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Sally Clark and the appalling cost of bad science


Last week’s news of the death of Sally Clark, who suffered the most awful injustice a mother could imagine, brought back all the anger. The case illustrated our poor ability to reason using probabilities. Sally’s fate was sealed not by an expert in statistics but by a paediatrician who used statistics outside his abilities and by a judicial system that failed to question the statistics, the reasoning applied to them and the implications for due process.

What might assuage the anger is knowing that judges and defence lawyers have learnt the lesson. From discussions with friends in the legal profession, I am not sure this has been given the importance it deserves. I hope I am wrong.

Professor Sir Roy Meadow’s error was to tell the court the chance of two cot deaths occurring innocently in the same family was one in about 72 million. The courts’ error, in the original trial, on appeal and in other similar trials, has a procedural dimension. It was fundamental to establish whether the probabilities quoted relied on what might be construed as a presumption of guilt rather than a presumption of innocence.

In statistical terms, the odds assumed that two deaths arising innocently in the same family had to be independent events, unconnected except by chance alone. Because the trials did not apparently consider the possibility that there might be dependencies other than a murdering hand connecting them, the chances quoted effectively presumed guilt, by trivialising the possibility of innocence.

If there was anything connecting them, the chance was at most one in 8,500. If it was possible to know the linkage, such as a shared genetic disorder, the true chance could be vastly greater. Eliminating any possible linkage other than murder trivialised Sally’s and other mothers’ claim of innocence.

Quite separately from the common statistical error in presenting the probabilities, it was also an error in logic to equate the likelihood of an unlikely event with the likelihood of innocence.

Both are common enough errors, well documented by statisticians. So how did they escape the attention of defence teams as well as the judges involved in these cases? How come no journalists picked them up or, more likely, informed members of the public reading about these legal cases?

If the errors are common and their consequences so tremendous, it is clearly vital that judges ensure juries are properly directed to help them cope with decisions that rely on reasoning with probabilities.

Much of what I have written about in the last few years, to do with the construction of financial products or claims about them, relates to similar problems of both presenting and sorting information about uncertainties. Although the cost of deception and self-deception can be high, and can also trigger an angry response, it is nothing like the price Sally Clark paid, whatever the proximate cause of her death last week.

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