When clever people do stupid things
The post below, with a few minor adjustments like putting in the exact date instead of "yesterday" to avoid confusion, is a repeat of an article first posted twelve years ago which I thought was worth running again.
I'm pleased to say that there has been some movement on the point made at the very end of the article about providing more information on statistics for people involved in court cases.
In November 2017 a UK Supreme Court judge launched the first of a series of scientific guides for the judiciary.
Lord Hughes had overseen a project to help the judiciary deal with scientific evidence in the courtroom. The first primers covered DNA fingerprinting and computer techniques to identify suspects from the manner of their walk. Guides on statistics and the physics of car crashes were to come next and one on "shaken baby syndrome" were planned.
Memo to self - I must find out whether these subsequent guides were issued and whether they were made available to juries as well as judges. Because they should be.
In November 2017 a UK Supreme Court judge launched the first of a series of scientific guides for the judiciary.
Lord Hughes had overseen a project to help the judiciary deal with scientific evidence in the courtroom. The first primers covered DNA fingerprinting and computer techniques to identify suspects from the manner of their walk. Guides on statistics and the physics of car crashes were to come next and one on "shaken baby syndrome" were planned.
Memo to self - I must find out whether these subsequent guides were issued and whether they were made available to juries as well as judges. Because they should be.
When Clever People Do Stupid Things
On 17th February 2006 a court quashed the disciplinary action taken by the General Medical Council against Professor Sir Roy Meadow, one of the most distinguished children’s doctors in the country. Professor Meadow had acted as an expert witness in the trials of many women accused of killing their own children. Unfortunately his great knowledge of medicine and convincing air of authority as a witness was matched by a gross ignorance of the principles of statistics which would have been unacceptable in a Lower VI former studying for Maths A-Level.
Professor Meadow convinced first himself, and then the juries, that at least three innocent women who were already suffering the agony of having lost their babies, should be jailed for murdering them. He told the trial of Sally Clark that the chances of her having two children lost to cot deaths through natural causes were one in 73 million, and the trial of Donna Anthony that the chances of her two children having died from natural causes were one in a million.
This evidence was based on a fundamental misunderstanding of statistics: Professor Meadow had assumed that the probability of each cot death was independent and had not taken into account the possibility that there could be a genetic predisposition to a higher risk of such fatalities or that the conditional probability of a further case of sudden infant death in the child of a mother who had already suffered one such death could be a lot higher. Other studies by doctors who do understand the relevant statistical principles suggest the odds in the Sally Clark and Donna Anthony cases were more like one chance in 77.
By overturning the finding that Professor Meadow was guilty of serious professional misconduct, the judge has effectively ruled that it is acceptable for a highly skilled professional who is being paid by the state to give expert evidence in one area of knowledge to neglect the basic mathematical understanding required to understand that knowledge. I think there are three implications for our society of this decision.
1) The stupid mistakes which do the most damage are rarely made by stupid individuals, but by intelligent ones – stupid people are rarely in a position to do as much damage as intelligent people.
2) Our society needs to recognise that expertise in one area often does not translate into expertise in others
3) It is high time we ensured that all lawyers, judges, expert witnesses, and juries had access to some basic training in statistics.
The classic example of a brilliant man who caused a major disaster with a stupid mistake that no stupid person could have made was Admiral Sir George Tryon. He became Commander in Chief of the Royal Navy’s Mediterranean Fleet, then the crack force of the most powerful and professional navy the world had ever seen, and did so purely on ability. His powers of intellect enabled him to best in argument any other officer who ventured to disagree with him. And more than eighty years after the accident in which he died I have met people who still believe that he was not responsible for that accident.
But there is no doubt that Tryon caused the collision which sank his flagship, HMS Victoria, drowned 357 officers and men, and made the world’s most formidable fleet look like idiots, with a basic mathematical error. Tryon was commanding two columns of battleships. Each column was formed in “line ahead” with one ship behind another, and the two columns were heading in the same direction, side by side and six cables or 1,200 yards apart. The turning circle of these ships was 1,600 yards. Tryon ordered the two columns to turn towards each other. Nobody will ever know exactly what he meant to happen, but as one of his officers pointed out, the two columns of battleships would have had to have started with a distance between them more than double that 1,600 yards turning circle to carry out any such manoeuvre safely.
