Groups, individuals, statistical disparities: What constitutes equity?

Much public discourse and many public policies feature and discuss statistical disparities between various groups. All too often, elementary statistical facts are ignored or misunderstood.

That correlations may have no causative basis is widely understood, but it is often given only lip service. Too rarely understood is that statistical disparities in group averages are inevitable because human beings typically belong to several, often many different groups: family, clan, national; religious, ideological; professional, vocational, recreational. Every individual is influenced to an individual degree by the beliefs and demands of the various groups. No two individuals are likely to be the same in that respect, so when people are grouped under one or other criterion, the group averages on any given characteristic will differ between groups. Beyond that, it is also inevitable but not as obvious that quite small differences in group-average scores can result in very large statistical disparities between groups.

An instructive example is that of racial-group differences. The Bell Curve [1] offers graphical representations of distributions of individual IQ scores separately for white and black populations.

Both distributions extend over approximately 80 units, but the group mean or average or median scores differ by perhaps 15 units, something like the magnitude of a standard deviation [2]. As The Bell Curve notes, the two distributions overlap to such a degree that, for populations of equal size, a large proportion of both would have similar scores: any random pair of random white and black individuals would be very likely to have approximately matching scores, scores not significantly different from one another, different, if at all, by much less than a standard deviation.. That is what should be borne in mind in the case of individuals, or in comparing or contrasting individuals.

However, in the United States the two populations are not of equal size; there are 7-8 times as many whites as blacks. The actual distributions therefore look like this:

For quite a range of scores around the median, relative numbers of white and black will be in proportions not very different from their relative numbers in the whole population; and again that is what should be kept in mind in the case of individuals. But towards the tails of the distributions, the statistical disparities will be much larger than the relative proportions in the population.

So for those outcomes for which IQ-type scores are good predictors of outcomes, and where unusually high or unusually low scores make a significant difference in achievements or failures, one should expect very large statistical disparities in absence of any deliberate discrimination on racial or other grounds.

The Bell Curve aims specifically to demonstrate that IQ-type scores are very good predictors of a variety of outcomes; and individual members of any group — including any racial group — who happen to have the same IQ score are quite likely to achieve similar outcomes.

I had not read The Bell Curve when it was published in the early 1990s, misled by many negative reviews and comments in much of the media that described it as racist bigotry [3]. Having now read the book, I can assert confidently that it is not racist at all, no matter that it accepts that there are racial-group-average differences in IQ scores, with Americans of East-Asian heritage significantly outscoring white Americans, and Ashkenazi Jews outscoring all other groups.

An even more a general discussion of disparities and discrimination has been offered by Thomas Sowell [4] ; one of his rather striking examples is that some 20% of men in the highest 1% of IQ scores achieved less than nothing of note [4: p.3].The salient point is that any specific type of achievement draws on some among a large number of possible different attributes and personal characteristics. Birth order, for example, is not often taken into consideration, yet it I associated with several personality traits, and significant differences even in IQ scores [4: p. 7]; Sulloway [5] has described the difference in type of discoveries made by first- and by later-born children.

Simply because every type of achievement may reflect a different combination of a large number of possible  factors — of course including historical discrimination and other disparities — it is perfectly natural and very likely for the comparison of any two groups on any one particular outcome or achievement to show significant statistical disparities.

Again: statistical disparities of this sort are no more than correlations and certainly not immediate evidence of discrimination.

What then would be evidence of discrimination? And what would constitute equity, what would be the characteristics of an equitable society?

An equitable society would have no mandatory negative treatment of individuals on irrelevant grounds, reasons irrelevant for the actions to be taken.

Of course that could not guarantee that every individual would be treated equitably, because actions are taken and decisions are made by human beings, not by robots. Robots could perhaps abide by what is mandated and by what is not mandated; but human beings come with ignorance, biases, good-will and ill-will, good judgment and poor judgment — all sorts of fallibilities. Even mandated equitable treatment could not guarantee that every individual would be treated equitably everywhere, because not every individual action or event could be controlled. So a socially, everyday and everywhere equitable society requires in practice a culture in which everyone treats everyone else as an individual, without bias as to appearance, dress, class, heredity, etc. etc.

