Who's Counting: Testing and Hiring Disparities Need Not Imply Bias

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Groups differ in history, interests, cultural values, and along a whole host of dimensions that are impossible to disentangle. Confronted with these social and historical dissimilarities, we shouldn't be astonished that members' scores on some standardized test are also likely to differ a bit in the mean and much more at the extremes. (Much of the discussion is valid even if the distribution is not the normal bell-shaped one.) Such statistical disparities are not necessarily evidence of racism or ethnic prejudice although, without doubt, they often are. One can and should debate whether the tests in question are appropriate for the purpose at hand, but one shouldn't be surprised when normal curves behave normally.

Mandating Proportional Representation Can't Work

To combat these disparities, strict quotas are sometimes promoted, but aside from having a dubious and occasionally illegal rationale, such schemes are impossible to implement. Another thought experiment, albeit unrealistic, illustrates this.

Imagine a company, PC Industries say, operating in a community that is 25% black, 75% white, and 5% homosexual, 95% heterosexual. (Again, I've plucked these numbers out of the air.) Unknown to PCI and the community in general is the fact that only 2% of the blacks are homosexual, whereas 6% of the whites are. Making a concerted attempt to assemble a workforce of 1,000 which "fairly" reflects the community, the company hires 750 whites and 250 blacks. However, just 5 of the blacks (or 2%) would be homosexual, whereas 45 of the whites (or 6%) would be (totaling 50, 5% of all workers).

Despite these efforts, the company could still conceivably be accused by its black employees of being homophobic since only 2% of the black employees (5 of 250) would be homosexual, not the community-wide 5%. The company's homosexual employees could likewise claim that the company was racist since only 10% of their members (5 of 50) would be black, not the community-wide 25%. White heterosexuals would certainly make similar complaints.

To complete the reductio ad absurdum, we can factor in other groups - Hispanics, women, surgeons, professors, handicapped people, Norwegians, whoever. Their memberships will also intersect to various unknown degrees, and their backgrounds and training are quite unlikely to be uniform. Once again, statistical disparities will necessarily result.

Sadly, racism and homophobia and all other forms of group hatreds are real enough without making them our unthinking first inference when confronted with such disparities.

John Allen Paulos, a professor of mathematics at Temple University in Philadelphia, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as, most recently, "Irreligion." He's on Twitter and his "Who's Counting?" column on ABCNews.com usually appears the first weekend of every month.

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