They STILL don't get it: Doctors and Hacks wrong again on statistics
A minor but infurating mistake was on display in the media yesterday demonstrating once again that too many doctors and journalists are prone to manufacture or repeat ridiculous statistics, most often through a misunderstanding of probability. I am sure that the same is true of many other categories of professionals, making mistakes about statistics when they should know better.
Karen Rodger from Renfrewshire has just given birth to her third set of twins. She is said to be "Over the Moon" about this and I am very happy for her, but I am not so happy that innumerate journalists all over the media are repeating a statement attributed to doctors, statistically illiterate doctors if the attribution is accurate, that the odds against this were half a million to one.
In the great scheme of things, as this is only a newspaper headline, it dosn't make a lot of difference whether the odds against the birth of three sets of twins was ten thousand to one against or half a million to one against. In some circumstances getting a figure wrong by more than an order of magnitude is important - when you're giving professional advice to a jury as an expert witness in a murder trial, for example or making a financial decision - and in others less so.
Why this wrong statistic upset me is that it was a harmless but otherwise egregious example of exactly the same mistake - EXACTLY the same mistake - made by the paediatrician Sir Roy Meadow when he persuaded juries to send women who were almost certainly innocent to jail for murdering babies whose deaths were very probably nobody's fault. You can read a summary of my previous comments on those cases here.
A less serious example perhaps, but it still demonstrates all too clearly that we need to improve the quality of statistical education in this country. For the benefit of anyone who is wondering what the mistake was, it was to treat the combined probability of three linked events as if they had been entirely independent.
Half a million to one is about the odds you would get if you took three specific random pregnancies of three unrelated women, and asked what the probability of all three being twin births would be.
But three pregnancies for the same mother are not three unrelated events.
Some families have a genetic predisposition to "Sudden infant death" syndrome or cot death, and much less tragically, others have a genetic predisposition to multiple births.
Just as a mother who has already lost one baby to cot death has a significantly worse conditional probability of losing more - which is excellent reason to watch subsequent babies very carefully, but not grounds to brand her a murderess if there is a second death unless there is other evidence of neglect or foul play - a mother who has already given birth to one set of twins or multiples has a significantly higher conditional probability of giving birth to subsequent sets of twins or having another multiple birth.
If a mother has already produced two twin or multiple births, the conditional probability of a third is higher still. To produce a three sets of twins in three pregnancies is still a very unlikely event, but it would be at least an order of magitude less unlikely than half a million to one against.
I have only anecdotal evidence for what I am about to write, such as the fact that when my wife and I were members of a twins club hardly any of the twins and multiples in that branch had younger siblings, but I suspect that a major reason families with more than one multiple birth are not more common is that parents who have been through a successful twin or multiple pregnancy are quite prone to decide that their family is now large enough. Certainly any social pressure to have more children stops dead - I lost count of the number of people who made comments when our twins arrived along the lines of "Oh well done, that's your family in one go." Even Margaret Thatcher stopped at one set of twins!
I wrote at the time of the Roy Meadow case that we ought to make a stats book available in jury rooms and give some training in stats to judges and barristers. The misquoting of the odds in the Renfrew twins story is a reminder that this still needs to be done.
Karen Rodger from Renfrewshire has just given birth to her third set of twins. She is said to be "Over the Moon" about this and I am very happy for her, but I am not so happy that innumerate journalists all over the media are repeating a statement attributed to doctors, statistically illiterate doctors if the attribution is accurate, that the odds against this were half a million to one.
In the great scheme of things, as this is only a newspaper headline, it dosn't make a lot of difference whether the odds against the birth of three sets of twins was ten thousand to one against or half a million to one against. In some circumstances getting a figure wrong by more than an order of magnitude is important - when you're giving professional advice to a jury as an expert witness in a murder trial, for example or making a financial decision - and in others less so.
Why this wrong statistic upset me is that it was a harmless but otherwise egregious example of exactly the same mistake - EXACTLY the same mistake - made by the paediatrician Sir Roy Meadow when he persuaded juries to send women who were almost certainly innocent to jail for murdering babies whose deaths were very probably nobody's fault. You can read a summary of my previous comments on those cases here.
A less serious example perhaps, but it still demonstrates all too clearly that we need to improve the quality of statistical education in this country. For the benefit of anyone who is wondering what the mistake was, it was to treat the combined probability of three linked events as if they had been entirely independent.
Half a million to one is about the odds you would get if you took three specific random pregnancies of three unrelated women, and asked what the probability of all three being twin births would be.
But three pregnancies for the same mother are not three unrelated events.
Some families have a genetic predisposition to "Sudden infant death" syndrome or cot death, and much less tragically, others have a genetic predisposition to multiple births.
Just as a mother who has already lost one baby to cot death has a significantly worse conditional probability of losing more - which is excellent reason to watch subsequent babies very carefully, but not grounds to brand her a murderess if there is a second death unless there is other evidence of neglect or foul play - a mother who has already given birth to one set of twins or multiples has a significantly higher conditional probability of giving birth to subsequent sets of twins or having another multiple birth.
If a mother has already produced two twin or multiple births, the conditional probability of a third is higher still. To produce a three sets of twins in three pregnancies is still a very unlikely event, but it would be at least an order of magitude less unlikely than half a million to one against.
I have only anecdotal evidence for what I am about to write, such as the fact that when my wife and I were members of a twins club hardly any of the twins and multiples in that branch had younger siblings, but I suspect that a major reason families with more than one multiple birth are not more common is that parents who have been through a successful twin or multiple pregnancy are quite prone to decide that their family is now large enough. Certainly any social pressure to have more children stops dead - I lost count of the number of people who made comments when our twins arrived along the lines of "Oh well done, that's your family in one go." Even Margaret Thatcher stopped at one set of twins!
I wrote at the time of the Roy Meadow case that we ought to make a stats book available in jury rooms and give some training in stats to judges and barristers. The misquoting of the odds in the Renfrew twins story is a reminder that this still needs to be done.
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