“Insignificant” Differences

Kevin Bird has a paper out in which he claims, more or less, to evidence “insignificant” race differences. There is a lot there to criticize: misinterpretations, odd analytic choices,  a crucial wrong formula [1], etc.

Maybe I will write a formal critique.

For now, it’s sufficient to point out that the results strongly agree with a hereditarian model:

  • The predicted differences, given the genetic divergence in the educational and intelligence SNPs, are medium to large given reasonable estimates of broad-sense heritability (H2)[2].
  • While there is inconsistent evidence of divergent selection (for this pairwise comparison), there is zero evidence of homogenizing or stabilizing selection.

To illustrate point (1), Table 1 shows the expected BGH given the 30.8 point continental European-African difference which Bird adopts along with the expected phenotypic gaps when environments are equal (i.e., when BGH is set to unity). I use the lowest Fst value Bird reports in his table. Proofs are provided for the formulas used in the .doc file.

Table 1. Expected Between Group Heritability (BGH)  and Expected IQ Point Differences between Europeans and Africans Given Different Values of the Genetic Intraclass Correlation (r and r_c) and H2 assuming  an eduSNP Fst  =.111 from Bird (2021; Table 1; 1301 clumped EA SNPs)

H2 r t_observed BGH t_expected Expected IQ difference Cohen’s Interpretation
0.20 0.1990 0.5132 0.047 0.0473 6.69 Medium
0.35 0.1990 0.5132 0.083 0.0800 8.85 Medium
0.50 0.1990 0.5132 0.118 0.1105 10.58 Medium
0.65 0.1990 0.5132 0.153 0.1391 12.06 Large
0.80 0.1990 0.5132 0.189 0.1658 13.38 Large
H2 r_c t_observed BGH t_expected Expected IQ difference Cohen’s Interpretation
0.20 0.2844 0.5132 0.075 0.0736 8.46 Medium
0.35 0.2844 0.5132 0.132 0.1221 11.19 Medium
0.50 0.2844 0.5132 0.188 0.1657 13.37 Large
0.65 0.2844 0.5132 0.245 0.2053 15.25 Large
0.80 0.2844 0.5132 0.302 0.2412 16.91 Large

Note: H2 = broad-sense heritability; r =  intraclass genetic correlation; r_c = intraclass genetic correlation corrected for mathematical constraints on Fst; t_observed = intraclass phenotypic correlation i.e., phenotypic variance between groups (given d = 2.053); BGH = between group heritability; t_expeced = expected phenotypic variance between groups when environments are equalized; Expected IQ difference = expected IQ differences when environments are equalized; Cohen’s Interpretation = conventional interpretation of effects sizes.

You can argue that one should use narrow-sense heritability, instead of broad-sense, contra Jensen (1972; 1998), then lowball the estimates, and finally take advantage of statistical illiteracy and portray the differences as ‘small’ or ‘insignificant’ by emphasizing the portion of variance explained. However, the expected differences (which are equal to sqrt(BGH) x observed phenotypic differences) are still medium to large. Of course, Bird (2021) argues that the differences could go either way with equal likelihood.  This would be true if you knew nothing else.  However, in his prior analyses, he uses polygenic score (PGS) weights, and the eduPGS weights are directional.  For the same set of eduSNPs the PGS differences are shown below:

Table 2. Mean MTAG-based PGS for CEU and YRI Calculated using population-GWAS and Within Family Betas.

  W/ population-GWAS   W/ Within Family Betas  
  CEU (N = 99) YRI (N = 108) CEU (N = 99) YRI (N = 108)
All SNPS 0.866 -0.794 0.614 -0.563
p-value (Welch’s Two Sample t-test)   < 0.0001   < 0.0001
Derived SNPs 0.938 -0.860 0.702 -0.643
p-value (Welch’s Two Sample t-test)   < 0.0001   < 0.0001
Ancestral SNPs 0.605 -0.554 0.528 -0.484
p-value (Welch’s Two Sample t-test)   < 0.0001   < 0.0001

Note: SNPs were filtered for MAF >0.01 for both CEU and YRI. Scores represent standard scores calculated using the standard deviation in the total sample. Sample sizes for the t-test were N = 99 for CEU and N=108 for YRI.

Thus, it makes no sense to say that the expected difference could go either way, with equal probability, when the eduPGS weights indicate a direction. When this is recognized, the only option is to declare that the eduPGS is biased between populations. This is possible, of course.

However, this leaves the evolutionary default or null, which is that differences will be commensurate with neutral variation. As Rosenberg, Edge, Pritchard, & Feldman (2019) note: “One key component of the inference of polygenic adaption is the use of an appropriate null expectation for polygenic scores distributions and phenotypic differences…[P]henotypic differences among populations are predicted under neutrality to be similar in magnitude to typical genetic differences among populations.”  The authors, of course, go on to cite Lewontin and slyly note that differences “are small in comparison with variation within populations”. But, of course, “large” differences in the conventional sense are also “small in comparison with variation within” (e.g., .80d = 14% variance). And while the evolutionary default is directionless, the totality of the behavioral genetic and psychometric data assembled on this topic points one way.

[1] See, for example, equation 4 in Bird (2021).  However,

total between phenotypic variance = phenotypic variance due to genes + phenotypic variance due to environment

which can be rewritten, in linear metrics, as PD^2 = GD^2 + ED^2  or PD = sqrt( GD^2 + ED^2 )

Since, BGH = phenotypic variance due to genes / total between phenotypic variance

BGH = GD^2 / PD^2 and, therefore, GD = sqrt(BGH)*PD

This is approximated but underestimated by 2*PD^2 * sqrt(2/pi) (*15) which Bird (2021) uses.

e.g., sqrt(.12)*30.8 = 10.67 (correct) versus 2*sqrt(.12)*sqrt(2/pi) (*15) = 8.29 (Bird, 2021)

[2] While the use of narrow-sense heritability is recommended for Qst-Fst comparisons and the assessment of directional selection, narrow-sense heritability, and the corresponding narrow-sense Qst underestimates between-group genetic variance by not taking into account non-additive genetic variation between populations, along with active gene-environment covariance (which is commonly classed as a genetic effect; Sesardic, 2005). Thus when it comes to calculating the expected difference due to genes, it makes sense to use the broad-sense heritability, at least for an upper-bounds estimate, as hereditarians have done (e.g., Jensen, 1998).


  1. John Estes

    Bird responded:

  2. visitor

    The link to “the totality of the behavioral genetic and psychometric data assembled on this topic” doesn’t work.

    • Chuck

      This should link to “The Persistence of Cognitive Inequality: Reflections on Arthur Jensen’s “Not Unreasonable Hypothesis” after Fifty Years”

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