Decision, release and written reasons are different dates
- First appeal judgment: . Dismissed on each count. SC1, para 258
- Later appeal heard: and . On the court's account it concluded then that the convictions were unsafe and gave brief reasons at the time. The excerpt does not say on which of the two days. SC4, para 5
- Release: the Crown did not seek a retrial and Mrs Clark was released. The excerpt gives no release date; the written judgment describes it as already past. SC4, para 5
- Written reasons handed down: . SC4, written judgment
Dated timeline
Statement, letter and appeal in date order. Dots sit on a to-scale year axis; labels are evenly spaced. Each label in the chart links to its source. The text list beside it carries the same content.
- Expert notice served. Expert notice served stating 1:8,543 and 1:73,000,000, as quoted in the 2000 judgment. SC1, para 118
- First appeal dismissed. Court of Appeal dismisses the appeal against conviction on each count; it calls the figure no help looking back. SC1, para 258
- RSS statement. Royal Statistical Society news release, embargoed until this date, criticises the independence assumption and the figure. SC2, page 1
- RSS letter. The Society's President writes to the Lord Chancellor on double use of data and relative likelihood. SC3, page 1
- and Appeal heard and decided; release. Court of Appeal hears the appeal on 28 and 29 January 2003, concludes the convictions are unsafe and gives brief reasons at the time. The Crown seeks no retrial and Mrs Clark is released. The excerpt gives no separate day for the decision or the release. SC4, para 5
- Written reasons handed down. Written judgment handed down setting out the reasons; para 6 names non-disclosure of the microbiological reports first and principally. SC4, paras 2, 5, 6
Two columns: the 2000 judgment against the later records
Each row sets what the 2000 judgment actually contained beside what came later. Every quotation names its speaker and links to its source.
The headline figure
In the 2000 judgment
The judgment records the figure as served in the expert notice and as given in testimony, where it was set against all live births in a year.
Thus the chances of two infant deaths within such a family being SIDS is 1:73,000,000.
It gives a chance of 1 in 73 million live births and in England, Wales and Scotland there are about, say, 700,000 live births a year, so it is saying by chance that happening will occur once every hundred years.
Established later
The Royal Statistical Society said the figure had no statistical basis. This is professional criticism, not a ruling.
The wellpublicised figure of 1 in 73 million thus has no statistical basis.
Independence of two deaths in one family
In the 2000 judgment
The 2000 record already showed that the study text excluded familial factors, and that Professor Dawid, as reported, called the figure a ball park estimate.
the risk of SIDS to a subsequent child in a family in which one infant has already died will range from one in 214 to one on 8,543. this does not take account of possible familial incidence of factors other than those included in Table 3.58.
He suggests, not unreasonably, that the 1:73 million must be regarded as a "ball park" estimate. We do not imagine that the Crown would demur from that suggestion.
Established later
The Society said squaring is valid only if deaths arise independently within families, and that there are strong reasons to expect that assumption to be false.
This approach is, in general, statistically invalid. It would only be valid if SIDS cases arose independently within families, an assumption that would need to be justified empirically. Not only was no such empirical justification provided in the case, but there are very strong a priori reasons for supposing that the assumption will be false.
Comparison with a competing explanation
In the 2000 judgment
The court accepted the figure was no help looking back, but said a statistical comparison with double murder was not an exercise courts would perform.
The competing possibility identified is a double infant murder by a mother. That may be capable of being expressed in terms of a statistical probability, but legally speaking the exercise is not realistic
Therefore we accept that when one is looking ex post at whether two deaths were natural or unnatural, the 1:73 million figure is no help. It is merely a distraction.
Established later
The Society said the relative likelihood under each explanation is what matters. Neither document gives a rate for two murders.
What matters is the relative likelihood of the deaths under each explanation, not just how unlikely they are under one explanation (in this case SIDS, according to the evidence as presented).
Two deaths by murder may well be even more unlikely. What matters is the relative likelihood of the deaths under each explanation, not just how unlikely they are under one explanation.
How the family was classified
In the 2000 judgment
The judgment quotes the three family characteristics used to select the 1 in 8,543 rate.
for a family in which the parents do not smoke, in which at least one has a waged income and in which the mother is over the age of 26 years, the risk is 1:8,543 live births.
Established later
The Society's letter raised a separate concern: the same data chose the characteristics and measured the rate.
A separate concern is that the characteristics used to classify the Clark family were chosen on the basis of the same data as was used to evaluate the frequency for that classification. This double use of data is well recognised by statisticians as perilous, since it can lead to subtle yet important biases.
Biological evidence, separate from the statistics
In the 2000 judgment
Nothing in the supplied 2000 excerpts concerns microbiological test results.
