Thursday, May 17, 2007

The limits of DNA testing

Suppose that police pick up a suspect and match his or her DNA to evidence collected at a crime scene. Suppose that the likelihood of a match, purely by chance, is only 1 in 10,000. Is this also the chance that they are innocent? It’s easy to make this leap, but you shouldn’t.

Here’s why. Suppose the city in which the person lives has 500,000 adult inhabitants. Given the 1 in 10,000 likelihood of a random DNA match, you’d expect that about 50 people in the city would have DNA that also matches the sample. So the suspect is only 1 of 50 people who could have been at the crime scene. Based on the DNA evidence only, the person is almost certainly innocent, not certainly guilty.
--Mark Buchanan, NYT, on the prosecutor's fallacy


Sophist said...

The multiple testing problem in action in criminology... very interesting!

josh said...

yes. but the qualifier "based on dna evidence only" renders the statement essentially meaningless (how did the police pick up the "suspect" in the first place?).

in the presence of even a modest amount of additional evidence, the DNA evidence helps shrink the odds of a false conviction rapidly. consider adding the condition that prior to seeing the DNA evidence, the suspect has a chance in 1000 of being guilty. DNA evidence increases the odds to around 90%.