Another research project at the RSS Centre was a collaborative venture with the College of Law in London. Phase 1 looked at lawyers’ understanding of likelihoods, adopting the well-established research procedures based on items designed to elicit particular error types (e.g. misapplication of the representativeness heuristic, over-reliance on the availability heuristic, the conjunction fallacy, ignoring base-rate information). This work was completed and presented at PME-21 (the 21st meeting of the International Group for the Psychology of Mathematics Education).
The results indicated that lawyers who had only studied mathematics up to compulsory level schooling did indeed manifest many probabilistic misconceptions of the kinds described in the research literature. However, those lawyers who had studied mathematics to higher levels were found to be at least as susceptible to these types of probabilistic misconceptions as was the former (lower mathematics) group. The researchers have put forward a number of recommendations concerning mathematical education and, more particularly, the training of lawyers. While this type of cognitive research aimed at diagnosing error types may be helpful for remediation purposes, it does not necessarily yield immediate pedagogic strategies where prevention should be the priority.
Phase 2 of the project focused on whether lawyers can make the sort of likelihood ratio estimates that Peter Donnelly, as expert witness, suggested would help the jurors in the now notorious (in statistical circles) Regina v Adams case (1996, 1997). Readers will no doubt remember that in the Court of Appeal, their Lordships ruled that ‘… the attempt to determine guilt or innocence on the basis of a mathematical formula …. is simply inappropriate to the jury’s task’. With this kind of restraining judgment, it is even more important for the lawyers themselves to have a thorough and reliable grasp of probability.
Preliminary results suggested that the areas of misunderstanding included not only problems in making coherent estimates of likelihood or probability, and then drawing logical inferences, but also difficulties with percentages and ratios, and even with the criminal and civil burdens of proof! The outcome of this phase of the research work was reported at ICOTS-5 (the 5th International Conference on Teaching Statistics) in June 1998.
