Biostatistics Takes the Stand

The Federal Trade Commission investigates a drug company’s advertised claims about the effectiveness of its sleeping pill. A Utah couple sues the federal government for damages, asserting that their child died of leukemia due to radioactive fallout from nuclear weapons testing. A class action lawsuit alleges that New York City’s stop-and-frisk tactic discriminates on the basis of race. All three cases hinged on one thing: statistics.

Now in its third edition, Statistics for Lawyers, co-authored by Bruce Levin, professor of Biostatistics, reviews over 160 case studies to introduce statistical methods to those who need to cite numerical arguments in the service of justice.

“These cases touch on the fundamentally important statistical question of how we weigh the evidence,” says Levin. “Different disciplines approach this question in different ways, but statistics offers a distinctly quantitative approach. Were the sleeping pills in question as effective as the drug company claimed? Different ways of calculating average sleep latency came up with different results, some supporting the drug maker’s claims, some not. And the claim was that the pill ‘puts you to sleep 26-percent faster.’ Faster than what? Should advertisers be allowed to include a partial placebo effect in their advertising claim?”

Levin met his co-author, Michael O. Finkelstein, adjunct professor at Columbia’s Law School, through Herbert Robbins, Levin’s faculty mentor in the Department of Mathematical Statistics, as the Department of Statistics on the Morningside Campus was then known. In 1972, Finkelstein recruited Robbins to testify in a case involving a challenged election in Brooklyn. The challenge was based on the fact that a certain number of invalid votes were included in the tallies. No fraud was alleged, but the intent of the invalid votes was unknown.

Then it was common for judges to use their intuition or a simple rule of thumb to decide close elections—for instance, if the plurality were less than 10 percent of the number of invalid votes, then a new election should be called. Robbins showed that a more sophisticated approach was needed: the Square Root of N Law in statistics shows that the probability that an election would be reversed upon removal of the invalid votes becomes increasingly remote as the size of the plurality grows large in relation to the square root of the number of invalid votes, not the number of invalid votes. In other words, the legal rule of thumb was out of sync with the actual probability of reversal.

In the time since Statistics for Lawyers came out in 1990, the legal world has become more accepting of statistical evidence—at least somewhat. “It’s a little better, but there are still miles to go,” says Levin. Today many law schools offer a course in statistics, although not as a requirement. “As our society becomes more litigious and data becomes a bigger part of our lives, quantitative methods are a must,” he says.

Levin himself has testified in numerous cases, the most memorable of which involved a 1991 E. coli outbreak at the Jack in the Box fast-food chain. The chain’s owners alleged that their meat supplier broke its promise to provide a safe and wholesome product. Levin was called in to perform a very simple calculation: count the number of times laboratory tests for the specific pathogen implicated in the outbreak were performed. His answer: zero.

While Levin’s statistical abilities weren’t tested, he came away with a new understanding of how to testify—a lesson he continues to impart to students in his Biostatistics in Legal Proceedings class.

“Statisticians get excited about state-of-the-art methods which are often quite complicated,” Levin says. “But that’s not how you want to testify in court. You want to keep it simple and transparent. You want the judge and jury to nod their heads and say ‘I understand what he’s saying.’”

History Lesson

Like Levin’s Statistics for Lawyers, a new book by Prakash Gorroochurn, associate professor of Biostatistics, provides ample evidence that the field reaches beyond the domain of scientific studies and peer-reviewed articles.

Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times situates the field’s advances in the lives of its progenitors. Released in March, the book is the second in what Gorroochurn hopes is a historical trilogy, following 2012’s Classic Problems of Probability, which won the PROSE Award for Mathematics from the American Publishers Awards for Professional and Scholarly Excellence.

The new book, one of the first exclusively focused on the history of modern statistics, introduces more than a dozen leading figures from the 19^th and 20^th centuries, including British statistician Ronald Fisher, who is largely credited with creating the field. Equal parts brilliant and egotistical, Fisher clashed with rivals like William Sealy Gosset, who published his statistical papers under the pseudonym Student while employed at the Guinness brewery. (Gorroochurn’s next book will take a deeper look at these statistical spats.)

Geared toward those with some knowledge of statistics, the book will also appeal to anyone with interest in historical drama like the story of Russian mathematician Aleksandr Lyapunov, who was so in love with his wife that on the day she succumbed to tuberculosis, he shot himself in the head. Or Robert Adrian, who fled Ireland for the United States after participating in a failed uprising against the British.   

While Gorroochurn’s history of modern statistics is largely the domain of European men, readers will also learn about David Blackwell, who combatted racism and segregation and became the first African-American tenured faculty member at UC Berkeley, and the Indian mathematician Calyampudi Radhakrishna Rao, who each worked independently on an influential theorem that today bears their names.

Statistics is inseparable from the people who developed the field, explains Gorroochurn. Knowing its proponents brings their equations to life. “I can’t imagine teaching statistics without talking about its rich history,” he says. “The past is the torch that guides us to the future.”