Posted by: Prospector PJ11 NOV 2011
A court ruling against the use of a certain type of statistical analysis in legal cases could lead to miscarriages of justice, according to an article in The Guardian. The statistical tool in question is called Bayes’s theorem, invented by 18th century English mathematician Thomas Bayes.
Bayes’ theorem calculates the odds of one event happening, given the odds of other related events, and has applications in law, science and engineering. Without getting too bogged down in the mathematics, the theorem links a conditional probability to its inverse, which has many practical applications.
In the case in question, which was overturned on appeal, the accused had been convicted on the evidence of a footprint from a Nike trainer at the murder scene that matched a pair of trainers found at the accused’s home. The data used in the conviction was based on the facts that Nike distributed 786,000 pairs of trainers between 1996 and 2006, that there are 1,200 different sole patterns on Nike trainers and that around 42 million pairs of sports shoes are sold every year. A matching print would therefore seem significant.
But the judge ruled that, since national sales figures for trainers are only rough estimates, it is impossible to say exactly how many of any one type of Nike trainer exist in Britain. He decided that Bayes’s theorem should not be used in similar cases in future unless the underlying statistics are “firm”. Forensic scientists have previously often used Bayes’s theorem even when data is limited, and the decision could affect drug traces and fibre matching from clothes, as well as footwear evidence.
Another application of the theorem is drug testing. A drug test that is 99 per cent sensitive and 99 per cent specific might sound fairly accurate. But if you factor in that only 0.5 per cent of the population are users of the drug in question, the probability that any individual who tests positive is a user of that drug is only 33.2 per cent. This surprising result arises because the number of non-users is huge compared to the number of users, so that the number of false positives outweighs the number of true positives.