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Social Class, Ken Richardson and “Modern Heresy”

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As RaceRealist has already noted, a recent YouTube video purports to critique Ken Richardson’s work on IQ tests and their relationship with social class. Since he already covered a number of the relevant parts about Goddard, construct validity and a number of other topics, I wanted to focus more on the question of social class. This is one of the claims that RaceRealist brings up from Richardson’s work quite frequently, so it’s probably the most pertinent at this point in time.

Note: I watched the video about a week ago, so if I get any of the details mixed up, please let me know.

One of the claims that the author of the YouTube video makes is that because a large proportion of the variation in IQ is within-family, rather than between-families, it cannot be that IQ is a metric of social class. The logic here is quite simple: behavioral genetic studies tell us that the average difference between two siblings in the same family is about 12 IQ points, while the average difference between two randomly selected individuals in the population is 15 points. That means that, according to the creator of the video, “about 70% of the IQ variation in society is due to within-family differences”. We should note two things. The first is that the figure cited here is incorrect, even if we accept the values for the standard deviations within the family. The video creator seems to have calculated the percent of variation as a proportion of the standard deviations (\sigma), rather than the actual variances (\sigma^2). The proper proportion would be \frac{12^2}{17^2}=0.498, which is 49.8%. That still leaves 50.2% of the variation between families. The other issue is that I very much doubt the figure of a typical difference of 12 IQ points between siblings. The formula for the expected absolute difference between two siblings in the same family is \frac{2\cdot\sqrt{\frac{V_a}{2}+V_e}}{\sqrt{\pi}} (here V_e=1-V_a. If we assume that the phenotypic standard deviation is 15 (as defined for IQ tests), we can compute the expected difference for different values of heritability. We can quickly note that the issue with this is that if the heritability of the trait is zero, then the expected phenotypic difference for siblings is \frac{2\cdot\sqrt{\frac{0\cdot15^2}{2}+(1-0)\cdot15^2}}{\sqrt{\pi}}=16.9, whereas two random strangers would have a difference of \int_{-\infty}^{\infty} \int_{-\infty}^{\infty}\text{PDF}(\mathcal{N}(0,1),\text{x})\cdot\text{PDF}(\mathcal{N}(0,1),y)|y-x|\cdot 15 dx dy=16.9 [1]. If we were to take the author’s proposal for how much of the variation is within-family vis a vis between-family, we would have to conclude that \frac{16.9}{16.9}=1 or 100% of the variance is within-family, while just 0% of the variance is between-families. Does it make sense that that even if heritability were zero that only 0% could represent social class? No, it doesn’t, because there are issues here. The first is that variation in IQ is not the relevant metric here. If we take the notion that there is a factor of the matter about the IQ score of someone (i.e. there exists a ‘true score’), then IQ would have measurement error (Whitaker 2010). The consequence of this alleged measurement error would be to inflate the proportion of variation that is within-family. First, denote variances as such: V_a for additive genetic variance, V_e for environmental variance, and V_m for measurement error variance. The within-family calculation would be \frac{2\sqrt{\frac{V_a}{2}+V_e+V_m}}{\sqrt{\pi}} (per the formula above) while the between-family calculation would be \frac{2\sqrt{2\cdot(V_a+V_e+V_m)}}{\sqrt{\pi}} for observed IQ scores, while the true relevant quantities would be \frac{2\sqrt{\frac{V_a}{2}+V_e}}{\sqrt{\pi}} and \frac{2\sqrt{2\cdot(V_a+V_e)}}{\sqrt{\pi}}. Note that our fractions (percent of variation within families) \frac{\frac{2\sqrt{\frac{V_a}{2}+V_e+V_m}}{\sqrt{\pi}}}{\frac{2\sqrt{2\cdot(V_a+V_e+V_m)}}{\sqrt{\pi}}} and \frac{\frac{2\sqrt{\frac{V_a}{2}+V_e}}{\sqrt{\pi}}}{\frac{2\sqrt{2\cdot(V_a+V_e)}}{\sqrt{\pi}}}. Some simple algebra can show that \frac{\frac{2\sqrt{\frac{V_a}{2}+V_e+V_m}}{\sqrt{\pi}}}{\frac{2\sqrt{2\cdot(V_a+V_e+V_m)}}{\sqrt{\pi}}} > \frac{\frac{2\sqrt{\frac{V_a}{2}+V_e}}{\sqrt{\pi}}}{\frac{2\sqrt{2\cdot(V_a+V_e)}}{\sqrt{\pi}}} [2], which means that so long as V_a (additive genetic variance) and V_m (measurement error variance) are both positive (e.g. there is both measurement error and heritability), then the fraction of variation that is between-families calculated from observed IQs will be an overestimate because of measurement error.