At least four of Tryon’s officers, including the captain of his flagship, HMS Victoria, which was leading one column, the fleet’s second in command in HMS Camperdown at the head of the other column, and two staff officers who queried the orders, realised that they were likely to result in the collision of the leading ships.
Faced with an apparently suicidal order, these officers reacted in different ways. The only person to come well out of the disaster, Commander Thomas Hawkins-Smith, initially pointed out the problem and then queried the order twice. Tryon at first accepted the point, but unfortunately he then apparently forgot that he had done so, brushing objections aside.
The captain of HMS Victoria is on record as saying that “Open criticism of one’s superior is not consistent with true discipline” and said nothing to Tryon until a collision was inevitable. However, he probably saved lives by asking for and getting permission to put the engines into reverse and by closing the ship’s watertight doors.
The Second-in Command, Admiral Markham in the Camperdown, saw the problem but didn’t know what to do, and while he was trying to make up his mind the entire fleet was heading for the Syrian coast on which they would all go aground unless something was done. While he was dithering, Tryon sent the signal “Why did you not obey my order?” and then Markham followed Tryon’s instructions, with the inevitable consequence that the Victoria and Camperdown collided. Ironically, just after the collision, Tryon was handed a note with Markham’s reply, “Because I did not quite understand your signal.”
Admiral Tryon appears to have realised his mistake just too late – his voice was almost a whisper as he gave permission to put the engines “full astern” to slow down the ship. In his last minutes he made no attempt to deflect responsibility for the disaster: his last recorded words were “It is all my fault.”
Tryon made no attempt to save himself and went down with the ship.
Admiral Tryon and Professor Meadow had in common that both were brilliant men at the head of their respective professions and internationally respected in their fields. Both made basic mathematical errors with grave consequences. Professor Meadow wrecked three lives where Admiral Tryon ended more than three hundred. But there are lessons we need to learn from both.
The first is that the more eminent you are the more you need to listen to others. If George Tryon or Roy Meadow had been less eminent, both they and others might have been less inclined to assume they were always right.
The second is that we should be much more careful about assuming that knowledge in one field carries over into another. Angela Cannings, one of the innocent women who was wrongly convicted on Professor Meadow’s evidence, was surely right when she said in February 2006 of expert witnesses that “It’s when they are approached about areas outside their expertise that they should look up and say ‘Sorry, I can’t deal with this’ and step back.”
That principle has much wider application. Let me give just one example. I am an economist by profession and a regular churchgoer. I have heard priests and bishops give sermons in which they talked about spiritual matters, theology or human motivation and I immediately recognise that they are vastly better informed than I about such subjects and I have things to learn from them.
However, when the subject turns to matters on which I have professional knowledge, it readily becomes apparent that neither theological college nor biblical study gives any insight into such matters as the relative merits of competing economic theories or tax rates. It pains me to say it, but when bishops for whom as pastors and theologians I have immense respect are invited to talk about government economic policy they often reveal themselves to be as misguided outside their field of expertise as Sir Roy Meadow was outside his.
I have also heard bishops say very intelligent things about politics and economics. But nine times out of ten, when this happens the idea or concern which is being raised has been put as a question. In other words, the most intelligent contributions often come from a speaker who is acutely aware of the limits of his or her expertise.
The same applies when politicians talk about football, or when successful football managers are invited by the media to talk about business, or when TV soap stars talk about politics, or successful authors are invited to talk about the law. In a democracy we are all entitled to a view about any subject but we should avoid the trap of assuming that an expert in one subject is certain to have valuable insights into another.
My final comment is that, to avoid the risk of sending more innocent people to prison, we must significantly raise the level of statistical expertise available to the courts. Expert witnesses who think they understand maths but don’t are not a problem unique to cases of cot death. Another example is genetic fingerprinting. This is an immensely powerful tool and there is no doubt whatsoever that it has sent many guilty people to justice. But statements of probability in relation to genetic evidence can sound more powerful than they really are unless there is corroborative evidence.
Let’s give an example. Supposing there is a crime for which there are no surviving witnesses, and the police have recovered genetic material which they are absolutely confident belongs to the perpetrator. They trawl through the genetic database and find a villain whose DNA has a sufficiently good match that only one person in five million would have a fit as good or better. They haul the suspect in, and find that he could have been in the right place at the right time and has no convincing alibi.
