal. Individ. Differ. 2000 28 593 599 10.1016/S0191-8869(99)00122-1 source

  • Classified as probably not a substantial claim.

    Premisecitation

    Hunter and Schmidt [39] use the sum of all participants in all groups from a study that is used as a datapoint in a meta-analysis as the value of the total sample size.

    “Hunter and Schmidt [39] use the sum of all participants in all groups from a study that is used as a datapoint in a meta-analysis as the value of the total sample size.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Hunter and Schmidt [39] Hunter, J.E., and Schmidt, F.L. (2004). Methods of Meta-Analysis: Correcting Error and Bias in Research Findings, Sage. [2nd ed.].

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    In this study, a bare-bones meta-analysis was carried out correcting only for sampling error.

    “In this study we carry out a bare-bones meta-analysis where we correct only for sampling error in the data, the error that is introduced into data due to the usage of small samples in studies.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    A White Spanish sample compared with a sample of Moroccans did not report a clear confirmation of Spearman's hypothesis.

    “More recently, a White Spanish sample was compared with a sample of Moroccans but did not report a clear confirmation of Spearman's hypothesis [16].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [16] Diaz, 2012, A comparative study of general intelligence in Spanish and Moroccan samples, Span. J. Psychol. source

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Tests with high g loadings demand higher cognitive complexity, and tests with low g loadings demand lower cognitive complexity.

    “Tests with high g loadings demand higher cognitive complexity, and tests with low g loadings demand lower cognitive complexity [3,5].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [3] Allik, 2015, Spearman’s hypothesis tested comparing Libyan secondary school children with various other groups of secondary school children on the items of the Standard Progressive Matrices, Intelligence source
    • cites [5] Gottfredson, 1997, Why g matters: The complexity of everyday life, Intelligence source

  • May combine two claims.

    Premisecitation

    Goldstein, Yusko, Braverman, Smith, and Chung found that the cognitive complexity of an Assessment Center exercise predicted group differences, in line with Spearman's hypothesis.

    “Goldstein, Yusko, Braverman, Smith, and Chung [9] tested whether the cognitive complexity of an AC exercise was a predictor of group differences, and their findings are in line with Spearman's hypothesis.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [9] Goldstein, 1998, The role of cognitive ability in the subgroup differences and incremental validity of assessment center exercises, Pers. Psychol. source

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    The g loading based on a large and representative sample will be more representative of the g loading of the population.

    “the g loading based on a large and representative sample will be more representative of the g loading of the population.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Spearman's hypothesis was confirmed in the large majority of comparisons of various groups and for all assessment instruments studied, and most studies compared Blacks and Whites in the US.

    “In sum, Spearman's hypothesis was confirmed in the large majority of comparisons of various groups and for all assessment instruments studied and most studies have been carried out comparing Blacks and Whites in the US.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [1] Jensen, A.R. (1998). The g Factor: The Science of Mental Ability, Praeger.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In the simplified procedure, meta-analytical corrections for unreliability are applied to the vectors.

    “In the simplified procedure, each subtest is not corrected for unreliability, but meta-analytical corrections for unreliability are applied to the vectors [36].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [36] 2007, Score gains on g-loaded tests: No g, Intelligence source

  • May combine two claims.

    Premisecitation

    The weak form of Spearman's hypothesis has been confirmed in many studies, meaning Black/White differences are differences in g to a strong degree.

    “Jensen chose to test the weak form of Spearman's hypothesis, and this weak form has been confirmed in many studies, which means that the Black/White differences are differences in g to a strong degree [1].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [1] Jensen, A.R. (1998). The g Factor: The Science of Mental Ability, Praeger.

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationnone given

    MGCFA is so demanding of data that only a fraction of available datasets can be analyzed using MGCFA, whereas in principle all or virtually all datasets can be analyzed with MCV.

    “However, there is a fundamental problem in that MGCFA is so demanding of the data that, in all likelihood, only a fraction of available datasets can be analyzed using MGCFA, whereas in principle all or virtually all datasets can be analyzed with MCV.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Most studies on Spearman's hypothesis are not representative of the normal working-age population, and more studies are needed to see whether findings from children and adolescents generalize to adults.

    “Thus, most studies on Spearman's hypothesis are not representative of the normal working-age population and more studies are needed to see whether the abundant findings from children and adolescents generalize to adults.”
    Quote in the paperSubstantial claim
46 of 46

  • The paper relies on this without support.

    The variables measure the same latent traits and the same g in the Black and White groups.

    “because of lack of access to the original data, we could not test for measurement invariance.”

  • The paper relies on this without support.

    The g loadings imported from other datasets or standardization samples are valid for the samples in the meta-analysis.

    “it allows importing the best available g loadings from other datasets, thereby strongly reducing the unreliability.”

  • The paper relies on this without support.

    The vector correlation method (correlating g loadings with score differences) is a valid test of Spearman's hypothesis for the included studies.

    “we employed a trade-off where we collected a substantial number of studies that could only be analyzed using non-optimal statistical techniques, but which allowed the use of the powerful technique of meta-analysis.”
3 of 3

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Previous meta-analyses and non-systematic reviews have generally supported Spearman's Hypothesis in US W-B comparisons, with positive vector correlations observed across all cognitive batteries and samples.

    “Previous meta-analyses and non-systematic reviews have generally supported SH in US W-B comparisons, with positive vector correlations observed across all cognitive batteries and samples (Jensen, 1985(Jensen, , 1998;;te Nijenhuis & van den Hoek, 2016).”

    From A Meta-Analysis of Spearman’s Hypothesis in the United States (2026) · cites this paper as te Nijenhuis & van den Hoek, 2016

    The Introduction (page unavailable) says Spearman’s Hypothesis was confirmed in the large majority of comparisons and for all assessment instruments studied. The Results (page unavailable) report positive vector correlations for all 15 data points in this meta-analysis of US Black and White adults. Those passages support the general pattern, but not the unrestricted claim that correlations were positive across all cognitive batteries and samples in prior US comparisons. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

  • 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.”

    From A Meta-Analysis of Spearman’s Hypothesis in the United States (2026) · cites this paper as te Nijenhuis & van den Hoek, 2016

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Sternberg harmonic sample size uses the wrong formula

    Minor

    For groups of 348 and 47, the paper's chosen harmonic-N formula gives approximately 166, not the 83 reported in Table 3. The reported value instead matches the first formula, which the paper says it did not use.

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Authors
Te Nijenhuis, J., & Van den Hoek, M.
Affiliations
Work and Organizational Psychology, University of Amsterdam, Weesperplein 4, 1018 XA Amsterdam, The Netherlands
ORCID
Te Nijenhuis, Jan
Venue
Journal of Intelligence
Publisher
MDPI AG
Published
2016-06-01
Volume
4
Issue
2
Pages
6
ISSN
2079-3200 (ISSN-L)
DOI
10.3390/jintelligence4020006
OpenAlex
W2413444144
Cited by
18
References
46
Citations by year
2026: 3 · 2025: 1 · 2022: 2 · 2021: 2 · 2019: 6 · 2018: 1 · 2017: 2 · 2016: 1
FWCI
0.44
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Intelligence (publishedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Topics
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Cognitive Abilities and Testing
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Education, Achievement, and Giftedness
Keywords
Spearman's hypothesis, general intelligence factor, general intelligence, black-white disparities, racial differences in intelligence, cognitive complexity, measurement invariance

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