The other issue with the creators claims is the “assumption that social class varies between families but not within families”. While it may seem obvious at first, there are a number of issues. The first is that an individual’s attained social class during adulthood (and thus the social class in which they inhabit) is not identical within families. Two kids may have started off with very similar IQs due to their family environments, but due to various reasons (random chance, developed interests, etc), they moved into different social classes in adulthood, following which their IQs diverged due to the different social classes they now inhabit. The reason why this is relevant is because the statistic that the creator is using to (erroneously) claim that 70% of the variation is within families does not specify the age at which these measurements were taken – it is likely that they were taken in later life, meaning that the social class of the individuals has already diverged.

Moreover, even when children are within the same family at earlier ages, there is reason to argue that their social class is also not identical. Sociologists now understand that social class is a dynamic structure that is not only reproduced by aspects of economic access, resources and opportunity that individuals have access to, but that sociocultural signifiers, subjective experiences, interests and other aspects also contribute to ones social class. As noted by Richardson himself, one’s subjective SES may better reflect the sociocognitive environment that one develops in (Richardson & Jones 2019):

It is self-conscious social status in relation to others in a class structure – i.e. what has been called subjective as opposed to objective social class – that seems to influence a wide range of educational and cognitive outcomes. There is only moderate correlation between that and current SES

And this subjective SES can quite evidently differ between siblings and differentially impact their IQs. Moreover, there are numerous other aspects of social class that can vary within-family such as: school quality (e.g. school resources; Leon & Valdiva 2015), peer effects (Hoxby 2000), teacher and classroom effects (Boyd-Zaharias 1999; Chetty et. al 2015), and societal expectations (Jensen & McHale 2016). Small initial differences in these environmental variables can be magnified through phenotype-environment processes (Beam & Turkheimer 2013) that can create a seemingly large within-family variation that cannot be attributed to social class, but could in fact be the result of it.

Another vitally important thing to note is that even if we accept the concept of social class as measured by socioeconomic status as a simple standardized combination of income, parental education and occupational status, that doesn’t mean that this variable can’t differ in important ways within the family. First note that siblings are not always the same age (the exception is with twins). As a result, the developmental environment in which each child grows up with is not identical. As Richardson noted over a decade ago, children within the family do not experience the same environment (Richardson & Norgate 2005). This is not only because of perceptual experiences, phenotype→environment feedback loops, but because the importance of the timing of developmental experiences means that changes in parental socioeconomic status over the time means that children are exposed to different socioeconomic environments during these critical periods (Sylva 1997). For instance, parental socioeconomic status and as a result maternal stress can differ during the mother’s pregnancies (Richardson 2019), causing differences between the two children’s development.

Social Class or Sociocognitive Preparedness?

We should note that this critique is premised entirely on the idea that Richardson is positing that social class is a gigantic determinant of IQ, to the neglect of other environmental factors. This is an erroneous assumption, as the paper in which Richardson lays out his theory of what IQ tests are a proxy for (Richardson 2002; “What IQ Tests Test”), he argues that ” population variance in IQ scores can be described in terms of a nexus of sociocognitive-affective factors that differentially prepares individuals for the cognitive, affective and performance demands of the test”, that in effect, makes the test a measure of social class. Note that he does not quantify the specific amount of variation that is explained by social class, and that over 50% of the variation (as a minimum using the assumptions questioned above) explainable by social class (meaning a correlation of 0.7) could definitely qualify under his meaning. Regardless, Richardson’s primary explication is in terms of the “nexus of sociocognitive-affective factors” is perfectly compatible with the within vs between population variance described in the video.

There are numerous factors that influence intelligence that Richardson describes that can differ within families, such as “individuals’ psychological proximity to that set” of cultural tools, parental interactions with children (Hart & Risley 1995; Jensen & McHale 2016), affective preparedness, etc. All of these factors can additionally explain the IQ variance, meaning that the critique of Richardson’s explanation of IQ variance does not go through.

Predictive (In)Validity?

The creator of the video also claims that the Bell Curve demonstrated that IQ remains predictive once SES is controlled for and that IQ is a much better predictor that SES. Despite this common claim by Bell Curve fanatics, it has been demonstrated to be incorrect more times than one can count (Fischer et. al 1996; Ragin & Fiss 2016). In fact, a closer analysis of the model Murray and Herrnstein fit shows that they predicted NOT ONE of their poverty cases correctly (Krenz n.d.; see also Dickens et. al 1995, Goldberger & Manski 1995). A more thorough examination of the claims related to the alleged predictive validity of IQ can be found here.

