Misleading statistics may have convicted a mother of murder. Adam James reports

Cheshire solicitor Sally Clark was sentenced to life imprisonment in 1999 for the murder of her two sons, 11-week-old Christopher and eight-week-old Harry.

But Clark's supporters, who believe a gross miscarriage of justice has been committed, are resting their hopes that a report by the Criminal Cases Review Commission issued today will either refer her case back to the Court of Appeal or quash the conviction altogether.

Among those awaiting the report will be Ray Hill, professor of mathematics at Salford University. The semi-retired 56-year-old, who earned his reputation as an expert in a branch of mathematics called "coding theory", does not know Clark. Neither has he ever before taken up an alleged miscarriage of justice. Yet he is certain that a statistic used by the prosecution in persuading the jury that Clark, an otherwise respectable mother, had murdered her children, was scandalously misleading.

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At Clark's trial, paediatrician Sir Roy Meadow announced to the jury that there was a "one-in-73 million" chance that two of Clark's children would have died of sudden infant death syndrome, commonly known as cot death. In light of the controversial forensic evidence in the case, Clark's conviction was widely judged to have rested on this statistic.

Yet afterwards statisticians and doctors condemned Meadow's statistic as "scientifically illiterate" and "absolute rubbish". The Royal Statistical Society also wrote to the lord chancellor stating that there was "no statistical basis" for the one-in-73 million figure.

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Hill, who remembers shouting in bewilderment on hearing the figure mentioned in a news report on the Clark trial, has gone one step further. After logging onto the campaign website, he started communicating with Clark's husband (pictured below with Sally). From there, he went on to write a paper titled "Why Sally Clark is, probably, innocent", to be presented at a Developmental Physiology Conference in Leicester tomorrow. It outlines both the mathematical flaws behind the figure, and proposes alternative probabilities.

Hill says the mathematics involved is "not in any way difficult". "No formulae are needed" and "all that is requiredI is a clear head and a logical mind".

His first assertion is that Meadow's figure - taken from data in a draft of The Confidential Enquiry for Stillbirths and Deaths in Infancy (CESDI), published in 2000 - was based on the presumption that there are no factors that would make it more likely that, if one infant dies from cot death, another infant of the same family would also suffer the same fate.

However, since the Clark trial, Manchester University researchers have reported that there may be a cot death gene, making it more likely a family would have two cot deaths. Moreover, the Foundation for the Study of Infant Death reports that at least one family a year in Britain loses a second child to cot death.

Hill proposes that the jury was faced with deciding between two events - a natural double-death or a double-murder - and that the jury's misinterpretation of Meadow's statistic - a "prosecutor's fallacy" - played a crucial role in Clark's conviction.

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It is acknowledged that the jury were likely, in their minds, to have interpreted the odds of Clark being innocent as 73 million to one. Clark, then, must have murdered her children? Hill writes: "The logic almost convinces me, and I know about the prosecutor's fallacy!"

Appeal judges, who upheld Clark's conviction, believed it was not wrong that this prosecutor's fallacy was not pointed out to the jury. But Hill disagrees.

"The mathematical community does not give the special name of prosecutor's fallacy to something that only dim schoolchildren might get wrong. They do so because it is a trap into which intelligent people often fall."

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Hill's crucial assertion, therefore, is that to estimate a correct statistical probability of innocence, the odds should be estimated based on information related to people who have suffered two cot deaths in the family.

Sourcing his data from the CESDI study, Hill found there were five double-cot deaths recorded from a sample of 470,000 births. When modified by a "scaling factor" (due to the fact that some parents of cot-death children declined to be interviewed during the study) this gives a probability that a family would have two cot deaths as around one in 84,000. Of those families who have suffered one cot death, he asserts that the odds of suffering a second one are one in 60.

Clark's defence team, who never challenged Meadow's statistic in court, might have helped their client more if they had quoted this alternative probability figure, he says. "What this statistic shows," claims Hill, "is that incidence of double sudden infant death syndrome can be expected to occur fairly frequently."

In light of his interest in the case, Hill has added his name to those campaigning to free Clark under the slogan "Lightning does strike twice".

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He says: "The evidence is so flawed that I cannot help but believe that she [Clark] is innocent."