What Went Wrong in the Case of Sally Clark? Amit Pundik Hughes Hall, Cambridge

Background The facts One trial and two appeals The missing evidence The statistical evidence (1 per 73 million)

The Research Question In general, if and how could the miscarriage of justice have been avoided? Presupposition: given the evidence available today, Sally Clark should not have been convicted. In particular, given the evidence available at the time Was the decision of the first appeal court to uphold the convictions erroneous, and if so why? (henceforth ‘the research question’)

Structure The statistical evidence explanations The flaws in Meadow’s calculation The legal failure to use Bayes' Theorem Overwhelming psychological influence The missing evidence explanation (second appeal) An alternative explanation

The Flaws in Meadow’s Calculation The explanation: flaws in Meadow’s calculation are responsible for the error (Dawid, Donnelly and media). Meadow’s Calculation: P(SIDS | The Clark’s traits) = 1 per 8,543 P(two SIDS in one family | traits) = 8,543* 8,543 = 73 million Flaws The probability of single cot death might be much higher The unfounded assumption of independence

The Flaws in Meadow’s Calculation Partial explanation: only establishes that the correct figure is much lower than Meadow’s. There was other incriminating evidence against Sally (bruises, torn frenulum and bleeding in the lungs). It does not show that if the calculation had been done properly, the first appeal court would not have upheld Sally’s convictions. Meadow’s flaws were known during the actual trial and the first appeal.

The Flaws in Meadow’s Calculation Meadow’s statistics were unessential to the prosecution’s case because the defence experts admitted both deaths were not SIDS. The first appeal court: [The statistical evidence] was very much a side-show at trial. The experts were debating the incidence of genuine SIDS (unexplained deaths with no suspicious circumstances) in a case where both sides agreed that neither Christopher's death nor Harry's death qualified as such. (R v Clark (No 1) [2000] EWCA Crim 54, [126], emphasis added)

Bayes' Theorem The explanation: the error resulted from failure to: use proper statistical methods (i.e. Bayes' Theorem); combine statistical and non-statistical evidence and assess accurately the probability of Sally’s guilt. Donnelly (on a DNA case): ‘[Bayes' Theorem] is the only logically sound and consistent approach to considering situations such as this’.

Bayes' Theorem General difficulties in applying Bayes' Theorem in the courtroom Prior probability of guilt Untrained juries cannot deploy it accurately How does one translate the posterior probability of guilt into guilty/not-guilty verdict? Some have argued that convicting individuals based on mathematical formulas undermines the legitimacy and the acceptability of the verdict. A judge who tried it admitted that he fiddled with the numbers until the formula yielded the answer he wanted to get.

Bayes’ Theorem Specific difficulties with its application in the case of Sally Clark, same as in the previous explanation: Partial explanation Other non-statistical evidence pointed to guilt (bruises, torn frenulum and bleeding in the lungs). The fact proven by the statistical evidence (No SIDS) was admitted by the defence experts. Even if using Bayes’ Theorem in courts would reduce the overall number of errors, Bayes' Theorem would not have prevented the error in this case.

The Psychological Effect of Statistics The explanation: 1 per 73 million is so impressive that it had a psychological impact which caused the under-appreciation of other non-statistical evidence more favourable to Sally Alternative explanation: confusion of P(E | ¬G) with P (¬G | E) (the prosecutor’s fallacy). Steve Clark: the statistics was ‘an arrow through the fog’. Tribe: ‘The problem of the overpowering number, that one hard piece of information, is that it may dwarf all efforts to put it into perspective with more impressionistic sorts of evidence.’ (Laurence Tribe, “Trial by Mathematics: Precision and Ritual in the Legal Process, Harvard Law Review, 1329, p. 1360).

The Psychological Effect of Statistics 1. Unfounded empirical assumptions Empirical evidence shows that humans tend to disregard statistical evidence (“background information”) when other specific evidence is also available (Kahneman and Tversky). Compare with a hypothetical when the statistical evidence is the only incriminating evidence.  The worry about the evaluation of the statistical evidence more likely to involve unjustified underweighting of it rather than any overwhelming effect.

The Psychological Effect of Statistics 2. The applicability to the judges in the first appeal Evaluation of complex and scientific evidence is a repeating task in judges’ day-to-day routine. The judges were equipped with expert opinions of two expert statisticians (Professor Phil Dawid and Dr Ian Evett).

The Psychological Effect of Statistics 3. The explanation assumes that without the statistics, the prosecution’s case would have been much weaker. However: In the weaker case of Christopher, the prosecution pointed to bruises, torn frenulum, and fresh bleeding in the lungs. ‘Each [of the defence medical experts] agreed that if there was bruising, the injury to the frenulum and bleeding in the lungs, it suggested asphyxia.’ (R v Clark (No 1) [2000] EWCA Crim 54, [40])

Conclusion Much of the scholarly literature and the public media focused on the statistical evidence (and the performance of the experts, lawyers, and judges in relation to this evidence). However, none of the explanations which are related to the statistical evidence is able to identify what went wrong in the case of Sally Clark. The role of the statistical evidence in this case might well be overrated.

Thank you!