Using statistics in court
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What is the main topic discussed in this episode?
You're listening to a More or Less podcast from the BBC. For more information about the programme, please go to the website bbc.co.uk slash radio4. Hello and welcome to More or Less, your weekly guide to the numbers in the news and in life. This week we intervene in another mathematical marital misunderstanding.
I've had an ongoing argument with my husband who insists the odds of getting six consecutive numbers in the i.e. 1, 2, 3, 4, 5, 6, are higher than getting six random numbers.
As the price of a train ticket rises yet again, we'll ask how the cost of UK rail travel really stacks up against continental opposition. But first, the conviction this week of Gary Dobson and David Norris for the murder of Stephen Lawrence 18 years ago is a good example of how important scientific evidence has become in the courtroom. the verdict hinged on tiny bits of circumstantial evidence, including clothing fibres and bloodstains. One way to make sense of evidence like this is by analysing it statistically. How, for example, might Stephen Lawrence's DNA have got onto the suspect's clothes? What was the chance that contamination might have happened, as well as the small odds of someone else having the same DNA profile?
After a while, though, these numbers can get confusing. Late last year, before the verdict in this trial was announced, I spoke to Angela Saini, a science journalist who's been investigating statistical mistakes in court. I began by asking her what sort of statistics tended to trip up the legal eagles.
Well, when lawyers and forensic experts start applying odds to evidence, it's so easy to get things wrong that they even have names for the different types of errors. One's called the defendant's fallacy, for instance, because it favours the defence. You may remember the trial of OJ Simpson. in the US in 1995 for the alleged murder of his ex-wife. So OJ Simpson had pleaded no contest to a charge of domestic violence and this could have made him look pretty guilty. But his defence team claimed that this was irrelevant because fewer than one in a thousand women who are abused by their male partners end up being killed by them. Now, if you look at the stats from a different direction, you'll find that if a woman is abused and later murdered, there's actually an 80% chance that her partner did it.
OK, so these statistics, they can be quite powerful in the courtroom and quite deceptive as well.
Exactly. So the most common error that you see is the prosecutor's fallacy, one that usually favours the prosecution. It's when the odds associated with a piece of evidence become confused with the odds of the suspect's innocence.
OK, my head's spinning. So what does that mean?
Well, let me give you a famous example from 1991 when a man called Andrew Dean was convicted for a rape in Manchester after he seemed to be a positive DNA match. Now, the DNA evidence was pretty vital in this case because, well, there just wasn't that much other evidence. Andrew Dean had no apparent connection to the victim. He even had an alibi from his girlfriend. But the jury was told that only around one in three million people would be a DNA match. And that made the DNA evidence look pretty compelling. The jury assumed that the chance of Andrew Dean being innocent must also be one in three million, so they found him guilty. But for a crime like this, the pool of suspects could be enormous, bringing down the odds of Andrew Dean's guilt quite dramatically.
In a population of 20 million adult men, just for the sake of example, you'd expect there to be around seven matches. And this is why, in the end... Andrew Dean's conviction was quashed.
How did the Stephen Lawrence conviction spotlight statistical evidence in court?
So one way of avoiding this kind of fallacy would presumably be to analyse the statistics a bit more carefully?
Well, that's right. The method often used is Bayes' theorem. In a courtroom, it forces you to logically examine how to revise your views of whether a suspect is more or less likely to be guilty given each new piece of evidence.
OK, but if Bayes' theorem is the straightforward way of doing this, why don't courts use it?
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Chapters
6 chapters
1
What is the main topic discussed in this episode?
0:00–3:38
2
How did the Stephen Lawrence conviction spotlight statistical evidence in court?
3:38–9:21
3
What common statistical errors (prosecutor's and defendant's fallacies) confuse juries?
9:21–18:28
4
How could Bayes' theorem change courtroom interpretation of DNA and fibre matches?
18:28–21:27
5
Why did the Court of Appeal limit the use of Bayesian reasoning in R v T?
21:27–22:41
6
How do statisticians explain Bayes' theorem and its role in cases like Sally Clark?
22:41–27:55