Take care with your calculations
“Chance of cot deaths in brothers ‘1 in 73 million’”
Sally Clark served three years of a life sentence for the murder of her two children before her conviction was overturned in 2003. In the original case, the defence had claimed that sudden infant death syndrome (SIDS) – commonly known as cot death – was responsible for the death of both boys, who died just over a year apart. The prosecution argued that such a double cot death was exceptionally unlikely and claimed murder.
The prosecution’s assertion was based on the expert testimony of Professor Sir Roy Meadow, a researcher in paediatrics. Meadow had said that the chances of one child dying from SIDS in a non-smoking, affluent family was 1 in 8,543. When working out the probability of two cot deaths in the same family, he squared this probability – multiplying 8,543 by 8,543 – to get 1 in 73 million.
This would have been the right thing to do if the two events were independent of each other, like tosses of a coin. The chance of getting two heads in a row is 1/2 x 1/2 (1/4). However, two cot deaths in the same family are not independent events; there could be underlying genetic or environmental factors that make them more likely. The Royal Statistical Society deemed Meadow’s account a “mis-use of statistics”.Lead image:
Questions for discussion
- Even if the chance of a double cot death in the same family really was 1 in 73 million, why would this not have meant there was only a 1 in 73 million (0.0000014 per cent) chance of the accused being innocent? Search for “prosecutor’s fallacy” online to find out more.
- What figure should this number have been compared with to work out the relative likelihood of guilt or innocence?
- Should statistical evidence in court only be presented by experts in statistics, rather than by experts in the field in which the statistics are being used?