Psychometricians have argued that measurement invariance (MI) testing is needed to know if the same psychological constructs are measured in different groups. Data from five experiments allowed that position to be tested. In the first, participants answered questionnaires on belief in free will and either the meaning of life or the meaning of a nonsense concept called “gavagai.” Since the meaning of life and the meaning of gavagai conceptually differ, MI should have been violated when groups were treated like their measurements were identical. MI was severely violated, indicating the questionnaires were interpreted differently. In the second and third experiments, participants were randomized to watch treatment videos explaining figural matrices rules or task-irrelevant control videos. Participants then took intelligence and figural matrices tests. The intervention worked and the experimental group had an additional influence on figural matrix performance in the form of knowing matrix rules, so their performance on the matrices tests violated MI and was anomalously high for their intelligence levels. In both experiments, MI was severely violated. In the fourth and fifth experiments, individuals were exposed to growth mindset interventions that a twin study revealed changed the amount of genetic variance in the target mindset measure without affecting other variables. When comparing treatment and control groups, MI was attainable before but not after treatment. Moreover, the control group showed longitudinal invariance, but the same was untrue for the treatment group. MI testing is likely able to show if the same things are measured in different groups.

Using data from the Philadelphia Neurodevelopmental Cohort, we examined whether European ancestry predicted cognitive ability over and above both parental socioeconomic status (SES) and measures of eye, hair, and skin color. First, using multi-group confirmatory factor analysis, we verified that strict factorial invariance held between self-identified African and European-Americans. The differences between these groups, which were equivalent to 14.72 IQ points, were primarily (75.59%) due to difference in general cognitive ability (g), consistent with Spearman’s hypothesis. We found a relationship between European admixture and g. This relationship existed in samples of (a) self-identified monoracial African-Americans (B = 0.78, n = 2,179), (b) monoracial African and biracial African-European-Americans, with controls added for self-identified biracial status (B = 0.85, n = 2407), and (c) combined European, African-European, and African-American participants, with controls for self-identified race/ethnicity (B = 0.75, N = 7,273). Controlling for parental SES modestly attenuated these relationships whereas controlling for measures of skin, hair, and eye color did not. Next, we validated four sets of polygenic scores for educational attainment (eduPGS). MTAG, the multi-trait analysis of genome-wide association study (GWAS) eduPGS (based on 8442 overlapping variants) predicted g in both the monoracial African-American (r = 0.111, n = 2179, p < 0.001), and the European-American (r = 0.227, n = 4914, p < 0.001) subsamples. We also found large race differences for the means of eduPGS (d = 1.89). Using the ancestry-adjusted association between MTAG eduPGS and g from the monoracial African-American sample as an estimate of the transracially unbiased validity of eduPGS (B = 0.124), the results suggest that as much as 20%–25% of the race difference in g can be naïvely explained by known cognitive ability-related variants. Moreover, path analysis showed that the eduPGS substantially mediated associations between cognitive ability and European ancestry in the African-American sample. Subtest differences, together with the effects of both ancestry and eduPGS, had near-identity with subtest g-loadings. This finding confirmed a Jensen effect acting on ancestry-related differences. Finally, we confirmed measurement invariance along the full range of European ancestry in the combined sample using local structural equation modeling. Results converge on genetics as a potential partial explanation for group mean differences in intelligence.

Little research has dealt with intragroup ancestry-related differences in intelligence in Black and White Americans. To help fill this gap, we examined the association between intelligence and both color and parent-reported ancestry using the NLSY97. We used a nationally-representative sample, a multidimensional measure of cognitive ability, and a sibling design. We found that African ancestry was negatively correlated with general mental ability scores among Whites (r = −0.038, N = 3603; corrected for attenuation, rc = −0.245). In contrast, the correlation between ability and parent-reported European ancestry was positive among Blacks (r = 0.137, N = 1788; rc = 0.344). Among Blacks, the correlation with darker skin color, an index of African ancestry, was negative (r = −0.112, N = 1455). These results remained with conspicuous controls. Among Blacks, both color and parent-reported European ancestry had independent effects on general cognitive ability (color: β = −0.104; ancestry: β = 0.118; N = 1445). These associations were more pronounced on g-loaded subtests, indicating a Jensen Effect for both color and ancestry (rs = 0.679 to 0.850). When we decomposed the color results for the African ancestry sample between and within families, we found an association between families, between singletons (β = −0.153; N = 814), and between full sibling pairs (β = −0.176; N = 225). However, we found no association between full siblings (β = 0.027; N = 225). Differential regression to the mean results indicated that the factors causing the mean group difference acted across the cognitive spectrum, with high-scoring African Americans no less affected than low-scoring ones. We tested for measurement invariance and found that strict factorial invariance was tenable. We then found that the weak version of Spearman’s hypothesis was tenable while the strong and contra versions were not. The results imply that the observed cognitive differences are primarily due to differences in g and that the Black-White mean difference is attributable to the same factors that cause differences within both groups. Further examination revealed comparable intraclass correlations and absolute differences for Black and White full siblings. This implied that the non-shared environmental variance components were similar in magnitude for both Blacks and Whites.

We sought to assess whether previous findings regarding the relationship between cognitive ability and religiosity could be replicated in a large dataset of online daters (maximum n = 67k). We found that self-declared religious people had lower IQs than nonreligious people (atheists and agnostics). Furthermore, within most religious groups, a negative relationship between the strength of religious conviction and IQ was observed. This relationship was absent or reversed in nonreligious groups. A factor of religiousness based on five questions correlated at −0.38 with IQ after adjusting for reliability (−0.30 before). The relationship between IQ and religiousness was not strongly confounded by plausible demographic covariates (β = −0.24 in final model versus −0.30 without covariates).