I hope and believe that most British police forces would do more work than this before bringing a prosecution, but let’s suppose for the sake of argument that we have a rare sloppy example, and they don’t. You are on the jury – you are told that the accused had the opportunity to commit the crime and that genetic fingerprinting suggests it is five million to one that he did it. Do you find him guilty?
If you said yes, I hope you’re not on the jury should I ever be wrongly accused of anything. Five million to one odds means there are about eleven people in Britain with an equivalent match, including about three or four adult males of an age to be strong and fit. I would want to have far more evidence against the accused than just the genetic fit statistics before I would be confident that we had correctly identified the culprit. Genetic fingerprinting evidence is only sufficient to be confident that we were convicting the guilty person if we have the evidence to rule out all other potential suspects with an equally good genetic fit, and that usually means that genetic fingerprinting on its own is not enough.
If we want to avoid such miscarriages of justice, we need to provide lawyers and judges with more training in statistics – and perhaps also provide more support for Juries. How about a handbook, “Probability for Jurors” ? You read it here first.
Professor Meadow convinced first himself, and then the juries, that at least three innocent women who were already suffering the agony of having lost their babies, should be jailed for murdering them. He told the trial of Sally Clark that the chances of her having two children lost to cot deaths through natural causes were one in 73 million, and the trial of Donna Anthony that the chances of her two children having died from natural causes were one in a million.
This evidence was based on a fundamental misunderstanding of statistics: Professor Meadow had assumed that the probability of each cot death was independent and had not taken into account the possibility that there could be a genetic predisposition to a higher risk of such fatalities or that the conditional probability of a further case of sudden infant death in the child of a mother who had already suffered one such death could be a lot higher. Other studies by doctors who do understand the relevant statistical principles suggest the odds in the Sally Clark and Donna Anthony cases were more like one chance in 77.
By overturning the finding that Professor Meadow was guilty of serious professional misconduct, the judge has effectively ruled that it is acceptable for a highly skilled professional who is being paid by the state to give expert evidence in one area of knowledge to neglect the basic mathematical understanding required to understand that knowledge. I think there are three implications for our society of this decision.
1) The stupid mistakes which do the most damage are rarely made by stupid individuals, but by intelligent ones – stupid people are rarely in a position to do as much damage as intelligent people.
2) Our society needs to recognise that expertise in one area often does not translate into expertise in others
3) It is high time we ensured that all lawyers, judges, expert witnesses, and juries had access to some basic training in statistics.
The classic example of a brilliant man who caused a major disaster with a stupid mistake that no stupid person could have made was Admiral Sir George Tryon. He became Commander in Chief of the Royal Navy’s Mediterranean Fleet, then the crack force of the most powerful and professional navy the world had ever seen, and did so purely on ability. His powers of intellect enabled him to best in argument any other officer who ventured to disagree with him. And more than eighty years after the accident in which he died I have met people who still believe that he was not responsible for that accident.
But there is no doubt that Tryon caused the collision which sank his flagship, HMS Victoria, drowned 357 officers and men, and made the world’s most formidable fleet look like idiots, with a basic mathematical error. Tryon was commanding two columns of battleships. Each column was formed in “line ahead” with one ship behind another, and the two columns were heading in the same direction, side by side and six cables or 1,200 yards apart. The turning circle of these ships was 1,600 yards. Tryon ordered the two columns to turn towards each other. Nobody will ever know exactly what he meant to happen, but as one of his officers pointed out, the two columns of battleships would have had to have started with a distance between them more than double that 1,600 yards turning circle to carry out any such manoeuvre safely.
At least four of Tryon’s officers, including the captain of his flagship, HMS Victoria, which was leading one column, the fleet’s second in command in HMS Camperdown at the head of the other column, and two staff officers who queried the orders, realised that they were likely to result in the collision of the leading ships.
Faced with an apparently suicidal order, these officers reacted in different ways. The only person to come well out of the disaster, Commander Thomas Hawkins-Smith, initially pointed out the problem and then queried the order twice. Tryon at first accepted the point, but unfortunately he then apparently forgot that he had done so, brushing objections aside.
The captain of HMS Victoria is on record as saying that “Open criticism of one’s superior is not consistent with true discipline” and said nothing to Tryon until a collision was inevitable. However, he probably saved lives by asking for and getting permission to put the engines into reverse and by closing the ship’s watertight doors.
