Two sons of Sally Clark, a London lawyer, died while very young about a year apart and both in mysterious circumstances. In 1998, seven months after the second death, Sally Clark was charged with murder. She was eventually tried, found guilty, and sentenced to two life terms of imprisonment in 1999.
Part of the evidence presented in her trial was that the probability of two children dying of cot death in the one family was vanishingly small (quoted in court as one in 73 million). This is essentially a p-value: the probability of the obtaining the data (two children dying) given the null hypothesis (Sally Clark was innocent). Since this probability is so small, the null hypothesis of innocence could be rejected and the alternative hypothesis (that Sally Clark murdered her children) accepted. As claimed by the prosecutor, two cot deaths were 'beyond coincidence'. Of course, this acceptance of the alternative hypothesis ignores whether the available evidence supports it and whether it is reasonable in the first place.
The application of null hypothesis testing in this case gets it alarmingly wrong. Despite the vanishingly small p-value, evidence came to light that demonstrated that Sally Clark was unlikely to have killed her two sons, and after spending more than three years in prison she was released. A small p-value does not necessarily mean that the alternative hypothesis is true.
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