Thursday June 23, 2005
Â· Of course, the past two years of Bad Science was nothing more than a cover for the “popular statistics” lecture series I really wanted to give, but knew I could never sell to a newspaper. So, on to Professor Roy Meadows and Meadows’ Law, that: “One sudden infant death is a tragedy, two is suspicious and three is murder until proved otherwise.” Pay attention: flaky statistics can get you jailed, or erased from the GMC register if you’re not careful. Meadows said the likelihood of there being two sudden infant deaths in the same family was one in 73 million. People are queueing up to point out that the Royal Statistical Society said this aspect of the case involved flaky reasoning. Nobody in newspapers was geeky enough to explain why.
Â· Welcome to my world. This is an example of a common error of reasoning known as “prosecutors’ fallacy”. It rests on creating a figure erroneously, and then applying it erroneously. First, let’s take where the 73m came from. Meadows appears to have taken a figure for sudden infant death syndrome (Sids), about one in 8,500, and squared it to find the likelihood of Sids happening twice in the same family. This would only be valid if we could be sure Sids always happened by chance and independently of family factors such as genetics and environment. In fact, there are strong reasons to believe that there are, unknown, genetic and environmental factors which will make Sids more likely in any child, and since genetic factors and environment tend to be shared in families, you may be more likely to find Sids twice in the same family than the initial calculation suggests. The error in the figure 73m is therefore likely to be extremely large, and in one direction only, that is, overestimating. The true figure may be much less incriminating.
Â· The real action is in how we use this inaccurate figure. Press reports at the time said 73m to one was the chance the two deaths of Clark’s children were “accidental”. The court appeared to concur. But this was an error. A very rare event has already occurred: the unexplained death of two siblings. What the jury ought to have considered is: which is the more likely rare event, double murder or double Sids? If anything we want the relative probabilities. The original case did not consider this; if it had, you would have thought a conviction to be less likely. The appeal court ruling accepted flaws with the figure, but said it established “a very broad point, namely the rarity of double Sids”. Scream now.