In the last week or so, I've discussed probability in medical testing, scientific research, and game show strategy. I've decided to conclude that streak with a look at how it affects institutions of law and order, and what better example than the Duke University rape case which officially concluded yesterday.
From day-one, I was suspicious of the case against him. Too much emphasis was being placed on a somewhat discombobulated (you gotta love that word) account from the "victim." In the era of DNA testing, we have been forced to revisit the statistical nature of all forms of evidence. Make no mistake, all evidence is statistical, especially eye witness account. In 1996, 28 people were released from prison due to DNA test after having served a combined 197 years of their terms. Of those 28 cases, 24 hinged on eye-witnesses. Studies have demonstrated that the human memory, which is equally good at registering patterns and completing ones that aren't really there, is wrong up to 50% of the time. That is no better than random chance, and certainly not good enough to convict someone. Many people mistakenly believe that adding corroborating witnesses reduce the odds of inaccuracy, but that is true only if they are kept in complete isolation. Even the slightest bit of innocent discussion between witnesses is enough to sway opinion in one direction or another.
Good prosecutors realize all this, which is how I know that the DA in this case, Michael Nifong, isn't one of those. Police line-ups have to be very careful to keep the odds as even as possible. The idea is to put the suspect in a line-up with a group of very similar people. If the victim alleged that the assailant was black and all of the ringers are white, what odds does the accused have? Not very good. In the Duke case, the odds were even worse than that. Upon hearing the "victim's" story, Nifong arranged for the following line-up procedure. He acquired photos of the entire lacrosse team, not just those known to be at the party, but the whole team. Then he asked the accuser to pick the men who had raped her. Quick, if I ask you to number out of a hat, what are your odds of picking a number out of that hat? This investigation was unethical to the point of being criminal. I hope Nifong is brought up on charges himself.
Unfortunately, high-tech DNA evidence is just as subject to this kind of misconduct. Even assuming that all human error has been removed from the gathering and processing, there is still a chance of misinterpretation of the data. The current CODIS registry that the FBI uses looks at 13 sites on the human genome. These sites are what is known as "junk" DNA, meaning that they appear to be artifacts of the complex code replication system, and they do not code for any traits. This allows them to vary widely in the population and makes them excellent choices for identification. Only just like in a traditional line-up, one must be very careful. Those sites, which vary so widely, have less variation within certain subsets. You are much more likely to match someone who is descended from a similar world region as you(i.e. sub-Saharan Africa.) You are extremely likely to match someone in your own immediate family, so if you're paternal uncle were to rape someone, all the fancy DNA testing could easily confirm that you did it. Juries are specifically selected by both prosecution and defense to be largely ignorant of statistical thinking, so this is a fact which can't be taken lightly.
Statistics affect our lives in more ways than I can possibly describe or even imagine. Understanding this kind of math is imperative for everyone.