The Winton Centre Quick Quiz for Legal Professionals
Are you the Lord Chief Justice of stats in the courtroom, or do you need a pupillage in probability? Cross-examine your skill at handling evidence-by-numbers with our quick quiz.
The Winton Centre for Risk and Evidence Communication
A lawyer once berated a statistician:
‘‘Look, the guy either did it or he didn’t do it. If he did then he is 100% guilty and if he didn’t then he is 0% guilty; so giving the chances of guilt as a probability somewhere in between makes no sense and has no place in the law.’’
But the lawyer is wrong - you can assign probabilities to events that have already happened but where you are uncertain of the outcome.
Imagine your friend tosses an (unbiased) coin two times but doesn’t show you the results. What is your probability that they got two heads?
Either 0 or 1
1/2 or 0.5
1/3 or 0.33
1/4 or 0.25
The probability of being a woman, given that you are pregnant is extremely high. But the probability of being pregnant, given that you are a woman is pretty low.
The two are obviously not the same. But consider the following:
The probability of getting a fingerprint match, given innocence.
The probability of innocence, given a fingerprint match.
Again, the probabilities are not the same but this example is much less obvious. Treating the first probability as equivalent to the second is a common (and sometimes wilful) error.
What is the name of this mistake?
The Judge's Muddle
The Prosecutor’s Fallacy
The Solicitor's Sophism
The Barrister's Balls Up
In 1994 OJ Simpson was put on trial for murder.
Blood samples found at the scene were matched to OJ Simpson’s blood type.
During the trial, the prosecution argued that there was only a 1 in 400 chance of gaining a positive blood type match at the scene, if Simpson was innocent.
They went on to commit the common mistake described in the previous question. Which of the following statements commits this error?
The probability of a positive match, given Simpson’s innocence, is 1 in 400
The probability of Simpson’s innocence, given the positive match, is 1 in 400.
The probability of Simpson’s guilt, given the positive match, is 1 in 400.
The probability of Simpson’s innocence, given the positive match, is 399 in 400.
In 1999 Sally Clark was convicted of murdering her first two children. It turned out to be a terrible miscarriage of justice.
The defence claimed that they had both died of Sudden Infant Death Syndrome (SIDS), also referred to as cot death.
One expert witness presented evidence at the trial that the probability of one child dying from SIDS was 1 in 8543. He argued that the probability of two children dying from SIDS in the same family was therefore 1/8543 multiplied by 1/8543, giving a chance of 1 in 73 million that both children died from SIDS.
This was used as part of the evidence against Sally Clark.
Why is this number wrong?
The two deaths were independent events, so probabilities cannot be multiplied
The two deaths were not independent events, so probabilities cannot be multiplied
The two deaths were not mutually exclusive, so probabilities cannot be multiplied
The two deaths were mutually exclusive, so probabilities cannot be multiplied
You are the legal representative for an athlete, Whizz Kid, who has been accused of doping.
Whizz tested positive as part of regular screening test given at random to athletes across the country. The test is known to be 95% accurate, meaning it will correctly identify 95% of non-dopers and 95% of dopers.
It is thought around 2% of all athletes are doping.
In the absence of other evidence, what do you think is the probability that Whizz truly was doping, given the positive test result?
Likelihood ratios are increasingly being used in court as a way of communicating the strength of forensic evidence.
A likelihood ratio is a ratio of two probabilities: they compare the relative support provided by a piece of evidence for two competing hypotheses
Which one of the following sentences expresses a likelihood ratio?
“The probability of any two random people matching at any one DNA locus is about 7 in 100.”
“The probability of any two random people matching at thirteen loci is about 1 in 400 trillion.”
“The probability of Mrs W’s DNA matching the sample, given innocence, is 1 in 2 million.”
“The probability of the evidence is 300 times more likely if the DNA sample came from Mr Smith than if it came from an unknown unrelated individual.”
The likelihood ratio can be calculated to give a precise number. Recall that they compare the relative support provided by a piece of evidence for two competing hypotheses (usually 'guilty' vs 'innocent' in some way).
Imagine a Likelihood Ratio has been calculated for the forensic evidence used in a trial, and comes out as around 1. What does this result mean?
The forensic findings provide extremely strong support for one hypothesis over the other
The forensic findings provide moderate support for one hypothesis over the other
The forensic findings are neutral & do not support one hypothesis over the other
The forensic findings are extremely improbable and should be checked
In a landmark ruling in the High Court in 2009, Corby Council was found responsible for allowing toxic waste to pollute the atmosphere, so causing a cluster of birth defects in the Corby area between 1989 and 1999.
This was partly based on statistical analysis comparing the number of cases of birth defects arising in the Corby area vs the cases of birth defects elsewhere. The conclusion was that there were “a statistically significant cluster of birth defects in Corby between 1989 and 1999", with a P value of 0.03.
The P-value of 0.03 (1 in 30) is an estimate of the probability that such a high number of birth defects in Corby would occur simply as a result of chance variation rather than toxic pollution.
So, assuming there are around 900 other areas the size of Corby in England and Wales, how many would we expect to show similar clusters of birth defects as in Corby just by chance alone?
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