The Curious Case of the Inexpert Witness

Although I am a cosmologist by trade, I am also interested in the fields of statistics and probability theory. I guess this derives from the fact that a lot of research in cosmology depends on inferences drawn from large data sets. By its very nature this process is limited by the fact that the information obtained in such studies is never complete. The analysis of systems based on noisy or incomplete data is exactly what probability is about.

Of course, statistics has much wider applications than in pure science and there are times when it is at the heart of controversies that explode into the public domain, particularly when involved in medicine or jurisprudence. One of the reasons why I wrote my book From Cosmos to Chaos was a sense of exasperation at how poorly probability theory is understood even by people who really should know better. Although statistical reasoning is at the heart of a great deal of research in physics and astronomy, there are many prominent practioners who don’t really know what they are talking about when they discuss probability. As I soon discovered when I started thinking about writing the book, the situation is even worse in other fields. I thought it might be fun to post a few examples of bad statistics from time to time, so I’ll start with this, which is accompanied by a powerpoint file of a lunchtime talk I gave at Cardiff.

I don’t have time to relate the entire story of Sally Clark and the monstrous miscarriage of justice she endured after the deaths of her two children. The wikipedia article I have linked to is pretty accurate, so I’ll refer you there for the details. In a nutshell, in 1999 she was convicted of the murder of her two children on the basis of some dubious forensic evidence and the expert testimony of a prominent paediatrician, Sir Roy Meadow. After appeal her convinction was quashed in 2003, but she died in 2007 from alcohol poisoning having apparently taken to the bottle after three years of wrongful imprisonment.

Professor Meadow had a distinguished (if somewhat controversial) career, becoming famous for a paper on Munchausen’s Syndrome by Proxy which appeared in the Lancet in 1977. He subsequently appeared as an expert witness in many trials of parents accused of murdering their children. In the Sally Clark case he was called as a witness for the prosecution, where his testimony included an entirely bogus and now infamous argument about the probability of two sudden infant deaths happening accidentally in the same family.

The argument is basically the following. The observed ratio of live births to cot deaths in affluent non-smoking families (like Sally Clark’s) is about 8,500:1. This means that about 1 in 8,500 children born to such families die in such a way. He then argued that the probability that two such tragedies happen in the same family is this number squared, i.e. about 73,000,000:1. In the mind of the jury this became the odds against the death of Mrs Clark’s children being accidental and therefore presumably the odds against her being innocent. The jury found her guilty.

For reasons why this argument is completely bogus, and more technical details, look in the following powerpoint file (which involves a bit of maths):


It is difficult to assess how important Roy Meadow’s testimony was in the collective mind of the Jury, but it was certainly erroneous and misleading. The General Medical Council decided that he should be struck off the medical register in July 2005 on the grounds of “serious professional misconduct”. He appealed, and the decision was partly overturned in 2006, the latest judgement basically being about what level of professional misconduct should be termed “serious”.

My reaction to all this is a mixture of anger and frustration. First of all, the argument presented by Meadow is so clearly wrong that any competent statistician could have been called as a witness to rebut it. The defence were remiss in not doing so. Second, the disciplinary action taken by the GMC seemed to take no account of the consequences his testimony had for Sally Clark. He was never even at risk of prosecution or financial penalty. Sally Clark spent three years of her life in prison, on top of having lost her children, and now is herself dead. Finally, expert testimony is clearly important in many trials, but experts should testify only on those matters that they are experts about! Meadow even admitted later that he didn’t really understand statistics. So why did he include this argument in his testimony? I quote from a press release produced by the Royal Statistical Society in the aftermath of this case:

Although many scientists have some familiarity with statistical methods, statistics remains a specialised area. The Society urges the Courts to ensure that statistical evidence is presented only by appropriately qualified statistical experts, as would be the case for any other form of expert evidence.

As far as I know, the criminal justice system has yet to implement such safeguards.

How many more cases like this need to happen before the Courts recognise the dangers of bad statistics?

4 Responses to “The Curious Case of the Inexpert Witness”

  1. […] a thinly disguised another example of the prosecutor’s fallacy which came up in my post about Sir Roy Meadow and his testimony in the case against Sally Clark that resulted in a wrongful conviction for the […]

  2. […] posed anything in the Bad Statistics file so I thought I’d return to the subject of one of my very first blog posts, although I’ll take a different tack this time and introduce it with different, though […]

  3. […] focussing on the forensic use of probabilistic reasoning. This all reminds me of the tragedy of the Sally Clark case and what a disgrace it is that nothing has been done since then to improve the misrepresentation of […]

  4. […] focussing on the forensic use of probabilistic reasoning. This all reminds me of the tragedy of the Sally Clark case and what a disgrace it is that nothing has been done since then to improve the misrepresentation of […]

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