Pipe bombs, marital infidelity and Donald Trump

The Russian dictator Joseph Stalin reputedly said that while the death of one person is a tragedy, the death of 1 million is merely a statistic. Stalin was probably not the first to observe that statistics can be manipulated by disreputable politicians.

Two politically explosive case files illustrate the power of statistical reasoning: pipe bombers and Trump's sexual scandals. In the first example I will give, statistics exonerate alleged wrongdoing; in the second, it indicts.

A professor of mine served as an expert witness to defend a suspected pipe bomber in the early 1990s. The police collected bomb fragments from the crime scene along with the suspect's tool kit and initially concluded that he was guilty on the basis of inconclusive forensic analysis.

By using a simple statistical test, my professor was able to destroy the prosecution's case against the purported bomber without having much knowledge of the case. I'll explain how he accomplished this remarkable feat in a moment.

Our second illustration is more timely: Melania Trump's public defense of her husband's reported assaults on women. Her comments raise troubling suspicions about her own honesty and intuition about the "man she knows."

Assuming Trump is equally likely to be guilty or innocent in these complaints, we can demonstrate that the probability of eight women accusing Trump of sexually inappropriate behavior is less than 1 percent.


The expectation that Trump is completely innocent is extremely remote, provided that his accusers are unknown to each other and separated by time and circumstance. So remote, in fact, that statisticians have a name for this predicament: It's called "rejecting the null hypothesis." This means that we reject the possibility of coincidence when there are too many coincidences.

This same reasoning applies to Trump's liability for misconduct. The probability of guilt is mathematically overwhelming in the face of multiple complaints. And Trump's denials become only slightly more plausible if the allegations are slightly less credible. That's the power of having multiple accusers.

I should note that only in a court of law could proper vetting take place. The stories attributed to these women must be completely independent and legally tenable (implying no collusion or ulterior motives). In other words, what if we discover an anti-Trump conspiracy responsible for a "November surprise"?

As they say in Las Vegas, such a turn of events would mean that all bets are off.

Are you still wondering how my professor got the alleged bomber off the hook? He told the police to give the suspect's tools, along with four other bogus tool kits, to three independent labs. Only if all three labs identified the right tool kit could the prosecution dismiss the element of luck and confidently charge their suspect.

The labs were unable reach a consensus, and the bombing suspect was released. Justice prevailed, thanks to the power of statistics.

Mark Travis has a masters degree in statistics from the University of Northern Colorado and is a former honorarium instructor in micro-economics at the University of Colorado