The Second-in Command, Admiral Markham in the Camperdown, saw the problem but didn’t know what to do, and while he was trying to make up his mind the entire fleet was heading for the Syrian coast on which they would all go aground unless something was done. While he was dithering, Tryon sent the signal “Why did you not obey my order?” and then Markham followed Tryon’s instructions, with the inevitable consequence that the Victoria and Camperdown collided. Ironically, just after the collision, Tryon was handed a note with Markham’s reply, “Because I did not quite understand your signal.”
Admiral Tryon appears to have realised his mistake just too late – his voice was almost a whisper as he gave permission to put the engines “full astern” to slow down the ship. In his last minutes he made no attempt to deflect responsibility for the disaster: his last recorded words were “It is all my fault.”
Tryon made no attempt to save himself and went down with the ship.
Admiral Tryon and Professor Meadow had in common that both were brilliant men at the head of their respective professions and internationally respected in their fields. Both made basic mathematical errors with grave consequences. Professor Meadow wrecked three lives where Admiral Tryon ended more than three hundred. But there are lessons we need to learn from both.
The first is that the more eminent you are the more you need to listen to others. If George Tryon or Roy Meadow had been less eminent, both they and others might have been less inclined to assume they were always right.
The second is that we should be much more careful about assuming that knowledge in one field carries over into another. Angela Cannings, one of the innocent women who was wrongly convicted on Professor Meadow’s evidence, was surely right when she said in February 2006 of expert witnesses that “It’s when they are approached about areas outside their expertise that they should look up and say ‘Sorry, I can’t deal with this’ and step back.”
That principle has much wider application. Let me give just one example. I am an economist by profession and a regular churchgoer. I have heard priests and bishops give sermons in which they talked about spiritual matters, theology or human motivation and I immediately recognise that they are vastly better informed than I about such subjects and I have things to learn from them.
However, when the subject turns to matters on which I have professional knowledge, it readily becomes apparent that neither theological college nor biblical study gives any insight into such matters as the relative merits of competing economic theories or tax rates. It pains me to say it, but when bishops for whom as pastors and theologians I have immense respect are invited to talk about government economic policy they often reveal themselves to be as misguided outside their field of expertise as Sir Roy Meadow was outside his.
I have also heard bishops say very intelligent things about politics and economics. But nine times out of ten, when this happens the idea or concern which is being raised has been put as a question. In other words, the most intelligent contributions often come from a speaker who is acutely aware of the limits of his or her expertise.
The same applies when politicians talk about football, or when successful football managers are invited by the media to talk about business, or when TV soap stars talk about politics, or successful authors are invited to talk about the law. In a democracy we are all entitled to a view about any subject but we should avoid the trap of assuming that an expert in one subject is certain to have valuable insights into another.
My final comment is that, to avoid the risk of sending more innocent people to prison, we must significantly raise the level of statistical expertise available to the courts. Expert witnesses who think they understand maths but don’t are not a problem unique to cases of cot death. Another example is genetic fingerprinting. This is an immensely powerful tool and there is no doubt whatsoever that it has sent many guilty people to justice. But statements of probability in relation to genetic evidence can sound more powerful than they really are unless there is corroborative evidence.
Let’s give an example. Supposing there is a crime for which there are no surviving witnesses, and the police have recovered genetic material which they are absolutely confident belongs to the perpetrator. They trawl through the genetic database and find a villain whose DNA has a sufficiently good match that only one person in five million would have a fit as good or better. They haul the suspect in, and find that he could have been in the right place at the right time and has no convincing alibi.
I hope and believe that most British police forces would do more work than this before bringing a prosecution, but let’s suppose for the sake of argument that we have a rare sloppy example, and they don’t. You are on the jury – you are told that the accused had the opportunity to commit the crime and that genetic fingerprinting suggests it is five million to one that he did it. Do you find him guilty?
If you said yes, I hope you’re not on the jury should I ever be wrongly accused of anything. Five million to one odds means there are about eleven people in Britain with an equivalent match, including about three or four adult males of an age to be strong and fit. I would want to have far more evidence against the accused than just the genetic fit statistics before I would be confident that we had correctly identified the culprit. Genetic fingerprinting evidence is only sufficient to be confident that we were convicting the guilty person if we have the evidence to rule out all other potential suspects with an equally good genetic fit, and that usually means that genetic fingerprinting on its own is not enough.
If we want to avoid such miscarriages of justice, we need to provide lawyers and judges with more training in statistics – and perhaps also provide more support for Juries. How about a handbook, “Probability for Jurors” ? You read it here first.
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