Have You Arrested the Wrong Man?

DNA profiling is a powerful and important tool for investigating crime, but are we relying too heavily on its evidence?

Apart from identical twins, everyone is genetically unique. This obviously has great potential in solving crime. Imagine the scenario: a man breaks into your house, steals your most treasured possessions and leaves without being seen, cutting his hand on a broken window in doing so. The police collect a sample of the blood and send it to the lab for analysis. The next day it is matched to a sample on the national DNA database, containing information on everyone in the country and your burglar is arrested.

All this is fine in theory, but police have neither the time nor the technology to base the profile on the entire DNA sequence. There is just far too much of it, and most is common to all humans anyway, so they rely on six stretches of DNA called short tandem repeats (STRs). These vary widely from person to person and are generally very reliable, but it is possible for an innocent person to produce a match.

The better profiling gets, the more danger there is that courts will rely too heavily on its evidence, possibly ignoring evidence in the suspect's defence. It is often possible to guess the probability that DNA samples will match even if the suspect is innocent. What is important is how this information is presented to the jury.

A psychologist, Jonathan Koehle, ran experiments to determine whether people understood probabilities better as percentages or frequencies. He asked his students to consider a hypothetical case in which a DNA sample found on a dress belonging to a former White House intern was found to match a DNA sample from a US President. One group was told that there was a 0.1 per cent probability that the President's DNA would match even if he were not responsible. The other group was told that 1 in 1000 men would produce a match. These two statements mean the same thing to statisticians, but the students responded very differently. In the first group, 28 per cent thought that the president was almost certain to be guilty, compared with 8 per cent in the second group.

It appears that frequencies are more easily understood by juries. When asked how many people in a city of 500 000 would have DNA samples matching the President's, 74 per cent of the second group responded correctly, compared with 26 per cent of the group given the number as a percentage.

• Should we as mathematicians make more effort to make our results more accessible to the general public?
• Should the education system make more effort to equip everyone with an understanding of statistics?
• Will jurors have to be given maths lessons before the case?

Credits: researched and written by Nicola Kerrison