[1] A simpler way to get the result is to calculate the variance from simple distribution addition/difference rules and then multiply that by the expected difference for normal distributions \frac{2}{\sqrt{\pi}}

[2] \frac{\frac{2\sqrt{\frac{V_a}{2}+V_e+V_m}}{\sqrt{\pi}}}{\frac{2\sqrt{2\cdot(V_a+V_e+V_m)}}{\sqrt{\pi}}}\geq \frac{\frac{2\sqrt{\frac{V_a}{2}+V_e}}{\sqrt{\pi}}}{\frac{2\sqrt{2\cdot(V_a+V_e)}}{\sqrt{\pi}}}\implies\frac{\sqrt{\frac{V_a}{2}+V_e+V_m}}{\sqrt{2\cdot(V_a+V_e+V_m)}}\geq\frac{\sqrt{\frac{V_a}{2}+V_e}}{\sqrt{2\cdot(V_a+V_e)}}\implies\frac{\frac{V_a}{2}+V_e+V_m}{2\cdot(V_a+V_e+V_m)}\geq\frac{\frac{V_a}{2}+V_e}{2\cdot(V_a+V_e)}\implies \frac{\frac{V_a}{2}+V_e+V_m}{V_a+V_e+V_m}\geq\frac{\frac{V_a}{2}+V_e}{V_a+V_e}\implies (\frac{V_a}{2}+V_e+V_m)(V_a+V_e)\geq(\frac{V_a}{2}+V_e)(V_a+V_e+V_m)\implies \frac{V_a^2}{2}+\frac{V_aV_e}{2}+V_eV_a+V_e^2+V_aV_m+V_eV_m\geq\frac{V_a^2}{2}+\frac{V_aV_e}{2}+\frac{V_aV_m}{2}+V_eV_a+V_e^2+V_eV_m\implies(\frac{V_a^2}{2}-\frac{V_a^2}{2})+(\frac{V_aV_e}{2}-\frac{V_aV_e}{2})+(V_eV_a-V_eV_a)+(V_e^2-V_e^2)+(V_aV_m-\frac{V_aV_m}{2})+(V_eV_m-V_eV_m)\geq0\implies \frac{V_aV_m}{2}\geq0


  1. dealwithit says:

    indeed. according to krugman the US is now so rigidly stratified that poor kids with high IQs are less likely to graduate from college or have high status occupations than rich kids with low IQs. i don’t know what his source was for this however.

    IQ is not entirely or primarily a measure of social class and claiming it is can actually result in more rigid stratification, such as has followed the closing of state grammar schools in the united kingdom of shit.

    if it were the variance of IQ in denmark would be much less than it is in great shitain and the unites states of shit because these shithole countries are much more unequal and rigidly stratified than denmark, or canada, or australia, or etc because they’re shithole countries which need to be nuked and then given rabies.

    the mean absolute difference for two random people is 30/sqrt(pi) = 16.93 for a normal distribution with SD 15.


    • sillyolyou says:

      Nobody claimed “entirely”, but it absolutely is a fact that is a strong metric for social class.

      Variance of IQ is definitionally 15; it can’t vary between country.

      You’re right, it is 16.93. I was stupid and forgot it’s a mean absolute difference – instead I calculated the SD for no goddamn reason


    • sillyolyou says:

      *but it absolutely is a fact that it is a strong metric for social class

      Variance of IQ is definitionally 225*


    • dealwithit says:

      so that’s why you have to look at tests which have been normed on british or americans and not danes and see how danes do?

      otherwise IQ is impossible to compare across nationalities.

      which it is, but this follows from the IQ-ist logic taken as given.

      that is, IQ and the Wealth of Nations offends an intelligent 5 year old, as eric weinstein might say.


    • sillyolyou says:

      Call me when they create one of those and actually do that.


    • dealwithit says:

      this can already be done by looking at danish version of the RPM vs a british version. if different, this difference can be corrected for and the danish SD compared to the british.

      i would say IQ tests are meaningless or much less meaningful for children raised in dire poverty or in foster homes or with truly horrible parents, but that’s maybe only 15% of kids. that is, the difference between the lower middle class and the rich will be smaller than between the lower middle class and that 15%. this because public libraries, the internet, public schools, etc. even though, of course, public schools are shit, they’re usually better than no school at all, not even home school.


  2. dealwithit says:

    if it were COMMA …


  3. Modern Heresy says:

    Concerning “70% of the variation”:

    What I should have said is “siblings differ by 70% of the amount of random strangers.”

    As Dealwithit correctly notes (and you acknowledge), we’re dealing with mean absolute difference which is 2stddev(1-r)^0.5 / (pi^0.5)

    For siblings raised in the same home, the mean of all studies is about r = 0.49. Obviously for strangers r = 0.

    So we get 12.08 for siblings and 16.93 for strangers. Close enough.

    Given those numbers, you’re correct that the within-family variance is about 49.8%.

    However, there’s quite a bit of evidence that that sibling correlations decrease with age. Sandra Scarr found when using biologically related siblings as a control in an adoption study that the correlation fell to about 0.35 by adolescence. Wikipedia cites (yes I know, but still) that by adulthood the correlation is as low as 0.24.

    Using those figures the within-family variance would be 65% and 75% respectively. Regardless, whatever the true number is, 49.8% is the lower bound.

    I acknowledge that in adults that they create their own SES or “social class”.

    If younger children within the same family have a different “social class”, are we really talking about what is colloquially known as social class anymore, or are we really talking about something more akin to “total environmental impact”?

    I’ll respond to the stuff about The Bell Curve separately, or maybe in its own video.


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