Such a culture cannot be created by fiat or by force, let alone in short order.

The overall culture of any sizable society that is not totally homogeneous is a conglomeration and mixture of a great number of groups that each have a culture of their own. Any given individual is likely to belong to quite a number of different groups, each of which carries with it some set of beliefs, attitudes, preferences, biases.

As West [6] has described cogently, membership in a group conveys some benefits, so the tendency is for individuals not to transgress their group’s general characteristics and attitudes. A rather obvious corollary is that overall societal cultures change — if at all! — usually only quite slowly, even when governments and institutions mandate a particular change.

For example, Australia enshrined the right to vote for women already in 1901-3 [7]; but half-a-century later, by the middle of the 20^th century, the overall Australian culture remained highly and overtly macho and discriminatory against women: “traditional” male and female roles were taken for granted; it was regarded as natural for men to be paid more than women; we spoke of women going to university as seeking an Mrs. degree; and so on. That discrimination had persisted for decades even in a society aggressively egalitarian overall — no one was allowed to pretend to be “better” than anyone else; but it took several centuries for that egality to include the indigenous aborigines.

Sometimes changes do happen with seeming rapidity, say, attitudes towards cigarette smoking or towards gay marriage; but “rapidity” here means a few decades, and in those cases had also been preceded by further decades of minority activism: there were gay-rights activists in Germany in the 19^th century, for example.

The irrationalities of “political correctness” or “wokeness” include demands for instantaneous mandated change; and not only in tangible matters but even in demanded displays of universal sensitivity to everyone. As I have written at length elsewhere [7], it has not been possible to attain even universal literacy, let alone universal sensitivity and tolerance.

I had been fortunate to grow up in that mid-20^th-century Australia that also took for granted, “sticks and stones may break my bones but names can never hurt me”; an environment in which innumerable cultural stereotypes were openly, forcefully, disdained and derided, even as individuals from those stereotyped groups, like myself, were treated as individuals, courteously and even sensitively.

No one can — or should be — blamed, let alone held accountable for what happened before that person’s birth. If continuing differences in opportunities, income, wealth, status, etc., are regarded as undesirable or improper, then the whole society has the task of making the needed changes, by properly equitable means.

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[1]   Richard J. Herrnstein & Charles Murray, The Bell Curve: Intelligence and Class Structure in American Life, Free Press, 1994; p. 279.

[2]    The difference between black and white group means or medians on various IQ-type tests may be a bit less than in this case, but it is typically about 10 ± 5 units.

[3]   Some remain misled about that even now, see for instance Baratunde Thurston, How to be Black, HarperCollins, 2012, p. 141

[4]   Thomas Sowell,  Discrimination and Disparities, Basic Books, 2018 (rev. ed. 2019)

[5]   Frank J. Sulloway,  Born to Rebel: Birth Order, Family Dynamics, and Creative Lives, Pantheon, 1996

[6]   Andy A. West, The Grip of Culture — The Social Psychology of Climate Change Catastrophism, The Global Warming Policy Foundation; https://www.thegwpf.org/content/uploads/2023/07/West-Catastrophe-Culture6by9-v28.pdf; described more gully at https://henryhbauer.substack.com/p/alternative-facts-naturally-trump

[7] [ https://en.wikipedia.org/wiki/Timeline_of_women%27s_suffrage#18th_century]

[8]   Diversity and Identity, Keynote Address, Proceedings of the 49th Annual Meeting of the American Conference of Academic Deans, 1993, 27-35; reprinted Martin Harlaar (ed.), Ben ik wel woke genoeg? Een ontdekkingstocht door het land der Social Justice Warriors, Gompel & Svacina, 2022, pp. 182-189; https://mega.nz/file/sGp2ibqQ#mLRMstFirE4ZrCOJVNbkWvV_VxGfvirgeA3OeIW3Pp4