Established later
The 2003 court recorded that microbiological results from post mortem samples were later discovered and had not been in the trial evidence. The court's principal reason is in the disclosure panel below.
In due course, records of the results of microbiological tests performed on samples of Harry's blood, body tissue and cerebrospinal fluid gathered at post mortem were discovered. These had not featured at all in the evidence at trial because all the lawyers involved on both sides were unaware of their existence.
Outcome
In the 2000 judgment
The 2000 appeal was dismissed on each count.
The appeal against conviction on each count is therefore dismissed.
Established later
The 2003 court heard the appeal in January, found the convictions unsafe, and gave brief reasons at the time; Mrs Clark was released after the Crown sought no retrial. Detailed written reasons followed on 11 April 2003.
On 28 and 29 January 2003 this court heard the appeal and concluded that the convictions were unsafe and must be set aside. The Crown did not seek a re-trial and accordingly Mrs Clark was released. In view of the public attention given to this case, we stated our reasons for our decision very briefly at the time but indicated that we would give detailed reasons at a later date. This judgment sets out our reasons.
The principal 2003 reason was biological evidence, not the statistics
The statistical question is whether 1 in 8,543 can be squared and what it should be compared with. The disclosure issue is separate: microbiological results from post mortem samples never reached the jury.
First and principally, the failure to disclose the information contained in the microbiological reports meant that important aspects of the case which should have been before the jury were never considered at trial.
Para 6 calls this the first and principal reason. The supplied excerpts do not set out the court's other reasons, so this page does not attribute the 2003 outcome to the statistics, in whole or in part.
The original arithmetic, recomputed from the 2000 text
8,543 × 8,543 = 72,982,849. Reported as 73,000,000, a gap of 17,151.
72,982,849 ÷ 700,000 live births a year = 104.26; 73,000,000 ÷ 700,000 = 104.29. The testimony called this once every hundred years, but the product is per family with two live births, not per live birth.
The study's range for a subsequent child was one in 214 to one in 8,543. If the second death is not independent of the first, the earlier output showed that the two-death rate could lie anywhere from one in 72,982,849 up to one in 8,543, assuming no protective dependence: a span of 8,543 fold.
The table below compares each recomputed value with the value in the earlier output, which is left unchanged. Nothing in the arithmetic changes after the reveal: the later criticism attacks the independence assumption and the missing comparison, both already listed as assumptions or gaps in the earlier output.
| Quantity | Recomputed now | Earlier output | Agreement |
|---|---|---|---|
| One SIDS death, per live birth, one in | 8,543 | 8,543 | Same |
| Two SIDS deaths if independent, one in | 72,982,849 | 72,982,849 | Same |
| Figure as reported, one in | 73,000,000 | 73,000,000 | Same |
| Rounding gap | 17,151 | 17,151 | Same |
| Live births a year, as testified | 700,000 | 700,000 | Same |
| Exact product over yearly births | 104.26 | 104.26 | Same |
| Reported figure over yearly births | 104.29 | 104.29 | Same |
| Subsequent child range, low end, one in | 214 | 214 | Same |
| Subsequent child range, high end, one in | 8,543 | 8,543 | Same |
| Fold span of possible two-SIDS rate | 8,543 | 8,543 | Same |
What is still unknown after the reveal
The later records change what can be said about the figure, not what can be counted. Two murders “may well be even more unlikely”, in the letter's words, is not a rate. A finding that convictions are unsafe is a legal conclusion, not a probability.
| Quantity | As of 2 October 2000 | After the later records | Why |
|---|---|---|---|
| Chance of a second SIDS death given a first, for this family profile | Unknown | Unknown | SC2 says independence would need empirical justification and is likely false, but gives no measured recurrence rate. |
| Incidence of two maternal homicides on the same denominator | Unknown | Unknown | SC3 says two murders may well be even more unlikely, which is not a rate; no later source supplies one. |
| Likelihood ratio for the medical findings | Unknown | Unknown | SC4 concerns undisclosed microbiological reports; the excerpts quantify nothing. |
| Probability of innocence | Unknown | Unknown | Prior odds and likelihood ratio stay unknown, and the hypotheses are not exhaustive. A finding that convictions are unsafe is a legal conclusion, not a probability. |
Sources
- SC1: R v Clark [2000] EWCA Crim 54. Court of Appeal (Criminal Division), dated 2 October 2000. Open source SC1
- SC2: RSS statement regarding statistical issues in the Sally Clark case. Royal Statistical Society, dated 23 October 2001. Open source SC2
- SC3: Letter from the President to the Lord Chancellor. Royal Statistical Society, dated 23 January 2002. Open source SC3
- SC4: R v Clark [2003] EWCA Crim 1020. Court of Appeal (Criminal Division), dated 11 April 2003. Open source SC4