Thursday, May 02, 2013

Why are two tests better than one?

In trial cases where you have two forensic tests.

You have to view the two forensic tests as not separate from one another.

But as one big test, says Colmez an expert on statistical usage in court cases. 

She compares it to an experiment to find out whether a coin is biased.

You do a first test and obtain nine heads and one tail... 

The probability that the coin is fair given this outcome is about 8%, and the probability that it is biased, about 92%. 

Pretty convincing, but not enough to convict your coin of being biased beyond a reasonable doubt.
10 coins (nine heads)
You do a second test, and this time you throw eight heads and two tails. 

Now the probability for a fair coin is about 16%, for a biased coin about 84%.
Ten coins (eight heads)
So the naive thought might be that you haven't gained any certainty from this second test.

But if you think about it differently, what you've really done is throw the coin 20 times and get 17 heads and three tails. 

This means there's a probability of 98.5% that the coin is biased.
Twenty coins (17 heads)
So what this means in the case of DNA on a knife in a murder trial is that if it were tested again, and once again the DNA was the accused's profile we could be a lot more certain that the DNA on the knife is indeed the accused's, Colmez says.

And if the knife were tested again and the DNA did not match the accused's profile? .

This would mean that a major piece of evidence would be discredited.
In Colmez's view this isn't a one-off. 

She says numbers get used and abused in court rooms all the time.

And more use should be made of proper mathematical and statistics experts.

A recent example she draws attention to is that of a Dutch nurse, Lucia de Berk, who was first arrested in 2001 after the death of a baby in her care at a hospital in The Hague, apparently from poisoning.

Afterwards, investigators found what they thought was a trend of suspicious deaths among 13 patients treated by De Berk in the previous four years. 

Five others almost died in what investigators said were suspicious circumstances.

In 2003, she was convicted of four murders and three attempted murders, and sentenced to life in prison.

Part of the evidence against her was the testimony of a statistician, who said the odds were 342 million-to-one that it was a coincidence she had been on duty when all the incidents occurred.

In 2004, an appeals court convicted her of three additional counts of murder and upheld the life sentence.

Lucia de Berk hugs her daughter after being acquittedLucia de Berk spent six years in prison
And in prison she might have stayed, if it hadn't been for the amateur statistical sleuthing of a doctor called Metta de Noo-Derksen, the sister-in-law of one of the doctors at the hospital where De Berk had worked. 

She had become suspicious of the reasoning used in the case and, along with her brother Ton, began a campaign to prove there had been a miscarriage of justice.

De Berk had been accused of causing some deaths, which she had later managed to prove had occurred when she hadn't been present in the hospital.

But these deaths were just forgotten about in the trial and never spoken about again. 

And they never recalculated the probabilities, Colmez says.

What the brother and sister team did was they went through all the
deaths she was accused of, struck off the ones she had proven she wasn't even there for, and they recalculated the probability.

The probability of her being present for all the unexplained deaths was still enough to raise questions but if you consider the number of nurses at work in the Netherlands, you'd expect to see some unusual-looking - but innocent - clusters of unexplained deaths on some of their watches.

Out of some 250,000 nurses, one would expect a couple of hundred to be involved in a set of circumstances similar to those of Lucia. 

It definitely wasn't proof that she was a murderer.

After six years in prison, Lucia de Berk was acquitted in April 2010.

It's a horrible, horrible story. 

But it's uplifting that it was just some members of the public who went through a lot of work - and freed her.

Coralie Colmez

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