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New paper, math theorem erode confidence in shaken baby syndrome

By John Masson
May 4, 2012

Scholarly debate over the prevalence of shaken baby syndrome intensifies in a paper coauthored by Michigan Law Prof. David Moran, scheduled for publication this summer in the Houston Journal of Health Law and Policy.

But the contribution of a scholar and litigator like Moran—who cofounded Michigan Law's Innocence Clinic and whose work so far has exonerated several Michigan prisoners serving long terms for crimes they didn't commit—sometimes comes in an unexpected way. Especially when that scholar's educational background includes degrees in physics, theoretical physics, and mathematics.

Who better to explain how a basic statistical blunder helped create the misperception at the root of the shaken baby debate: that any child with certain symptoms must, ipso facto, have been abusively shaken by a caretaker?

"My contribution was pretty minimal. I only wrote a couple of pages of the paper," Moran said.

But those couple of pages explained a statistics concept known as Bayes' Theorem. It's a mistake so common it has its own grimly ironic nickname: the Prosecutor's Fallacy. Here's how Moran explains it in the paper, which is available now for free download via the Social Science Research Network:

Suppose that an airport machine that checks for explosives hidden in checked bags is 99% accurate in detecting explosives. This means that the machine will sound an alarm 99 times if 100 bags with explosives are fed through the machine, and will sound an alarm only once if 100 bags without explosives are fed through the machine. In other words, bags containing explosives are 99 times as likely to make the alarm sound as bags not containing explosives. If the alarm sounds, how likely is it that the bag contains explosives? Probably not very likely at all. If one million bags are checked by machine, one of which contains explosives (a number that is almost certainly too high), there would be approximately 10,000 false alarms for every true alarm.

Similarly, if significantly more children suffer a particular injury from natural or accidental causes than suffer the same injury as a result of abuse, then it's clearly wrong to extrapolate, from the set that was abused, that that particular injury is a clear sign of abuse.

The paper is one sign that the diagnosis of shaken baby syndrome, once accepted as virtually indisputable scientific fact, is now a highly controversial one. Another is the recent California wrongful conviction case Cavazos v. Smith, which worked its way to the Supreme Court before ultimately ending with a grant of clemency last month. And Moran's successful Innocence Clinic case involving Julie Baumer, who was exonerated in 2010 after being wrongfully convicted in a shaken baby case, is a third.

Nevertheless, Moran hopes the article helps bring the two sides of the debate closer together.

"The article is written in a mostly conciliatory tone. What we're really hoping is to get a dialogue going within the medical community," Moran said. "Nobody is well served when people who didn't commit child abuse are punished—and we know that happens. We've seen the cases."


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