Supreme Court Justice Jackson’s statistical incompetence

 From Ted Frank at the Wall Street Journal

TF is on target.

The sad part is that Justice Jackson is so confident about something she knows little about. She is not alone in this. It is seems relatively rare that people have much idea about what they don't know.

The consequence is, as in this case, important decisions based on strongly held opinions that are wrong. Such decisions are not likely to make things better.

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Even Supreme Court justices are known to be gullible. In a dissent from last week’s ruling against racial preferences in college admissions, Justice Ketanji Brown Jackson enumerated purported benefits of “diversity” in education. “It saves lives,” she asserts. “For high-risk Black newborns, having a Black physician more than doubles the likelihood that the baby will live.”

A moment’s thought should be enough to realize that this claim is wildly implausible. Imagine if 40% of black newborns died—thousands of dead infants every week. But even so, that’s a 60% survival rate, which is mathematically impossible to double. And the actual survival rate is over 99%.


How could Justice Jackson make such an innumerate mistake? A footnote cites a friend-of-the-court brief by the Association of American Medical Colleges, which makes the same claim in almost identical language. It, in turn, refers to a 2020 study whose lead author is Brad Greenwood, a professor at the George Mason University School of Business.

The study makes no such claims. It examines mortality rates in Florida newborns between 1992 and 2015 and shows a 0.13% to 0.2% improvement in survival rates for black newborns with black pediatricians (though no statistically significant improvement for black obstetricians).

The AAMC brief either misunderstood the paper or invented the statistic. (It isn’t saved by the adjective “high-risk,” which doesn’t appear and isn’t measured in Greenwood’s paper.)

Even the much more modest Greenwood result—which amounts to a difference of fewer than 10 Florida newborns a year—is flawed. It uses linear regression, appropriate for modeling continuous normally distributed variables like height or LSAT scores but not for categorical low-probability events like “newborn death.” The proper methodology would be a logistic model. The authors did one, hidden deep in an appendix rather than the body of the paper.

There, the most highly specified model still shows an improvement in black newborn survival. But if you know how to read the numbers—the authors don’t say it—it also shows black doctors with a statistically significant higher mortality rate for white newborns, and a higher mortality rate overall, all else being equal.

So we have a Supreme Court justice parroting a mathematically absurd claim coming from an interested party’s mischaracterization of a flawed study. Her opinion then urges “all of us” to “do what evidence and experts tell us is required to level the playing field and march forward together.” Instead we should watch where we’re going.